Papers by Parthasarathi Majumdar
Physical review, Jan 31, 2011
We discuss the effect of different choices in partial gauge fixing of bulk local Lorentz invarian... more We discuss the effect of different choices in partial gauge fixing of bulk local Lorentz invariance, on the description of the horizon degrees of freedom of a Schwarzschild black hole as an SU (2) Chern-Simons theory with specific sources. A classically equivalent description in terms of an ISO(2) Chern-Simons theory is also discussed. Further, we demonstrate that both these descriptions can be partially gauge fixed to a horizon theory with U (1) local gauge invariance, with the solder form sources being subject to extra constraints in directions orthogonal to an internal vector field left invariant by U (1) transformations. Seemingly disparate approaches on characterization of the horizon theory for the Schwarzschild black hole (as well as spherical Isolated Horizons in general) are thus shown to be equivalent physically.
Physical Review Letters, Jun 5, 2000
The European Physical Journal C
Inspired by the reported existence of substantive magnetic fields in the vicinity of the central ... more Inspired by the reported existence of substantive magnetic fields in the vicinity of the central supermassive black holes in Sagittarius A* and Messier 87*, we consider test particle motion in the spacetime close to a generic spherical black hole in the presence of magnetic fields in its vicinity. Modelling such a spacetime in terms of an axisymmetric, non-rotating Ernst–Melvin–Schwarzschild black hole geometry with appropriate parameters, we compute the geodesic nodal-plane precession frequency for a test particle with mass, for such a spacetime, and obtain a non-vanishing result, surpassing earlier folklore that only axisymmetric spacetimes with rotation (non-vanishing Kerr parameter) can generate such a precession. We call this magnetic field-generated phenomenon Gravitational Larmor Precession. What we present here is a Proof of Concept incipient assay, rather than a detailed analysis of supermassive black holes with magnetic fields in their neighbourhood. However, for completen...
arXiv: General Relativity and Quantum Cosmology, 2003
The relation between logarithmic corrections to the area law for black hole entropy, due to therm... more The relation between logarithmic corrections to the area law for black hole entropy, due to thermal fluctuations around an equilibrium canonical ensemble, and those originating from quantum spacetime fluctuations within a microcanonical framework, is explored for three and four dimensional asymptotically anti-de Sitter black holes. For the BTZ black hole, the two logarithmic corrections are seen to precisely cancel each other, while for four dimensional adS-Schwarzschild black holes a partial cancellation is obtained. We discuss the possibility of extending the analysis to asymptotically flat black holes.
We propose here that certain observational features of granular matter in the infrared limit, exh... more We propose here that certain observational features of granular matter in the infrared limit, exhibiting the phenomenon of jamming, arise from an underlying effective general relativistic description. The proposal stems from the assumption (which we justify on physical grounds) that grains in granular matter move freely in an effective curved Riemannian space. The termination of their trajectories at the onset of jamming is obtained from the focussing of a converging congruence of geodesics in such a space, as a solution of the Raychaudhuri equation for such congruences. This may happen irrespective of whether or not the curvature is sourced by external stresses (via an effective Einstein equation), although the properties of the resultant jammed state solution do differ in the two cases. A definite prediction of this geometrical approach is the negative role played by those trajectories which twist about each other, in reaching the jammed state. The local symmetries of granular int...
The European Physical Journal C, 2020
Compact orbiting binaries like the black hole binary system observed in GW150914 carry large amou... more Compact orbiting binaries like the black hole binary system observed in GW150914 carry large amount of orbital angular momentum. The post-ringdown compact object formed after merger of such a binary configuration has only spin angular momentum, and this results in a large orbital angular momentum excess. One significant possibility is that the gravitational waves generated by the system carry away this excess orbital angular momentum. An estimate of this excess is made. Arguing that plane gravitational waves cannot possibly carry any orbital angular momentum, a case is made in this paper for gravitational wave beams carrying orbital angular momentum, akin to optical beams. Restricting to certain specific beam-configurations, we predict that such beams may produce a new type of strain, in addition to the longitudinal strains measured at aLIGO for GW150914 and GW170817. Current constraints on post-ringdown spins, derived within the plane-wave approximation of gravitational waves, ther...
Universe, Mar 25, 2022
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
Circular geodesic orbits, both timelike and null, in extremal Reissner-Nordstrom spacetimes, are ... more Circular geodesic orbits, both timelike and null, in extremal Reissner-Nordstrom spacetimes, are examined with regard to their stability, and compared with similar orbits in the non-extremal situation, focusing for simplicity on the near extremal case. Innermost Stable Circular Orbits (ISCOs), when they exist in the extremal case, are shown to lie infinitesimally close to the event horizon in coordinate distance, and correspond to zero energy trajectories. It is shown that this class of ISCOs are absent in the corresponding near-extremal spacetime.
arXiv: Classical Physics, 2018
A fully relativistically covariant formulation of the classical Maxwell electrodynamics of an arb... more A fully relativistically covariant formulation of the classical Maxwell electrodynamics of an arbitrarily-moving point charge is presented, purely in terms of gauge invariant potentials without entailing any gauge fixing. A new, relativistically covariant energy-momentum tensor for the radiation fields is derived and yields results for the angular power distribution, in full agreement with results derived in a frame-dependent manner in standard texts of classical electrodynamics. This is then used to present a full derivation, not available in standard texts, of the energy-momentum and orbital angular momentum of a relativistic point charge. Radiation backreaction is turned on and the system reanalyzed Lorentz-covariantly, including effects of mass renormalization. This leads us to reiterate earlier conclusions regarding the inherent inadequacy of classical Maxwell electrodynamics. The Abraham-Lorentz equation is derived en passant in appropriate limits without requiring any extrane...
Generalizing Deser's work on pure $SU(2)$ gauge theory, we consider scalar, spinor and vector... more Generalizing Deser's work on pure $SU(2)$ gauge theory, we consider scalar, spinor and vector matter fields transforming under arbitrary representations of a non-Abelian, compact, semisimple internal Lie group which is a global symmetry of their actions. These matter fields are coupled to Abelian gauge fields through the process of {\it iterative N\"other coupling}. This procedure is shown to yield precisely the same locally gauge invariant theory (with the non-Abelian group as the gauge group) as obtained by the usual `minimal coupling' prescription originating from the {\it Gauge Principle}. Prospects of this non-geometrical formulation, towards better understanding of physical aspects of gauge theories, are briefly discussed.
Symmetry, 2019
A fully relativistically covariant and manifestly gauge-invariant formulation of classical Maxwel... more A fully relativistically covariant and manifestly gauge-invariant formulation of classical Maxwell electrodynamics is presented, purely in terms of gauge-invariant potentials without entailing any gauge fixing. We show that the inhomogeneous equations satisfied by the physical scalar and vector potentials (originally discovered by Maxwell) have the same symmetry as the isometry of Minkowski spacetime, thereby reproducing Einstein’s incipient approach leading to his discovery of special relativity as a spacetime symmetry. To arrive at this conclusion, we show how the Maxwell equations for the potentials follow from stationary electromagnetism by replacing the Laplacian operator with the d’Alembertian operator, while making all variables dependent on space and time. We also establish consistency of these equations by deriving them from the standard Maxwell equations for the field strengths, showing that there is a unique projection operator which projects onto the physical potentials....
The European Physical Journal C, 2019
While computing the Fermi degeneracy pressure of electrons in a white dwarf star within the frame... more While computing the Fermi degeneracy pressure of electrons in a white dwarf star within the framework of hydrostatic equilibrium, we depart from the extant practice of treating the electrons as a free fermion gas, by including the effect of the background gravitational potential experienced by the electrons in the star, resulting from the mass of its constituent atoms (being the mass of all nucleons). Modifying the free particle Hamiltonian with this effective potential, we employ first order quantum mechanical perturbation theory to compute the degeneracy pressure, in order to study the effect of inclusion of this self-gravity of the star on the limiting mass. The final effect is found to be non-trivial, but perhaps a shade too small to alter any major observational result.
The leading order correction to the metric of a Schwarzschild black hole, due to the backreaction... more The leading order correction to the metric of a Schwarzschild black hole, due to the backreaction of infalling fermionic matter fields, is shown to produce a shift of the event horizon such that particles that would constitute Hawking radiation at late retarded times are now trapped. Fermionic field operators associated with infalling and outgoing modes at the horizon behave canonically in the semiclassical approximation. They are, however, shown to satisfy a nontrivial exchange algebra given in terms of the backreaction, when the shift is ‘quantized ’ by means of correspondence. The consequent exchange algebra for bilinear fermionic densities is also obtained. Pacs nos.: 04.62.+v, 04.70.-s, 04.70.dy Typeset using REVTEX
arXiv: General Relativity and Quantum Cosmology, 2018
Motivated by the need to conceive freely-precessing gyroscopes for detecting acoustic frame-dragg... more Motivated by the need to conceive freely-precessing gyroscopes for detecting acoustic frame-dragging predicted recently in rotating acoustic analogue black holes, we report an incipient investigation on the hydrodynamics of nematic active fluids. With a specific assumption on barotropicity of a nematic fluid, we discern acoustic analogue black hole spacetimes experienced by linear perturbations of the velocity potential. For vanishingly small diffusivity of the active particles, linear perturbations of the active particle concentration reveal a profile with an enhancement close to the acoustic horizon, hinting towards the possibility of partial trapping of active matter by the acoustic black hole. We further show that, as anticipated, the dynamical nature of the orientation (`polarization') of individual particles indeed opens up the possibility of their use as freely-precessing gyroscopes. In addition, inclusion of diffusivity of active particles in the inviscid solvent is show...
arXiv: General Relativity and Quantum Cosmology, 2018
Motivated by the need to conceive freely-precessing gyroscopes for detecting acoustic frame-dragg... more Motivated by the need to conceive freely-precessing gyroscopes for detecting acoustic frame-dragging predicted recently in rotating acoustic analogue black holes, we report an incipient investigation on the hydrodynamics of nematic active fluids. With a specific assumption on barotropicity of a nematic fluid, we discern acoustic analogue black hole spacetimes experienced by linear perturbations of the velocity potential. For vanishingly small diffusivity of the active particles, linear perturbations of the active particle concentration reveal a profile with an enhancement close to the acoustic horizon, hinting towards the possibility of partial trapping of active matter by the acoustic black hole. We further show that, as anticipated, the dynamical nature of the orientation (`polarization') of individual particles indeed opens up the possibility of their use as freely-precessing gyroscopes. In addition, inclusion of diffusivity of active particles in the inviscid solvent is show...
Vedic Astrology in the Universities A Virtual Dialogue MANABI MAJUMDAR, PARTHASARATHI MAJUMDAR R... more Vedic Astrology in the Universities A Virtual Dialogue MANABI MAJUMDAR, PARTHASARATHI MAJUMDAR Recently, the issue of introduction of vedic astrology as an independent, if optional, course programme in universities has come into a great deal of focus (
Physical Review D, 2020
We establish a formal connection between the K-essence emergent gravity scenario and generalizati... more We establish a formal connection between the K-essence emergent gravity scenario and generalizations of Vaidya spacetime. Choosing the K-essence action to be of the Dirac-Born-Infeld variety, the physical spacetime to be a general static spherically symmetric black hole and restricting the K-essence scalar field to be a function solely of the advanced or the retarded time, we show that the emergent gravity metric resembles closely the generalized Vaidya metrics for null fluid collapse proposed by Husain. Imposing null energy conditions on the emergent energy-momentum tensor derived from the emergent Einstein equation, restrictions are obtained on the functions characterizing the emergent metric for consistent identification with generalized Vaidya spacetimes. Admissible explicit black hole metrics are discussed as examples.
Modern Physics Letters A, 2017
Criteria for thermal stability of charged rotating black holes of any dimension are derived for h... more Criteria for thermal stability of charged rotating black holes of any dimension are derived for horizon areas that are large relative to the Planck area (in these dimensions). The derivation is based on generic assumptions of quantum geometry, supported by some results of loop quantum gravity, and equilibrium statistical mechanics of the Grand Canonical ensemble. There is no explicit use of classical spacetime geometry in this analysis. The only assumption is that the mass of the black hole is a function of its horizon area, charge and angular momentum. Our stability criteria are then tested in detail against specific classical black holes in spacetime dimensions 4 and 5, whose metrics provide us with explicit relations for the dependence of the mass on the charge and angular momentum of the black holes. This enables us to predict which of these black holes are expected to be thermally unstable under Hawking radiation.
We study the geometry of the two dimensional string theoretic black hole under tachyonic perturba... more We study the geometry of the two dimensional string theoretic black hole under tachyonic perturbations. These perturbations are restricted to affect only the metric and the dilaton, while other string theoretic excitations (like the axion) are ignored. The metric and linearized dilaton perturbations are determined to lowest non-trivial order of the tachyonic hair in the presence of back reaction. We evaluate the Kretschmann scalar and argue that the horizon does not become singular in the presence of tachyon perturbations (to the order of our consideration). A closed-form solution of the allowed tachyon field and that of the allowed tachyon potential emerges as a requirement of self-consistency of our solution.
Modern Physics Letters A, 1989
The superparticle model with Siegel's modification is generalized to include a one-dimensiona... more The superparticle model with Siegel's modification is generalized to include a one-dimensional local world line supersymmetry. The constraints of the model are shown to yield a Poisson bracket algebra that closes. The quantization of the system in the light cone gauge produces a spectrum of states identical to that obtained for the spinning superparticle model without Siegel's modification.
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Papers by Parthasarathi Majumdar