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Sarbari Guha

Publications and source records attributed to Sarbari Guha.

31 records · Page 2Linked to original sources
arXiv2019

Propagation of Gravitational Waves in Anisotropic Universe

In this paper, we have considered a toy model of an anisotropic universe and studied the propagation of gravitational waves in such a universe. The consideration of this toy model simplifies the analysis and helps us to illustrate the effects of anisotropy. Incorporating linear perturbations on this anisotropic background, we have considered the synchronous, transverse, traceless gauge conditions and evaluated the perturbations of the Ricci tensor. The energy-momentum tensor is that of a perfect fluid, for which the Einstein's field equations are determined in presence of perturbations. We arrive at the set of linearised Einstein's equations explicitly and find solutions for gravitational waves propagating along the direction of anisotropy. We also study the propagation along a direction perpendicular to the direction of anisotropy. Subsequently we have validated the assumption of the tracelessness of the linear perturbations. Finally we determine the amount of tidal acceleration caused by the propagation of gravitational waves in this background spacetime.

gr-qc↗
arXiv2019

Evolution of FRW universe in variable modified Chaplygin gas model

In this paper we study the evolution of the FRW universe filled with variable modified Chaplygin gas (VMCG). We begin with a thermodynamical treatment of VMCG described by the equation of state $P = Aρ-Bρ^{-α}$, and obtain its temperature as a function of redshift $z$. We show that the results are consistent with similar works on other types of Chaplygin gas models. In addition to deriving the exact expression of temperature of the fluid in terms of the boundary conditions and redshift, we also used observational data to determine the redshift at the epoch of transition from the decelerated to the accelerated phase of expansion of the universe. The values of other relevant parameters like the Hubble parameter, the equation-of-state parameter and the speed of sound are obtained in terms of the redshift parameter, and these values are compared with the results obtained from previous works on MCG and other Chaplygin gas models for the various values of $n$ permitted by thermodynamic stability. We assume the present value of temperature of the microwave background radiation to be given by $ T_0 = 2.7 K $, and the parameter $ A $ in the equation of state is taken as $ 1/3 $ since it corresponds to the radiation-dominated phase of the universe. The value of the parameter $Ω_x$ has been assumed to be $0.7$ in our calculation. Since it is known that the redshift of photon decoupling is $ z\simeq 1100 $, we used this value to calculate the temperature of decoupling.

gr-qc↗
arXiv2018

Five-dimensional warped product space-time with time-dependent warping and a scalar field in the bulk

We have considered gravity in a five-dimensional warped product space-time, with a time-dependent warp factor and a time-dependent extra dimension. The five-dimensional field equations are derived for a spatially flat FRW brane and the energy conditions and the nature of bulk geometry have been examined. It is found that the expansion of the four-dimensional universe depends on its location along the extra dimension and will be different at different locations in the bulk spacetime. At low energies, the trapping of fields within the brane implies a specific correlation between the warp factor and the extra-dimensional scale factor. Generally, the bulk is not conformally flat. At high energies, the bulk is assumed to be sourced by a scalar field with self-interaction. The analysis shows that the potential of the scalar field source of gravity at a given position along the fifth dimension, is related to the Hubble parameter on the brane at that position in the bulk.

gr-qc↗
arXiv2015

Particle Motion and Perturbed Dynamical System in Warped Product Spacetimes

In this paper we have used the dynamical systems analysis to study the dynamics of a five-dimensional universe in the form of a warped product spacetime with a spacelike dynamic extra dimension. We have decomposed the geodesic equations to get the motion along the extra dimension and have studied the associated dynamical system when the cross-diagonal element of the Einstein tensor vanishes, and also when it is non-vanishing. In the first case, introducing the concept of an energy function along the phase path in terms of the extra-dimensional coordinate, we have examined how the energy function depends on the warp factor. The energy function has been used as a measure of the amount of perturbation caused by a brane displacement. Geometrically the effect of brane displacement is manifested in terms of a coordinate translation along the extra dimension, thereby producing a change in the geodesic motion along the extra dimension in the region close to the brane. Then we studied the geodesic motion under a conventional metric perturbation in the form of homothetic motion and conformal motion and examined the nature of critical points for a Mashhoon-Wesson-type metric. Finally we investigated the motion for null and timelike geodesics under the condition when the cross-diagonal element of the Einstein tensor is non-vanishing and examined the effects of perturbation on the critical points of the dynamical system.

gr-qc↗
arXiv2015

Confinement and stability of dynamical system in presence of scalar fields and perturbation in the bulk

In this paper we have considered a five-dimensional warped product spacetime with spacelike extra dimension and with a scalar field source in the bulk. We have studied the dynamics of the scalar field under different types of potential in an effort to explain the confinement of particles in the five-dimensional spacetime. The behavior of the system is determined from the nature of damping force on the system. We have also examined the nature of the effective potential under different circumstances. Lastly we have studied the system to determine whether or not the system attains asymptotically stable condition for both unperturbed and perturbed conditions. The analysis throws significant light on the nature confinement of particles and the stability of the dynamical system under these conditions.

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arXiv2013

Dissipative Cylindrical Collapse of Charged Anisotropic Fluid

We have studied the dynamics of a cylindrical column of anisotropic, charged fluid which is experiencing dissipation in the form of heat flow, free-streaming radiation, and shearing viscosity, undergoing gravitational collapse. We calculate the Einstein-Maxwell field equations and, using the Darmois junction conditions, match the interior non-static cylindrically symmetric space-time with the exterior anisotropic, charged, cylindrically symmetric space-time. The behavior of the density, pressure and luminosity of the collapsing matter has been analyzed. From the dynamical equations, the effect of charge and dissipative quantities over the cylindrical collapse are studied. Finally, we have derived the solutions for the collapsing matter which is valid during the later stages of collapse and have discussed the significance from a physical standpoint.

gr-qc↗
arXiv2012

Particle motion in the field of a five-dimensional charged black hole

In this paper, we have investigated the geodesics of neutral particles near a five-dimensional charged black hole using a comparative approach. The effective potential method is used to determine the location of the horizons and to study radial and circular trajectories. This also helps us to analyze the stability of radial and circular orbits. The radius of the innermost stable circular orbits have also been determined. Contrary to the case of massive particles for which, the circular orbits may have up to eight possible values of specific radius, we find that the photons will only have two distinct values for the specific radii of circular trajectories. Finally we have used the dynamical systems analysis to determine the critical points and the nature of the trajectories for the timelike and null geodesics.

gr-qc↗
arXiv2011

Five-dimensional warped product space-time with time-dependent warp factor and cosmology of the four-dimensional universe

In this paper, we have studied a 5-dimensional warped product space-time with a time-dependent warp factor. This warp factor plays an important role in localizing matter to the 4-dimensional hypersurface constituting the observed universe and leads to a geometric interpretation of dynamical dark energy. The five-dimensional field equations are constructed and its solutions are obtained. The nature of modifications produced by this warp factor in the bulk geometry is discussed. The hypersurface is described by a flat FRW-type metric in the ordinary spatial dimension. It is found that the effective cosmological constant of the four-dimensional universe is a variable quantity monitored by the time-dependent warp factor. The universe is initially decelerated, but subsequently makes a transition to an accelerated phase at later times.

gr-qc↗
arXiv2010

Models of Gravity in Five-dimensional Warped Product Spactimes

In this paper, we have considered gravity in a 5-dimensional warped product space-time with a time-dependent warp factor, time-dependent extra dimension and a bulk cosmological constant. The braneworld is described by a spatially flat FRW-type metric. The five-dimensional field equations have been constructed and solved for various cases of the warp factor and the extra-dimensional scale factor, starting from very general type of the metric and then reducing down to specific cases. In the low energy regime, a stabilized bulk with constant curvature has been considered, from which the cosmological behavior of the corresponding observed universe has been interpreted. In the high energy regime, the bulk is assumed to be sourced by an ordinary massless scalar field and thereafter the type of the scalar field source and the different scale factors have been investigated.

gr-qc↗
arXiv2010

Five-dimensional bulk with a time-dependent warp factor and its consequences on brane cosmology

In this paper, we have considered a 5-dimensional warped product space-time with a timedependent warp factor. The time-dependent warp factor plays an important role in localizing matter to the 4-dimensional hypersurface constituting the observed universe. We then proceed to determine the nature of modifications produced in the bulk geometry as well as the consequences on the corresponding braneworld. The five-dimensional field equations are constructed. For the bulk metric chosen, the Weyl tensor is found to vanish under a certain condition, thereby satisfying the conditions of a constant curvature bulk. Consequently we have constructed the solutions to the field equations for such a bulk and have studied its physical properties. The braneworld is described by a flat FRW-type metric in the ordinary spatial dimension. It is found that the the effective cosmological constant for the induced matter is a variable quantity monitored by the time-dependent warp factor and is associated with the bending of the braneworlds. The universe is initially decelerated, but subsequently makes a transition to an accelerated phase at later times, when its dynamics is dominated by the dynamical dark energy component. For a particular choice of the warp factor, it has been found that the universe is represented by a model of dark energy with the age of the universe as the measure of length, driving the universe to a state of accelerated expansion at later times.

gr-qc↗
arXiv2010

Brane Cosmology and Motion of Test Particles in Five-Dimensional Warped Product Spacetimes

In the braneworld scenario ordinary standard model matter and on-gravitational fields are confined by some trapping mechanism to the 4-dimensional universe constituting the D3-branes which are embedded in a (4 + n)-dimensional manifold referred to as the bulk (n being the number of extra dimensions). The notion of particle confinement is necessary for theories with non-compact extra dimensions, otherwise, the particles would escape from our 4-dimensional world along unseen directions. In this paper, we have considered a five-dimensional warped product space-time having an exponential warping function which depends both on time as well as on the extra coordinates and a non-compact fifth dimension. Further, we have assumed that the lapse function may either be a constant or a function of both time and of the extra coordinates, and have studied the nature of the geodesics of test particles and analyzed the conditions of stability in this geometrical framework. We have also discussed the possible cosmology of the corresponding (3 + 1)-dimensional hypersurfaces.

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arXiv2008

Higher-dimensional Embedding of Four-dimensional Hypersurfaces: Chronological Development of Co-dimension-1 Embedding

Here we present an overview of the work done over the years on the embedding of hypersurfaces in a space of higher dimension, with particular reference to the embedding of four-dimensional hypersurfaces in five-dimensional space-times. The concept of embedding was developed by geometers starting from Gauss. Applications in physics started with the embedding of the Schwarzschild metric and through the works of Kaluza and Klein. The program on the embedding of four-dimensional hypersurfaces in five-dimensional spacetimes gathered strength with the formulation of the induced matter theory by Wesson and his collaborators. Close on its heels followed the works on the braneworld scenario. Simultaneously, the mathematical aspects of the embedding of four-dimensional hypersurfaces in five-dimensional spacetimes were developed as an application of the Campbell-Magaard theorem. In this paper we have tried to have a panoramic view of the major works done in these fields and have tried to focus on the recent trends in this context.

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