European physical journal. C, Particles and fields, May 24, 2024
In this paper, we obtain analytical solutions of Einstein field equations for a spherically symme... more In this paper, we obtain analytical solutions of Einstein field equations for a spherically symmetric anisotropic matter distributions. For this purpose physically meaningful metric potential corresponds to g rr and a particular choice of the anisotropy has been utilized to obtain the solutions in closed form. This class of solution has been used to characterized observed pulsars from different aspects. Smooth matching of interior spacetime metric with the exterior Schwarzschild metric and in addition with the condition of vanishing radial pressure across the boundary leads us to determine the model parameters. Pulsar 4U 1820−30 with its current estimated data for mass and radius (Mass = 1.58M and radius = 9.1 km) has been allowed for testing the physical acceptability of our developed model. We have graphically analyzed the gross physical features of the observed pulsar. The stability of the model is also discussed under the conditions of causality, adiabatic index and generalized Tolman-Oppenheimer-Volkov (TOV) equation under the forces acting on the system. Few more pulsars with their have been considered, to show that this model is compatible with observational data, and all the requirements of a realistic star are highlighted. Mass-radius (M-R) relationship have been generated for our model. The impact of anisotropy on the gross physical features of stars have been explored with the graphical presentation.
European physical journal. C, Particles and fields, May 7, 2024
In this article, we apply the Finsler spacetime to develop the Einstein field equations in the ex... more In this article, we apply the Finsler spacetime to develop the Einstein field equations in the extension of modified geometry. Following Finsler geometry, which is focused on the tangent bundle with a scalar function, a scalar equation should be the field equation that defines this structure. This spacetime maintains the required causality properties on the generalized Lorentzian metric manifold. The matter field is coupled with the Finsler geometry to produce the complete action. The developed Einstein field equations are employed on the strange stellar system to improve the study. The interior of the system is composed of a strange quark matter, maintained by the MIT bag equation of state. In addition, the modified Tolman-Oppenheimer-Volkov (TOV) equation is formulated. In particular, the anisotropic stress attains the maximum at the surface. The mass-central density variation confirms the stability of the system.
European physical journal. C, Particles and fields, Jan 28, 2024
A new class of exact solutions depicting anisotropic compact objects is presented in the current ... more A new class of exact solutions depicting anisotropic compact objects is presented in the current work. This spherically symmetric matter distribution assumes a specific form of anisotropy to obtain the exact solution for the field equations. The obtained interior solutions are smoothly matched with the Schwarzschild exterior metric over the bounding surface of a compact star and together with the condition that the radial pressure vanishes at the boundary, the form of the model parameters are attained. One of the interesting features of the obtained solutions is the codependency of the metric potentials. We have considered the pulsar 4U1608-52 with its current estimated data (mass = 1.57 +0.30 −0.29 M and radius = 9.8±1.8 km [Özel in Astrophys J 820(1):28, 2016]) to study the model graphically. Moreover, we have studied the physical features and some important stability conditions for the model. Tabular comparison with other known pulsars infers that the obtained model represents a compact star within a radius of 8-12 km. Finally, we have found the angular momentum that causes the dragging of inertial frames of the slowly rotating equilibrium compact objects.
In this paper, we study the gravitational field of a non-stationary global monopole in higher dim... more In this paper, we study the gravitational field of a non-stationary global monopole in higher dimension by using field-theoretic energy-momentum tensors for monopole configuration. The solutions are obtained using the functional separability of the metric coefficients. We have shown that the monopole exerts attractive gravitational effects on test particles.
An expression for mass of a spherically symmetric system is obtained by solving the Tolman-Oppenh... more An expression for mass of a spherically symmetric system is obtained by solving the Tolman-Oppenheimer-Volkoff equation, employing the homotopy perturbation method. With the help of this expression and the Einstein field equations, a set of interior solutions is arrived at. Thereafter, different aspects of the solution are explained as regards mass, density, pressure, energy, stability, mass-radius ratio, compactness factor and surface redshift. This analysis shows that all the physical properties, in connection to brown dwarf stars, are valid with the observed features.
In the scenario of an optimal consideration that is, homogeneous and flat spacetime, we study the... more In the scenario of an optimal consideration that is, homogeneous and flat spacetime, we study the Black Hole (BH) formation from the gravitational collapse of a spherical symmetric clump of matter in the case of the specific Dark Matter (DM) model interacting with Dark Energy (DE) in the context of the brane world regime. This clump of matter constituted of DM, [Formula: see text] and DE, [Formula: see text]. In the present model, we consider anisotropic pressure in the energy–momentum tensor with a polytropic equation of state (EoS), [Formula: see text] and [Formula: see text], [Formula: see text]. Our results show that the gravitational collapse of an interacting combination of DM and DE leads to the formation of BH in the presence of brane tension. Recent work provides the generalization of isotropic pressure to an-isotropic pressure in the energy–momentum tensor for the specific interacting combination model of DM and DE in a brane world regime.
Abstract.We have presented a new anisotropic solution of Einstein’s field equations for compact-s... more Abstract.We have presented a new anisotropic solution of Einstein’s field equations for compact-star models. Einstein’s field equations are solved by using the class-one condition (S.N. Pandey, S.P. Sharma, Gen. Relativ. Gravit. 14, 113 (1982)). We constructed the expression for the anisotropy factor ($ \Delta$ by using the pressure anisotropy condition and thereafter we obtained the physical parameters like energy density, radial and transverse pressure. These models parameters are well-behaved inside the star and satisfy all the required physical conditions. Also we observed the very interesting result that all physical parameters depend upon the anisotropy factor ($ \Delta$. The mass and radius of the present compact-star models are quite compatible with the observational astrophysical compact stellar objects like Her X-1, RXJ 1856-37, SAX J1808.4-3658(SS1), SAX J1808.4-3658(SS2).
Present paper provides a new model for perfect fluid sphere filled with charge in higher dimensio... more Present paper provides a new model for perfect fluid sphere filled with charge in higher dimensional spacetime admitting conformal symmetry. We consider a linear equation of state with coefficients fixed by the matching conditions at the boundary of the source corresponding to the exterior Reissner-Nordström higher dimensional spacetime. Several physical features for different dimensions, starting from four up to eleven, are briefly discussed. It is shown that all the features as obtained from the present model are physically desirable and valid as far as the observed data set for the compact star SAX J1808.4 − 3658 (SS2) is concerned.
To find more deliberate f (R, T) astrophysical solutions, we proceed by studying wormhole geometr... more To find more deliberate f (R, T) astrophysical solutions, we proceed by studying wormhole geometries under the assumption of spherical symmetry and the existence of a conformal Killing symmetry to attain the more acceptable astrophysical results. To do this, we consider a more plausible and simple model f (R, T) = R + 2χT , where R is the Ricci scalar and T = −ρ + pr + 2pt denotes the trace of the energy-momentum tensor of the matter content. We explore and analyze two cases separately. In the first part, wormhole solutions are constructed for the matter sources with isotropic pressure. However, the obtained solution does not satisfy the required wormhole conditions. In the second part, we introduce an EoS relating to pressure (radial and lateral) and density. We constrain the models with phantom energy EoS i.e. ω = pr/ρ < −1, consequently violating the null energy condition. Next, we analyze the model via pt = npr. Several physical properties and characteristics of these solutions are investigated which are consistent with previous references about wormholes. We mainly focus on energy conditions (NEC, WEC and SEC) and consequently for supporting the respective wormhole geometries in details. In both cases it is found that the energy density is positive as seen by any static observer. To support the theoretical results, we also plotted several figures for different parameter values of the model that helps us to confirm the predictions. Finally, the volume integral quantifier, which provides useful information about the total amount of exotic matter required to maintain a traversable wormhole is discussed briefly.
We here investigate a cosmological model in which three fluids interact with each other involving... more We here investigate a cosmological model in which three fluids interact with each other involving certain coupling parameters and energy exchange rates. The motivation of the problem stems from the puzzling 'triple coincidence problem' which naively asks why the cosmic energy densities of matter, radiation and dark energy are almost of the same order of magnitude at the present time. In our model, we determine the conditions under triple interacting fluids will cross the phantom divide.
We provide a new matter source that supplies fuel to construct wormhole spacetime. The exact worm... more We provide a new matter source that supplies fuel to construct wormhole spacetime. The exact wormhole solutions are found in the model having, besides real matter, an anisotropic dark energy. We have shown that the exotic matters that are the necessary ingredients for wormhole physics violate null and weak energy conditions but obey strong energy condition marginally. Though the wormhole comprises of exotic matters yet the effective mass remains positive. We have calculated the effective mass of the wormhole up to 8 km from the throat (assuming throat radius as 4 km) as 1.3559M ⊙. Some physical features are briefly discussed.
In this paper, we show that no solutions exist for Bianchi type VI 0 cosmological model in the mo... more In this paper, we show that no solutions exist for Bianchi type VI 0 cosmological model in the modified gravity theories, namely in self-creation theory and in gravity theory based on Lyra geometry under the two physical conditions: The pressure p and the density q of the fluid are related by the equation of state p ¼ kq; 0 k 1; and the scalar expansion H of the cosmological model is proportional to the eigenvalue r 3 3 of the shear tensor. In self-creation theory, only the possible solutions are found for dust and radiation cases. Physical and geometrical properties of the obtained models are discussed for different cases of matter distribution. Also, we study the effect of the scalar field / on the entropy S of our universe with an expression for the entropy for all different cases of matter distribution. Also we have proved that the Lyra term has no effect on the entropy of the universe.
In this paper, we propose the braneworld gravastar configuration which is an alternative to the b... more In this paper, we propose the braneworld gravastar configuration which is an alternative to the braneworld black hole. We study the Mazur and Mottola gravastar model within the context of the Randall-Sundrum type II braneworld scenario, based on the fact that our four dimensional spacetime is a three-brane, embedded in a five dimensional bulk. We present exact solutions of the modified field equations in each of the three regions making up the gravastar, namely, (I) the core, (II) the shell, and (III) the vacuum exterior. The junction conditions at each interface are fulfilled and we further explore interesting physical properties such as length, energy and entropy of the spherical distribution.
We here investigate a cosmological model in which three fluids interact with each other involving... more We here investigate a cosmological model in which three fluids interact with each other involving certain coupling parameters and energy exchange rates. The motivation of the problem stems from the puzzling 'triple coincidence problem' which naively asks why the cosmic energy densities of matter, radiation and dark energy are almost of the same order of magnitude at the present time. In our model, we determine the conditions under triple interacting fluids will cross the phantom divide.
We have presented a new anisotropic solution of Einstein's field equations for compact star model... more We have presented a new anisotropic solution of Einstein's field equations for compact star models. The Einstein's field equations are solved by using the class one condition [1]. We constructed the expression for anisotropy factor (∆) by using the pressure anisotropy condition and there after we obtained physical parameters like energy density, radial and transverse pressure. These models parameters are well behaved inside the star and satisfy all the required physical conditions. Also we observed a very interesting result that all physical parameters are depending upon the anisotropy factor (∆). The mass and radius (Tab. 1) of the present compact star models are quite compatible with the observational astrophysical compact stellar objects like Her X-1, RXJ 1856-37, SAX J1808.4-3658(SS1), SAX J1808.4-3658(SS2).
European physical journal. C, Particles and fields, May 24, 2024
In this paper, we obtain analytical solutions of Einstein field equations for a spherically symme... more In this paper, we obtain analytical solutions of Einstein field equations for a spherically symmetric anisotropic matter distributions. For this purpose physically meaningful metric potential corresponds to g rr and a particular choice of the anisotropy has been utilized to obtain the solutions in closed form. This class of solution has been used to characterized observed pulsars from different aspects. Smooth matching of interior spacetime metric with the exterior Schwarzschild metric and in addition with the condition of vanishing radial pressure across the boundary leads us to determine the model parameters. Pulsar 4U 1820−30 with its current estimated data for mass and radius (Mass = 1.58M and radius = 9.1 km) has been allowed for testing the physical acceptability of our developed model. We have graphically analyzed the gross physical features of the observed pulsar. The stability of the model is also discussed under the conditions of causality, adiabatic index and generalized Tolman-Oppenheimer-Volkov (TOV) equation under the forces acting on the system. Few more pulsars with their have been considered, to show that this model is compatible with observational data, and all the requirements of a realistic star are highlighted. Mass-radius (M-R) relationship have been generated for our model. The impact of anisotropy on the gross physical features of stars have been explored with the graphical presentation.
European physical journal. C, Particles and fields, May 7, 2024
In this article, we apply the Finsler spacetime to develop the Einstein field equations in the ex... more In this article, we apply the Finsler spacetime to develop the Einstein field equations in the extension of modified geometry. Following Finsler geometry, which is focused on the tangent bundle with a scalar function, a scalar equation should be the field equation that defines this structure. This spacetime maintains the required causality properties on the generalized Lorentzian metric manifold. The matter field is coupled with the Finsler geometry to produce the complete action. The developed Einstein field equations are employed on the strange stellar system to improve the study. The interior of the system is composed of a strange quark matter, maintained by the MIT bag equation of state. In addition, the modified Tolman-Oppenheimer-Volkov (TOV) equation is formulated. In particular, the anisotropic stress attains the maximum at the surface. The mass-central density variation confirms the stability of the system.
European physical journal. C, Particles and fields, Jan 28, 2024
A new class of exact solutions depicting anisotropic compact objects is presented in the current ... more A new class of exact solutions depicting anisotropic compact objects is presented in the current work. This spherically symmetric matter distribution assumes a specific form of anisotropy to obtain the exact solution for the field equations. The obtained interior solutions are smoothly matched with the Schwarzschild exterior metric over the bounding surface of a compact star and together with the condition that the radial pressure vanishes at the boundary, the form of the model parameters are attained. One of the interesting features of the obtained solutions is the codependency of the metric potentials. We have considered the pulsar 4U1608-52 with its current estimated data (mass = 1.57 +0.30 −0.29 M and radius = 9.8±1.8 km [Özel in Astrophys J 820(1):28, 2016]) to study the model graphically. Moreover, we have studied the physical features and some important stability conditions for the model. Tabular comparison with other known pulsars infers that the obtained model represents a compact star within a radius of 8-12 km. Finally, we have found the angular momentum that causes the dragging of inertial frames of the slowly rotating equilibrium compact objects.
In this paper, we study the gravitational field of a non-stationary global monopole in higher dim... more In this paper, we study the gravitational field of a non-stationary global monopole in higher dimension by using field-theoretic energy-momentum tensors for monopole configuration. The solutions are obtained using the functional separability of the metric coefficients. We have shown that the monopole exerts attractive gravitational effects on test particles.
An expression for mass of a spherically symmetric system is obtained by solving the Tolman-Oppenh... more An expression for mass of a spherically symmetric system is obtained by solving the Tolman-Oppenheimer-Volkoff equation, employing the homotopy perturbation method. With the help of this expression and the Einstein field equations, a set of interior solutions is arrived at. Thereafter, different aspects of the solution are explained as regards mass, density, pressure, energy, stability, mass-radius ratio, compactness factor and surface redshift. This analysis shows that all the physical properties, in connection to brown dwarf stars, are valid with the observed features.
In the scenario of an optimal consideration that is, homogeneous and flat spacetime, we study the... more In the scenario of an optimal consideration that is, homogeneous and flat spacetime, we study the Black Hole (BH) formation from the gravitational collapse of a spherical symmetric clump of matter in the case of the specific Dark Matter (DM) model interacting with Dark Energy (DE) in the context of the brane world regime. This clump of matter constituted of DM, [Formula: see text] and DE, [Formula: see text]. In the present model, we consider anisotropic pressure in the energy–momentum tensor with a polytropic equation of state (EoS), [Formula: see text] and [Formula: see text], [Formula: see text]. Our results show that the gravitational collapse of an interacting combination of DM and DE leads to the formation of BH in the presence of brane tension. Recent work provides the generalization of isotropic pressure to an-isotropic pressure in the energy–momentum tensor for the specific interacting combination model of DM and DE in a brane world regime.
Abstract.We have presented a new anisotropic solution of Einstein’s field equations for compact-s... more Abstract.We have presented a new anisotropic solution of Einstein’s field equations for compact-star models. Einstein’s field equations are solved by using the class-one condition (S.N. Pandey, S.P. Sharma, Gen. Relativ. Gravit. 14, 113 (1982)). We constructed the expression for the anisotropy factor ($ \Delta$ by using the pressure anisotropy condition and thereafter we obtained the physical parameters like energy density, radial and transverse pressure. These models parameters are well-behaved inside the star and satisfy all the required physical conditions. Also we observed the very interesting result that all physical parameters depend upon the anisotropy factor ($ \Delta$. The mass and radius of the present compact-star models are quite compatible with the observational astrophysical compact stellar objects like Her X-1, RXJ 1856-37, SAX J1808.4-3658(SS1), SAX J1808.4-3658(SS2).
Present paper provides a new model for perfect fluid sphere filled with charge in higher dimensio... more Present paper provides a new model for perfect fluid sphere filled with charge in higher dimensional spacetime admitting conformal symmetry. We consider a linear equation of state with coefficients fixed by the matching conditions at the boundary of the source corresponding to the exterior Reissner-Nordström higher dimensional spacetime. Several physical features for different dimensions, starting from four up to eleven, are briefly discussed. It is shown that all the features as obtained from the present model are physically desirable and valid as far as the observed data set for the compact star SAX J1808.4 − 3658 (SS2) is concerned.
To find more deliberate f (R, T) astrophysical solutions, we proceed by studying wormhole geometr... more To find more deliberate f (R, T) astrophysical solutions, we proceed by studying wormhole geometries under the assumption of spherical symmetry and the existence of a conformal Killing symmetry to attain the more acceptable astrophysical results. To do this, we consider a more plausible and simple model f (R, T) = R + 2χT , where R is the Ricci scalar and T = −ρ + pr + 2pt denotes the trace of the energy-momentum tensor of the matter content. We explore and analyze two cases separately. In the first part, wormhole solutions are constructed for the matter sources with isotropic pressure. However, the obtained solution does not satisfy the required wormhole conditions. In the second part, we introduce an EoS relating to pressure (radial and lateral) and density. We constrain the models with phantom energy EoS i.e. ω = pr/ρ < −1, consequently violating the null energy condition. Next, we analyze the model via pt = npr. Several physical properties and characteristics of these solutions are investigated which are consistent with previous references about wormholes. We mainly focus on energy conditions (NEC, WEC and SEC) and consequently for supporting the respective wormhole geometries in details. In both cases it is found that the energy density is positive as seen by any static observer. To support the theoretical results, we also plotted several figures for different parameter values of the model that helps us to confirm the predictions. Finally, the volume integral quantifier, which provides useful information about the total amount of exotic matter required to maintain a traversable wormhole is discussed briefly.
We here investigate a cosmological model in which three fluids interact with each other involving... more We here investigate a cosmological model in which three fluids interact with each other involving certain coupling parameters and energy exchange rates. The motivation of the problem stems from the puzzling 'triple coincidence problem' which naively asks why the cosmic energy densities of matter, radiation and dark energy are almost of the same order of magnitude at the present time. In our model, we determine the conditions under triple interacting fluids will cross the phantom divide.
We provide a new matter source that supplies fuel to construct wormhole spacetime. The exact worm... more We provide a new matter source that supplies fuel to construct wormhole spacetime. The exact wormhole solutions are found in the model having, besides real matter, an anisotropic dark energy. We have shown that the exotic matters that are the necessary ingredients for wormhole physics violate null and weak energy conditions but obey strong energy condition marginally. Though the wormhole comprises of exotic matters yet the effective mass remains positive. We have calculated the effective mass of the wormhole up to 8 km from the throat (assuming throat radius as 4 km) as 1.3559M ⊙. Some physical features are briefly discussed.
In this paper, we show that no solutions exist for Bianchi type VI 0 cosmological model in the mo... more In this paper, we show that no solutions exist for Bianchi type VI 0 cosmological model in the modified gravity theories, namely in self-creation theory and in gravity theory based on Lyra geometry under the two physical conditions: The pressure p and the density q of the fluid are related by the equation of state p ¼ kq; 0 k 1; and the scalar expansion H of the cosmological model is proportional to the eigenvalue r 3 3 of the shear tensor. In self-creation theory, only the possible solutions are found for dust and radiation cases. Physical and geometrical properties of the obtained models are discussed for different cases of matter distribution. Also, we study the effect of the scalar field / on the entropy S of our universe with an expression for the entropy for all different cases of matter distribution. Also we have proved that the Lyra term has no effect on the entropy of the universe.
In this paper, we propose the braneworld gravastar configuration which is an alternative to the b... more In this paper, we propose the braneworld gravastar configuration which is an alternative to the braneworld black hole. We study the Mazur and Mottola gravastar model within the context of the Randall-Sundrum type II braneworld scenario, based on the fact that our four dimensional spacetime is a three-brane, embedded in a five dimensional bulk. We present exact solutions of the modified field equations in each of the three regions making up the gravastar, namely, (I) the core, (II) the shell, and (III) the vacuum exterior. The junction conditions at each interface are fulfilled and we further explore interesting physical properties such as length, energy and entropy of the spherical distribution.
We here investigate a cosmological model in which three fluids interact with each other involving... more We here investigate a cosmological model in which three fluids interact with each other involving certain coupling parameters and energy exchange rates. The motivation of the problem stems from the puzzling 'triple coincidence problem' which naively asks why the cosmic energy densities of matter, radiation and dark energy are almost of the same order of magnitude at the present time. In our model, we determine the conditions under triple interacting fluids will cross the phantom divide.
We have presented a new anisotropic solution of Einstein's field equations for compact star model... more We have presented a new anisotropic solution of Einstein's field equations for compact star models. The Einstein's field equations are solved by using the class one condition [1]. We constructed the expression for anisotropy factor (∆) by using the pressure anisotropy condition and there after we obtained physical parameters like energy density, radial and transverse pressure. These models parameters are well behaved inside the star and satisfy all the required physical conditions. Also we observed a very interesting result that all physical parameters are depending upon the anisotropy factor (∆). The mass and radius (Tab. 1) of the present compact star models are quite compatible with the observational astrophysical compact stellar objects like Her X-1, RXJ 1856-37, SAX J1808.4-3658(SS1), SAX J1808.4-3658(SS2).
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Papers by Farook Rahaman