We describe a large class of two-dimensional conformal field theories based on a current algebra ... more We describe a large class of two-dimensional conformal field theories based on a current algebra construction of Virasoro representations due to Goddard, Kent, and Olive. The basic tool is a generalization of the Feigin-Fuchs representation. All the theories are organized by chiral algebras, the simplest examples being the Virasoro and super-Virasoro algebras.
Constructs from conformal geometry are important in low dimensional gravity models, while in high... more Constructs from conformal geometry are important in low dimensional gravity models, while in higher dimensions the higher curvature interactions of Lovelock gravity are similarly prominent. Considering conformal invariance in the context of Lovelock gravity leads to natural, higher-curvature generalizations of the Weyl, Schouten, Cotton and Bach tensors, with properties that straightforwardly extend those of their familiar counterparts. As a first application, we introduce a new set of conformally invariant gravity theories in D = 4k dimensions, based on the squares of the higher curvature Weyl tensors.
We study extremal black hole solutions of D = 5 Gauss-Bonnet gravity coupled to a system of gauge... more We study extremal black hole solutions of D = 5 Gauss-Bonnet gravity coupled to a system of gauge and scalar fields. As in Einstein gravity, we find that the values of the scalar fields on the horizon must extremize a certain effective potential that depends on the black hole charges. If the matrix of second derivatives of the effective potential at this extremum has positive eigenvalues, we give evidence, based on a near horizon perturbative expansion, that the attractor mechanism continues to hold in this general class of theories. We numerically construct solutions to a particular simple single scalar field model that display the attractor mechanism over a wide range of asymptotic values for the scalar field. We also numerically construct non-extremal solutions and show that the attractor mechanism fails to hold away from extremality.
We study a class of D = 11 BPS spacetimes that describe M-branes wrapping supersymmetric 2 and 4-... more We study a class of D = 11 BPS spacetimes that describe M-branes wrapping supersymmetric 2 and 4-cycles of Calabi-Yau 3-folds. We analyze the geometrical significance of the supersymmetry constraints and gauge field equations of motion for these spacetimes. We show that the dimensional reduction to D = 5 yields known BPS black hole and black string solutions of D = 5, N = 2 supergravity. The usual ansatz for the dimensional reduction is valid only in the linearized regime of slowly varying moduli and small gauge field strengths. Our identification of the massless D = 5 modes with D = 11 quantities extends beyond this regime and should prove useful in constructing non-linear ansatze for Calabi-Yau dimensional reductions of supergravity theories.
We find that topological invariants, isomorphic to Donaldson Polynomials, exist in chiral superfi... more We find that topological invariants, isomorphic to Donaldson Polynomials, exist in chiral superfield theories. Twists between these invariants and those of the corresponding : TQFT are given. In the topological sigma model, anti-commuting charges of integer spin are found which together with the BRST charge, fill out a D=2, N=2 supersymmetry algebra.
We analyze the neighborhoods of superconformal fixed points in the FQS discrete series through th... more We analyze the neighborhoods of superconformal fixed points in the FQS discrete series through the use of composite operator perturbation theory and Landau-Ginsburg type effective lagrangians. In particular, we demonstrate the existence of spontaneous supersymmetry breaking in models with zero supersymmetry index, and argue for the existence of renormalization group flows which change the index.
Higher curvature Lovelock gravity theories can have a number of maximally symmetric vacua with di... more Higher curvature Lovelock gravity theories can have a number of maximally symmetric vacua with different values of the curvature. Critical surfaces in the space of Lovelock couplings separate regions with different numbers of such vacua, and there exist symmetry breaking regions with no maximally symmetric vacua. Especially in such regimes, it is interesting to ask what reduced symmetry vacua may exist. We study this question, focusing on vacua that are products of maximally symmetric spaces. For low order Lovelock theories, we assemble a map of such vacua over the Lovelock coupling space, displaying different possibilities for vacuum symmetry breaking. We see indications of interesting structure, with e.g. product vacua in Gauss-Bonnet gravity covering the entirety of the symmetry breaking regime in 5-dimensions, but only a limited portion of it in 6-dimensions.
We describe a large class of two-dimensional conformal field theories based on a current algebra ... more We describe a large class of two-dimensional conformal field theories based on a current algebra construction of Virasoro representations due to Goddard, Kent, and Olive. The basic tool is a generalization of the Feigin-Fuchs representation. All the theories are organized by chiral algebras, the simplest examples being the Virasoro and super-Virasoro algebras.
The Komar integral relation of Einstein gravity is generalized to Lovelock theories of gravity. T... more The Komar integral relation of Einstein gravity is generalized to Lovelock theories of gravity. This includes, in particular, a new boundary integral for the Komar mass in Einstein gravity with a nonzero cosmological constant, which has a finite result for asymptotically AdS black holes, without the need for an infinite background subtraction. Explicit computations of the Komar mass are given for black holes in pure Lovelock gravities of all orders and in general Gauss-Bonnet theories.
Janis-Newman-Winicour (JNW) spacetimes generalize the Schwarzschild solution to include a massles... more Janis-Newman-Winicour (JNW) spacetimes generalize the Schwarzschild solution to include a massless scalar field. Although suffering from naked singularities, they share the 'frozen star' features of Schwarzschild black holes. Cosmological versions of the JNW spacetimes were discovered some time ago by Husain, Martinez and Nunez and by Fonarev. Unlike Schwarzschild-deSitter black holes, these solutions are dynamical, and the scarcity of exact solutions for dynamical black holes in cosmological backgrounds motivates their further study. Here we show how the cosmological JNW spacetimes can be built, starting from simpler, static, higher dimensional, vacuum 'JNW brane' solutions via two different generalized dimensional reduction schemes that together cover the full range of JNW parameter space. Cosmological versions of a BPS limit of charged dilaton black holes are also known. JNW spacetimes represent a different limiting case of the charged, dilaton black hole family. We expect that understanding this second data point may be key to finding cosmological versions of general, non-BPS black holes.
We study fully localized BPS brane solutions in classical supergravity using a perturbative appro... more We study fully localized BPS brane solutions in classical supergravity using a perturbative approach to the coupled Born-Infeld/bulk supergravity system. We derive first order bulk supergravity fields for world-volume solitons corresponding to intersecting M2branes and to a fundamental string ending on a D3-brane. One interesting feature is the appearance of certain off-diagonal metric components and corresponding components of the gauge potentials. Making use of a supersymmetric ansatz for the exact fields, we formulate a perturbative expansion which applies to M2⊥M2 (0), M5⊥M5 (3) and Dp⊥Dp (p − 2) intersections. We find that perturbation theory qualitatively distinguishes between certain of these cases: perturbation theory breaks down at second order for intersecting M2-branes and Dp-branes with p ≤ 3 while it is well behaved, at least to this order, for the remaining cases. This indicates that the behavior of the full non-linear intersecting Dp-brane solutions may be qualitatively different for p ≤ 3 than for p ≥ 4, and that fully localized asymptotically flat solutions for p ≤ 3 may not exist. We discuss the consistency of these results with world-volume field theory properties.
The first law for the holographic entanglement entropy of spheres in a boundary CFT with a bulk L... more The first law for the holographic entanglement entropy of spheres in a boundary CFT with a bulk Lovelock dual is extended to include variations of the bulk Lovelock coupling constants. Such variations in the bulk correspond to perturbations within a family of boundary CFTs. The new contribution to the first law is found to be the product of the variation δa of the A-type trace anomaly coefficient for even dimensional CFTs, or more generally its extension δa * to include odd dimensional boundaries, times the ratio S/a *. Since a * is a measure of the number of degrees of freedom N per unit volume of the boundary CFT, this new term has the form µδN, where the chemical potential µ is given by the entanglement entropy per degree of freedom.
We present an analytic, perturbative solution to the Einstein equations with a scalar field that ... more We present an analytic, perturbative solution to the Einstein equations with a scalar field that describes dynamical black holes in a slow-roll inflationary cosmology. We show that the metric evolves quasi-statically through a sequence of Schwarzschild-de Sitter like metrics with time dependent cosmological constant and mass parameters, such that the cosmological constant is instantaneously equal to the value of the scalar potential. The areas of the black hole and cosmological horizons each increase in time as the effective cosmological constant decreases, and the fractional area increase is proportional to the fractional change of the cosmological constant, times a geometrical factor. For black holes ranging in size from much smaller than to comparable to the cosmological horizon, the pre-factor varies from very small to order one. The "mass first law" and the "Schwarzchild-de Sitter patch first law" of thermodynamics are satisfied throughout the evolution.
We study the problem of linear instability in non-vacuum spacetimes. For vacuum spa.cetimes linea... more We study the problem of linear instability in non-vacuum spacetimes. For vacuum spa.cetimes linear instability occurs when the spacetime has Killing vectors. In the non-vacuum case, one must prescribe how the sources are to vary. For one natural choice, we show that the signal for instability is the existence of Integral Constraint Vector fields. These vector fields lead, as in the vacuum case, to nonlinear constraints on the first order perturbations to the metric and momentum. For other choices for variations of the sources, we show how to modify the definition of Integral Constra,int Vectors appropriately. Since Robertson-Walker spacetimes have Integral Constraint Vectors our results may have cosmological applications.
We study evolution and thermodynamics of a slow-roll transition between early and late time de Si... more We study evolution and thermodynamics of a slow-roll transition between early and late time de Sitter phases, both in the homogeneous case and in the presence of a black hole, in a scalar field model with a generic potential having both a maximum and a positive minimum. Asymptotically future de Sitter spacetimes are characterized by ADM charges known as cosmological tensions. We show that the late time de Sitter phase has finite cosmological tension when the scalar field oscillation around its minimum is underdamped, while the cosmological tension in the overdamped case diverges. We compute the variation in the cosmological and black hole horizon areas between the early and late time phases, finding that the fractional change in horizon area is proportional to the corresponding fractional change in the effective cosmological constant. We show that the extended first law of thermodynamics, including variation in the effective cosmological constant, is satisfied between the initial and final states, and discuss the dynamical evolution of the black hole temperature.
We derive new thermodynamic relations for asymptotically planar AdS black hole and soliton soluti... more We derive new thermodynamic relations for asymptotically planar AdS black hole and soliton solutions. In addition to the ADM mass, these spacetimes are characterized by gravitational tensions in each of the planar spatial directions. We show that with planar AdS asymptotics, the sum of the ADM mass and tensions necessarily vanishes, as one would expect from the AdS /CFT correspondence. Each Killing vector of such a spacetime leads to a Smarr formula relating the ADM mass and tensions, the black hole horizon and soliton bubble areas, and a set of thermodynamic volumes that arise due to the non-vanishing cosmological constant. These Smarr relations display an interesting symmetry between black holes and bubbles, being invariant under the simultaneous interchange of the mass and black hole horizon area with the tension and soliton bubble area. This property may indicate a symmetry between the confining and deconfined phases of the dual gauge theory.
We study two systems of BPS solitons in which spin-spin interactions are important in establishin... more We study two systems of BPS solitons in which spin-spin interactions are important in establishing the force balances which allow static, multi-soliton solutions to exist. Solitons in the Israel-Wilson-Perjes (IWP) spacetimes each carry arbitrary, classical angular momenta. Solitons in the Aichelburg-Embacher "superpartner" spacetimes carry quantum mechanical spin, which originates in the zero-modes of the gravitino field of N = 2 supergravity in an extreme Reissner-Nordstrom background. In each case we find a cancellation between gravitational spin-spin and magnetic dipole-dipole forces, in addition to the usual one between Newtonian gravitational attraction and Coulombic electrostatic repulsion. In both cases, we analyze the forces between two solitons by treating one of the solitons as a probe or test particle, with the appropriate properties, moving in the background of the other. In the IWP case, the equation of motion for a spinning test particle, originally due to Papapetrou, includes a coupling between the background curvature and the spin of the test particle. In the superpartner case, the relevant equation of motion follows from a κ-symmetric superparticle action.
We show that asymptotically future deSitter (AFdS) spacetimes carry 'genuine' cosmic hair; inform... more We show that asymptotically future deSitter (AFdS) spacetimes carry 'genuine' cosmic hair; information that is analogous to the mass and angular momentum of asymptotically flat spacetimes and that characterizes how an AFdS spacetime approaches its asymptotic form. We define new 'cosmological tension' charges associated with future asymptotic spatial translation symmetries, which are analytic continuations of the ADM mass and tensions of asymptotically planar AdS spacetimes, and which measure the leading anisotropic corrections to the isotropic, exponential deSitter expansion rate. A cosmological Smarr relation, holding for AFdS spacetimes having exact spatial translation symmetry, is derived. This formula relates cosmological tension, which is evaluated at future infinity, to properties of the cosmology at early times, together with a 'cosmological volume' contribution that is analogous to the thermodynamic volume of AdS black holes. Smarr relations for different spatial directions imply that the difference in expansion rates between two directions at late times is related in a simple way to their difference at early times. Hence information about the very early universe can be inferred from cosmic hair, which is potentially observable in a late time deSitter phase. Cosmological tension charges and related quantities are evaluated for Kasner-deSitter spacetimes, which serve as our primary examples.
A Killing bubble is a minimal surface that arises as the fixed surface of a spacelike Killing fie... more A Killing bubble is a minimal surface that arises as the fixed surface of a spacelike Killing field. We compute the bubble contributions to the Smarr relations and the mass and tension first laws for spacetimes containing both black holes and Killing bubbles. The resulting relations display an interesting interchange symmetry between the properties of black hole horizons and those of KK bubbles. This interchange symmetry reflects the underlying relation between static bubbles and black holes under double analytic continuation of the time and Kaluza-Klein directions. The thermodynamics of bubbles involve a geometrical quantity that we call the bubble surface gravity, which we show has several properties in common with the black hole surface gravity.
We construct a set of conserved charges for asymptotically deSitter spacetimes that correspond to... more We construct a set of conserved charges for asymptotically deSitter spacetimes that correspond to asymptotic conformal isometries. The charges are given by boundary integrals at spatial infinity in the flat cosmological slicing of deSitter. Using a spinor construction, we show that the charge associated with conformal time translations is necessarilly positive and hence may provide a useful definition of energy for these spacetimes. A similar spinor construction shows that the charge associated with the time translation Killing vector of deSitter in static coordinates has both positive and negative definite contributions. For Schwarzshild-deSitter the conformal energy we define is given by the mass parameter times the cosmological scale factor. The time dependence of the charge is a consequence of a non-zero flux of the corresponding conserved current at spatial infinity. For small perturbations of deSitter, the charge is given by the total comoving mass density.
We describe a large class of two-dimensional conformal field theories based on a current algebra ... more We describe a large class of two-dimensional conformal field theories based on a current algebra construction of Virasoro representations due to Goddard, Kent, and Olive. The basic tool is a generalization of the Feigin-Fuchs representation. All the theories are organized by chiral algebras, the simplest examples being the Virasoro and super-Virasoro algebras.
Constructs from conformal geometry are important in low dimensional gravity models, while in high... more Constructs from conformal geometry are important in low dimensional gravity models, while in higher dimensions the higher curvature interactions of Lovelock gravity are similarly prominent. Considering conformal invariance in the context of Lovelock gravity leads to natural, higher-curvature generalizations of the Weyl, Schouten, Cotton and Bach tensors, with properties that straightforwardly extend those of their familiar counterparts. As a first application, we introduce a new set of conformally invariant gravity theories in D = 4k dimensions, based on the squares of the higher curvature Weyl tensors.
We study extremal black hole solutions of D = 5 Gauss-Bonnet gravity coupled to a system of gauge... more We study extremal black hole solutions of D = 5 Gauss-Bonnet gravity coupled to a system of gauge and scalar fields. As in Einstein gravity, we find that the values of the scalar fields on the horizon must extremize a certain effective potential that depends on the black hole charges. If the matrix of second derivatives of the effective potential at this extremum has positive eigenvalues, we give evidence, based on a near horizon perturbative expansion, that the attractor mechanism continues to hold in this general class of theories. We numerically construct solutions to a particular simple single scalar field model that display the attractor mechanism over a wide range of asymptotic values for the scalar field. We also numerically construct non-extremal solutions and show that the attractor mechanism fails to hold away from extremality.
We study a class of D = 11 BPS spacetimes that describe M-branes wrapping supersymmetric 2 and 4-... more We study a class of D = 11 BPS spacetimes that describe M-branes wrapping supersymmetric 2 and 4-cycles of Calabi-Yau 3-folds. We analyze the geometrical significance of the supersymmetry constraints and gauge field equations of motion for these spacetimes. We show that the dimensional reduction to D = 5 yields known BPS black hole and black string solutions of D = 5, N = 2 supergravity. The usual ansatz for the dimensional reduction is valid only in the linearized regime of slowly varying moduli and small gauge field strengths. Our identification of the massless D = 5 modes with D = 11 quantities extends beyond this regime and should prove useful in constructing non-linear ansatze for Calabi-Yau dimensional reductions of supergravity theories.
We find that topological invariants, isomorphic to Donaldson Polynomials, exist in chiral superfi... more We find that topological invariants, isomorphic to Donaldson Polynomials, exist in chiral superfield theories. Twists between these invariants and those of the corresponding : TQFT are given. In the topological sigma model, anti-commuting charges of integer spin are found which together with the BRST charge, fill out a D=2, N=2 supersymmetry algebra.
We analyze the neighborhoods of superconformal fixed points in the FQS discrete series through th... more We analyze the neighborhoods of superconformal fixed points in the FQS discrete series through the use of composite operator perturbation theory and Landau-Ginsburg type effective lagrangians. In particular, we demonstrate the existence of spontaneous supersymmetry breaking in models with zero supersymmetry index, and argue for the existence of renormalization group flows which change the index.
Higher curvature Lovelock gravity theories can have a number of maximally symmetric vacua with di... more Higher curvature Lovelock gravity theories can have a number of maximally symmetric vacua with different values of the curvature. Critical surfaces in the space of Lovelock couplings separate regions with different numbers of such vacua, and there exist symmetry breaking regions with no maximally symmetric vacua. Especially in such regimes, it is interesting to ask what reduced symmetry vacua may exist. We study this question, focusing on vacua that are products of maximally symmetric spaces. For low order Lovelock theories, we assemble a map of such vacua over the Lovelock coupling space, displaying different possibilities for vacuum symmetry breaking. We see indications of interesting structure, with e.g. product vacua in Gauss-Bonnet gravity covering the entirety of the symmetry breaking regime in 5-dimensions, but only a limited portion of it in 6-dimensions.
We describe a large class of two-dimensional conformal field theories based on a current algebra ... more We describe a large class of two-dimensional conformal field theories based on a current algebra construction of Virasoro representations due to Goddard, Kent, and Olive. The basic tool is a generalization of the Feigin-Fuchs representation. All the theories are organized by chiral algebras, the simplest examples being the Virasoro and super-Virasoro algebras.
The Komar integral relation of Einstein gravity is generalized to Lovelock theories of gravity. T... more The Komar integral relation of Einstein gravity is generalized to Lovelock theories of gravity. This includes, in particular, a new boundary integral for the Komar mass in Einstein gravity with a nonzero cosmological constant, which has a finite result for asymptotically AdS black holes, without the need for an infinite background subtraction. Explicit computations of the Komar mass are given for black holes in pure Lovelock gravities of all orders and in general Gauss-Bonnet theories.
Janis-Newman-Winicour (JNW) spacetimes generalize the Schwarzschild solution to include a massles... more Janis-Newman-Winicour (JNW) spacetimes generalize the Schwarzschild solution to include a massless scalar field. Although suffering from naked singularities, they share the 'frozen star' features of Schwarzschild black holes. Cosmological versions of the JNW spacetimes were discovered some time ago by Husain, Martinez and Nunez and by Fonarev. Unlike Schwarzschild-deSitter black holes, these solutions are dynamical, and the scarcity of exact solutions for dynamical black holes in cosmological backgrounds motivates their further study. Here we show how the cosmological JNW spacetimes can be built, starting from simpler, static, higher dimensional, vacuum 'JNW brane' solutions via two different generalized dimensional reduction schemes that together cover the full range of JNW parameter space. Cosmological versions of a BPS limit of charged dilaton black holes are also known. JNW spacetimes represent a different limiting case of the charged, dilaton black hole family. We expect that understanding this second data point may be key to finding cosmological versions of general, non-BPS black holes.
We study fully localized BPS brane solutions in classical supergravity using a perturbative appro... more We study fully localized BPS brane solutions in classical supergravity using a perturbative approach to the coupled Born-Infeld/bulk supergravity system. We derive first order bulk supergravity fields for world-volume solitons corresponding to intersecting M2branes and to a fundamental string ending on a D3-brane. One interesting feature is the appearance of certain off-diagonal metric components and corresponding components of the gauge potentials. Making use of a supersymmetric ansatz for the exact fields, we formulate a perturbative expansion which applies to M2⊥M2 (0), M5⊥M5 (3) and Dp⊥Dp (p − 2) intersections. We find that perturbation theory qualitatively distinguishes between certain of these cases: perturbation theory breaks down at second order for intersecting M2-branes and Dp-branes with p ≤ 3 while it is well behaved, at least to this order, for the remaining cases. This indicates that the behavior of the full non-linear intersecting Dp-brane solutions may be qualitatively different for p ≤ 3 than for p ≥ 4, and that fully localized asymptotically flat solutions for p ≤ 3 may not exist. We discuss the consistency of these results with world-volume field theory properties.
The first law for the holographic entanglement entropy of spheres in a boundary CFT with a bulk L... more The first law for the holographic entanglement entropy of spheres in a boundary CFT with a bulk Lovelock dual is extended to include variations of the bulk Lovelock coupling constants. Such variations in the bulk correspond to perturbations within a family of boundary CFTs. The new contribution to the first law is found to be the product of the variation δa of the A-type trace anomaly coefficient for even dimensional CFTs, or more generally its extension δa * to include odd dimensional boundaries, times the ratio S/a *. Since a * is a measure of the number of degrees of freedom N per unit volume of the boundary CFT, this new term has the form µδN, where the chemical potential µ is given by the entanglement entropy per degree of freedom.
We present an analytic, perturbative solution to the Einstein equations with a scalar field that ... more We present an analytic, perturbative solution to the Einstein equations with a scalar field that describes dynamical black holes in a slow-roll inflationary cosmology. We show that the metric evolves quasi-statically through a sequence of Schwarzschild-de Sitter like metrics with time dependent cosmological constant and mass parameters, such that the cosmological constant is instantaneously equal to the value of the scalar potential. The areas of the black hole and cosmological horizons each increase in time as the effective cosmological constant decreases, and the fractional area increase is proportional to the fractional change of the cosmological constant, times a geometrical factor. For black holes ranging in size from much smaller than to comparable to the cosmological horizon, the pre-factor varies from very small to order one. The "mass first law" and the "Schwarzchild-de Sitter patch first law" of thermodynamics are satisfied throughout the evolution.
We study the problem of linear instability in non-vacuum spacetimes. For vacuum spa.cetimes linea... more We study the problem of linear instability in non-vacuum spacetimes. For vacuum spa.cetimes linear instability occurs when the spacetime has Killing vectors. In the non-vacuum case, one must prescribe how the sources are to vary. For one natural choice, we show that the signal for instability is the existence of Integral Constraint Vector fields. These vector fields lead, as in the vacuum case, to nonlinear constraints on the first order perturbations to the metric and momentum. For other choices for variations of the sources, we show how to modify the definition of Integral Constra,int Vectors appropriately. Since Robertson-Walker spacetimes have Integral Constraint Vectors our results may have cosmological applications.
We study evolution and thermodynamics of a slow-roll transition between early and late time de Si... more We study evolution and thermodynamics of a slow-roll transition between early and late time de Sitter phases, both in the homogeneous case and in the presence of a black hole, in a scalar field model with a generic potential having both a maximum and a positive minimum. Asymptotically future de Sitter spacetimes are characterized by ADM charges known as cosmological tensions. We show that the late time de Sitter phase has finite cosmological tension when the scalar field oscillation around its minimum is underdamped, while the cosmological tension in the overdamped case diverges. We compute the variation in the cosmological and black hole horizon areas between the early and late time phases, finding that the fractional change in horizon area is proportional to the corresponding fractional change in the effective cosmological constant. We show that the extended first law of thermodynamics, including variation in the effective cosmological constant, is satisfied between the initial and final states, and discuss the dynamical evolution of the black hole temperature.
We derive new thermodynamic relations for asymptotically planar AdS black hole and soliton soluti... more We derive new thermodynamic relations for asymptotically planar AdS black hole and soliton solutions. In addition to the ADM mass, these spacetimes are characterized by gravitational tensions in each of the planar spatial directions. We show that with planar AdS asymptotics, the sum of the ADM mass and tensions necessarily vanishes, as one would expect from the AdS /CFT correspondence. Each Killing vector of such a spacetime leads to a Smarr formula relating the ADM mass and tensions, the black hole horizon and soliton bubble areas, and a set of thermodynamic volumes that arise due to the non-vanishing cosmological constant. These Smarr relations display an interesting symmetry between black holes and bubbles, being invariant under the simultaneous interchange of the mass and black hole horizon area with the tension and soliton bubble area. This property may indicate a symmetry between the confining and deconfined phases of the dual gauge theory.
We study two systems of BPS solitons in which spin-spin interactions are important in establishin... more We study two systems of BPS solitons in which spin-spin interactions are important in establishing the force balances which allow static, multi-soliton solutions to exist. Solitons in the Israel-Wilson-Perjes (IWP) spacetimes each carry arbitrary, classical angular momenta. Solitons in the Aichelburg-Embacher "superpartner" spacetimes carry quantum mechanical spin, which originates in the zero-modes of the gravitino field of N = 2 supergravity in an extreme Reissner-Nordstrom background. In each case we find a cancellation between gravitational spin-spin and magnetic dipole-dipole forces, in addition to the usual one between Newtonian gravitational attraction and Coulombic electrostatic repulsion. In both cases, we analyze the forces between two solitons by treating one of the solitons as a probe or test particle, with the appropriate properties, moving in the background of the other. In the IWP case, the equation of motion for a spinning test particle, originally due to Papapetrou, includes a coupling between the background curvature and the spin of the test particle. In the superpartner case, the relevant equation of motion follows from a κ-symmetric superparticle action.
We show that asymptotically future deSitter (AFdS) spacetimes carry 'genuine' cosmic hair; inform... more We show that asymptotically future deSitter (AFdS) spacetimes carry 'genuine' cosmic hair; information that is analogous to the mass and angular momentum of asymptotically flat spacetimes and that characterizes how an AFdS spacetime approaches its asymptotic form. We define new 'cosmological tension' charges associated with future asymptotic spatial translation symmetries, which are analytic continuations of the ADM mass and tensions of asymptotically planar AdS spacetimes, and which measure the leading anisotropic corrections to the isotropic, exponential deSitter expansion rate. A cosmological Smarr relation, holding for AFdS spacetimes having exact spatial translation symmetry, is derived. This formula relates cosmological tension, which is evaluated at future infinity, to properties of the cosmology at early times, together with a 'cosmological volume' contribution that is analogous to the thermodynamic volume of AdS black holes. Smarr relations for different spatial directions imply that the difference in expansion rates between two directions at late times is related in a simple way to their difference at early times. Hence information about the very early universe can be inferred from cosmic hair, which is potentially observable in a late time deSitter phase. Cosmological tension charges and related quantities are evaluated for Kasner-deSitter spacetimes, which serve as our primary examples.
A Killing bubble is a minimal surface that arises as the fixed surface of a spacelike Killing fie... more A Killing bubble is a minimal surface that arises as the fixed surface of a spacelike Killing field. We compute the bubble contributions to the Smarr relations and the mass and tension first laws for spacetimes containing both black holes and Killing bubbles. The resulting relations display an interesting interchange symmetry between the properties of black hole horizons and those of KK bubbles. This interchange symmetry reflects the underlying relation between static bubbles and black holes under double analytic continuation of the time and Kaluza-Klein directions. The thermodynamics of bubbles involve a geometrical quantity that we call the bubble surface gravity, which we show has several properties in common with the black hole surface gravity.
We construct a set of conserved charges for asymptotically deSitter spacetimes that correspond to... more We construct a set of conserved charges for asymptotically deSitter spacetimes that correspond to asymptotic conformal isometries. The charges are given by boundary integrals at spatial infinity in the flat cosmological slicing of deSitter. Using a spinor construction, we show that the charge associated with conformal time translations is necessarilly positive and hence may provide a useful definition of energy for these spacetimes. A similar spinor construction shows that the charge associated with the time translation Killing vector of deSitter in static coordinates has both positive and negative definite contributions. For Schwarzshild-deSitter the conformal energy we define is given by the mass parameter times the cosmological scale factor. The time dependence of the charge is a consequence of a non-zero flux of the corresponding conserved current at spatial infinity. For small perturbations of deSitter, the charge is given by the total comoving mass density.
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Papers by David Kastor