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Ujjal Debnath

Publications and source records attributed to Ujjal Debnath.

At least 181 records · Page 10Linked to original sources
arXiv2007

Quasi-Spherical Gravitational Collapse in higher dimension and the effect of equation of state

Gravitational collapse in (n+2) dimensional quasi-spherical space-time is studied for a fluid with non vanishing radial pressure. An exact analytic solution is obtained (ignoring the arbitrary integration function) for the equation of state $p_{r}=(γ-1)ρ.$ The singularity is studied locally by comparing the time of formation of apparent horizon and the central shell focusing singularity while the global nature of the final fate of collapse is characterized by the existence of radial null geodesic. It is revealed that the end state of collapse for D dimension with equation of state $p=-ρ$, for (D$-$1) dimensional dust and (D$-$2)dimension with equation of state $p=ρ$ are identical.

gr-qc↗
arXiv2007

Gravitational Collapse in Higher Dimensional Husain Space-Time

We investigate exact solution in higher dimensional Husain model for a null fluid source with pressure $p$ and density $ρ$ are related by the following relations (i) $p=kρ$, (ii) $p=kρ-\frac{B(v)}{ρ^α}$ (variable modified Chaplygin) and (iii) $p=kρ^α$ (polytropic). We have studied the nature of singularity in gravitational collapse for the above equations of state and also for different choices of the of the parameters $k$ and $B$ namely, (i) $k=0$, $B=$ constant (generalized Chaplygin), (ii) $B=$ constant (modified Chaplygin). It is found that the nature of singularity is independent of these choices of different equation of state except for variable Chaplygin model. Choices of various parameters are shown in tabular form. Finally, matching of Szekeres model with exterior Husain space-time is done.

gr-qc↗
arXiv2007

Is the shell-focusing singularity of Szekeres space-time visible?

The visibility of the shell-focusing singularity in Szekeres space-time - which represents quasi-spherical dust collapse - has been studied on numerous occasions in the context of the cosmic censorship conjecture. The various results derived have assumed that there exist radial null geodesics in the space-time. We show that such geodesics do not exist in general, and so previous results on the visibility of the singularity are not generally valid. More precisely, we show that the existence of a radial geodesic in Szekeres space-time implies that the space-time is axially symmetric, with the geodesic along the polar direction (i.e. along the axis of symmetry). If there is a second non-parallel radial geodesic, then the space-time is spherically symmetric, and so is a Lema\^ıtre-Tolman-Bondi (LTB) space-time. For the case of the polar geodesic in an axially symmetric Szekeres space-time, we give conditions on the free functions (i.e. initial data) of the space-time which lead to visibility of the singularity along this direction. Likewise, we give a sufficient condition for censorship of the singularity. We point out the complications involved in addressing the question of visibility of the singularity both for non-radial null geodesics in the axially symmetric case and in the general (non-axially symmetric) case, and suggest a possible approach.

gr-qc↗
arXiv2007

Effect of Dynamical Cosmological Constant in presence of Modified Chaplygin Gas for Accelerating Universe

In this paper we have considered the Universe to be filled with Modified Gas and the Cosmological Constant $Λ$ to be time-dependent with or without the Gravitational Constant $G$ to be time-dependent. We have considered various phenomenological models for $Λ$, viz., $Λ\proptoρ, Λ\propto\frac{\dot{a}^{2}}{a^{2}}$ and $Λ\propto\frac{\ddot{a}}{a}$. Using these models it is possible to show the accelerated expansion of the Universe at the present epoch. Also we have shown the natures of $G$ and $Λ$ over the total age of the Universe. Using the statefinder parameters we have shown the diagramamtical representation of the evolution of the Universe starting from radiation era to $Λ$CDM model.

gr-qc↗
arXiv2007

Varying Speed of Light, Modified Chaplygin Gas and Accelerating Universe

In this paper, we have considered a model of modified Chaplygin gas in VSL theory with variable gravitational constant $G$. We have shown that the evolution of the universe starts from radiation era to phantom model. The whole evolution of the universe has been shown diagramatically by using statefinder parameters.

gr-qc↗
arXiv2006

Quasi-spherical collapse with cosmological constant

The junction conditions between static and non-static space-times are studied for analyzing gravitational collapse in the presence of a cosmological constant. We have discussed about the apparent horizon and their physical significance. We also show the effect of cosmological constant in the collapse and it has been shown that cosmological constant slows down the collapse of matter.

gr-qc↗
arXiv2006

The effect of Pressure in Higher Dimensional Quasi-Spherical Gravitational Collapse

We study gravitational collapse in higher dimensional quasi-spherical Szekeres space-time for matter with anisotropic pressure. Both local and global visibility of central curvature singularity has been studied and it is found that with proper choice of initial data it is possible to show the validity of CCC for six and higher dimensions. Also the role of pressure in the collapsing process has been discussed.

gr-qc↗
arXiv2006

A New Result on the Dynamical Symmetry of Spherical Collapse

A dynamical symmetry for spherical collapse has been studied using a linear transformation of the initial data set (mass and kinetic energy function) and the area radius. With proper choice of the initial area radius, the evolution as well as the physical parameters namely energy density and shear remain invariant both initially and at any time instant. Finally, it is found that the final outcome of collapse depends on the initial choice of the area radius.

gr-qc↗
arXiv2006

Tolman-Bondi Space-Time in Brane World Scenario

In the present work, inhomogeneous Tolman-Bondi type dust space-time is studied on the brane. There are two sets of solutions of the above model. The first solution represents either a collapsing model starting from an infinite volume at infinite past to the singularity or a model starting from a singularity and expanding for ever having a transition from decelerating phase to accelerating phase. The first solution shows that the end state of collapse may be black hole or a naked singularity depending signs of various parameters involved. The second solution represents a bouncing model where the bounce occurs at different comoving radii at different epochs.

gr-qc↗
arXiv2006

Role of Modified Chaplygin Gas as a Dark Energy Model in Collapsing Spherically Symmetric Cloud

In this work, gravitational collapse of a spherical cloud, consists of both dark matter and dark energy in the form of modified Chaplygin gas is studied. It is found that dark energy alone in the form of modified Chaplygin gas forms black hole. Also when both components of the fluid are present then the collapse favors the formation of black hole in cases the dark energy dominates over dark matter. The conclusion is totally opposite to the usually known results.

gr-qc↗
arXiv2005

Classical Solutions in Einstein's Gravity and Study of some Collapsing Models

My research work can be classified into two parts namely, (i) Cosmological phenomena with varying speed of light and (ii) Gravitational collapse and black holes. We have investigated several cosmological phenomena when velocity of light varies with time. We have considered the variation of light as power-law in time and have studied the Brans-Dicke cosmology, Quintessence problem and others. We have also examined whether some cosmological problems can be solved using it for anisotropic space-time model. In brane scenario we have studied some cosmological implications namely, the Cosmic No-Hair Conjecture (CNHC) and variable gravity theory. In CNHC we have shown that in realistic situation no more extra conditions are needed in brane scenario. In gravitational collapse, we have mainly concentrated to spherical collapse for dust distribution. We have considered both four and higher dimensional space-time and have examined the possibility for formation of black hole or naked singularity. In marginally bound case we have found naked singularity is possible only for four and five dimension, while for non-marginally bound case the possibility of black hole increases with the increase in the dimension of the space-time. In quasi-spherical gravitational collapse for dust distribution, we have (n+2) dimensional Szekeres space-time and have examined the possibility for formation of black hole or naked singularity. In marginally bound case, we have found that possibility of naked singularity depends on dimension of the space-time.

gr-qc↗
arXiv2005

Space-time curvature coupling of spinors in early universe: Neutrino asymmetry and a possible source of baryogenesis

It is well known that when a fermion propagates in curved space-time, its spin couples to the curvature of background space-time. We propose that this interaction for neutrinos propagating in early curved universe could give rise to a new set of dispersion relations and then neutrino asymmetry at equilibrium. We demonstrate this with the Bianchi models which describe the homogeneous but anisotropic and axially symmetric universe. If the lepton number violating processes freeze out at 10^{-37} second when temperature T ~ 10^{15} GeV, neutrino asymmetry of the order of 10^{-10} can be generated. A net baryon asymmetry of the same magnitude can thus be generated from this lepton asymmetry either by a GUT B-L symmetry or by the electro-week sphaleron processes which have B+L symmetry.

hep-ph↗
arXiv2005

Gravitational collapse due to dark matter and dark energy in the brane world scenario

Gravitational collapse of FRW brane world embedded in a conformaly flat bulk is considered for matter cloud consists of dark matter and dark energy with equation of state $p=ερ$ $(ε<-{1/3})$. The effect of dark matter and dark energy is being considered first separately and then a combination of them both with and without interaction. In some cases the collapse leads to black hole in some other cases naked singularity appears.

gr-qc↗
arXiv2005

Adiabatic Particle Production with Decaying $Λ$ and Anisotropic Universe

Here we study an anisotropic model of the universe with constant energy per particle. A decaying cosmological constant and particle production in an adiabatic process are considered as the sources for the entropy. The statefinder parameters $\{r,s\}$ are defined and their behaviour are analyzed graphically in some cases.

gr-qc↗
arXiv2005

Godel Type Metrics in Randall Sundrum Model

Anisotropic cosmological models such as the Gödel universe and its extensions - Gödel type solutions, are embedded on a visible 3-brane in the Randall-Sundrum 1 model. The size of the extra dimension is stabilized by tuning the rotation parameter to a very small value so that hierarchy problem can be solved. A limiting case also yields the Randall-Sundrum 2 model. The rotation parameter on the visible brane turns out to be of order $10^{-32}$, which implies that visible brane essentially lacks rotation.

gr-qc↗
arXiv2005

Role of Pressure in Quasi-Spherical Gravitational Collapse

We study quasi-spherical Szekeres space-time (which possess no killing vectors) for perfect fluid, matter with tangential stress only and matter with anisotropic pressure respectively. In the first two cases cosmological solutions have been obtained and their asymptotic behaviour have been examined while for anisotropic pressure, gravitational collapse has been studied and the role of the pressure has been discussed.

gr-qc↗
arXiv2004

Anisotropic Brane Cosmology with Variable $G$ and $Λ$

In this work, the cosmological implications of brane world scenario are investigated when the gravitational coupling $G$ and the cosmological term $Λ$ are not constant but rather there are time variation of them. From observational point of view, these time variations are taken in the form $\frac{\dot{G}}{G}\sim H$ and $Λ\sim H^{2}$. The behavior of scale factors and different kinematical parameters are investigated for different possible scenarios where the bulk cosmological constant $Λ_{5}$ can be zero, positive or negative.

gr-qc↗