arXiv subjects
Publications and source records attributed to Narayan Banerjee.
This work deals with the violation or retention of symmetries associated with the self-adjoint extension of the Hamiltonian for homogeneous but anisotropic Bianchi I cosmological model. This extension is required to make sure the quantum evolution is unitary. It is found that the scale invariance is lost, but the Noether symmetries are preserved.
Though the cosmic censorship conjecture states that spacetime singularities must be hidden from an asymptotic observer by an event horizon, naked singularities can form as the end product of a gravitational collapse under suitable initial conditions, so the question of how to observationally distinguish such naked singularities from standard black hole spacetimes becomes important. In the present paper, we try to address this question by studying the ringdown profile of the Janis-Newman-Winicour (JNW) naked singularity under axial gravitational perturbation. The JNW spacetime has a surfacelike naked singularity that is sourced by a massless scalar field and reduces to the Schwarzschild solution in absence of the scalar field. We show that for low strength of the scalar field, the ringdown profile is dominated by echoes which mellows down as the strength of the field increases to yield characteristic quasinormal mode frequency of the JNW spacetime.
The present work deals with the evolution of the density contrasts for a cosmological model where along with the standard cold dark matter (CDM), the present Universe also contains holographic dark energy (HDE). The characteristic infra-red (IR) cut-off is taken as the future event horizon. The HDE is allowed to interact with the CDM. The equations for the density contrasts are integrated numerically. It is found that irrespective of the presence of an interaction, the matter perturbation has growing modes. The HDE is also found to have growth of perturbation, so very much like the CDM, thus can also cluster. The interesting point to note is that the density contrast corresponding to HDE has a peak at recent past and is decaying at the present epoch. Another feature is that IR cut-off as the event horizon does not naturally produce accelerated expansion of the Universe in the presence of an interaction.
The cosmological jerk parameter $j$ is reconstructed in a non-parametric way from observational data independent of a fiducial cosmological model. From this kinematical quantity, the equation of state parameter for composite matter distribution is also found out. The result shows that there is a deviation from the $Λ$CDM model close to $z=1.5$, at the $3σ$ confidence level.
We consider radiation from cosmological apparent horizon in Friedmann-Lemaitre-Robertson-Walker(FLRW) model in a double-null coordinate setting. As the spacetime is dynamic, there is no timelike Killing vector, instead we have Kodama vector which acts as dynamical time. We construct the positive frequency modes of the Kodama vector across the horizon. The conditional probability that a signal reaches the central observer when it is crossing from the outside gives the temperature associated with the horizon.
In the present paper, we explore the possible effects of a second rank antisymmetric tensor field, known as Kalb-Ramond (KR) field, on cosmological particle production as well as on quantum entanglement for a massive scalar field propagating in a four dimensional FRW spacetime evolves through a symmetric bounce. For this purpose, the scalar field is considered to be coupled with the KR field and also with the Ricci scalar via the term $\sim ξRΦ^2$ (with $ξ$ be the coupling). The presence of KR field spoils the conformal symmetry of a massless scalar field even for $ξ= 1/6$ in four dimensional context, which has interesting consequences on particle production and consequently on quantum entanglement as we will discuss. In particular, the presence of KR field in a FRW bouncing universe allows a greater particle production and consequently the upper bound of the entanglement entropy becomes larger in comparison to the case when the KR field is absent. This may provide an interesting testbed for the existence of Kalb-Ramond field in our universe.
The `no-hair' conjecture claims that for a spherically symmetric black hole, only the information regarding the mass and charge of the black hole is available to an external observer. However, there are numerous counterexamples to the `no-hair' conjecture. In this work, we consider a particular counter-example to the `no-hair' conjecture in (3+1) dimensions, namely, a static spherically symmetric charged black hole with a scalar hair. We provide semi-analytic bounds on the greybody factors and study the sparsity of Hawking radiation of mass-less uncharged scalar fields. Our results show that the scalar and electric charges contribute oppositely to the greybody factor and the sparsity of the Hawking radiation cascade. Also, the greybody factor decreases and the Hawking emission spectra become more sparse with the reduction in the black hole (ADM) mass.
The role of the Raychaudhuri equation in studying gravitational collapse is discussed. A self-similar distribution of a scalar field along with an imperfect fluid in a conformally flat spacetime is considered for the purpose. The general focusing condition is found out and verified against the available exact solutions. The connection between the Raychaudhuri equation and the critical phenomena is also explored.
A scalar hair is used to generate a mutated black hole, which mimics an Einstein-Rosen bridge or a wormhole. The superradiant stability of the spacetime is studied under perturbation by an electrically charged massive scalar field. The system appears to be stable against superradiance irrespective of the mass of the test field.
Brans-Dicke cosmological models for a spatially isotropic and homogeneous universe are tested in terms of the validity of the Generalized Second Law of Thermodynamics (GSL). The investigation is carried out in the Einstein frame. It is found that the models are thermodynamically viable for negative values of the Brans-Dicke parameter w and thus are quite consistent with the recent accelerated expansion of the universe.
We consider a class of interacting dark energy models in a flat and nonflat FLRW universe where the interaction is characterized by the modified evolution of the pressureless dark matter as $a^{-3+δ(a)}$, $a$ being the FLRW scale factor and $δ(a)$ quantifies the interaction rate. By assuming the most natural and nonsingular parametrization for $δ(a)$ as $δ\left( a\right) =\sum_{i} δ_i (1-a)^i $, where $δ_{i}$'s ($i=0,1,2,3,..$) are constants, we reconstruct the expansion history of the universe for three particular choices of the DE sector using different cosmological datasets. Our analyses show that the non-interacting scenario is consistent with the observations while the interaction is not strictly ruled out. We reconstruct in the following way. We start with the first two terms of $δ(a)$ above and constrain $δ_0$, $δ_1$. Then we consider up to the second order terms in $δ(a)$ but fix $δ_0$, $δ_1$ to their constrained values and constrain $δ_2$; similarly we constrain $δ_3$, and finally we constrain $(δ_0, δ_1, δ_1, δ_3)$ by keeping all of them to be free as a generalized case. Our reconstruction technique shows that the constraints on $δ_2$ (fixing $δ_0$ and $δ_1$) and $δ_3$ (fixing $δ_0$, $δ_1$ and $δ_2$) are almost zero for any interaction model and thus the effective scenario is well described by the linear parametrization $δ(a)\simeq δ_{0}+δ_{1}(1-a)$. Additionally, a strong negative correlation between $δ_0$, $δ_1$ is observed independently of the dark energy fluid and the curvature of our universe.
Black hole radiation from an infinitesimally thin massive collapsing shell, possessing a global monopole charge, which in turn leads to a Schwarzschild black hole with a global monopole charge has been shown to be processed by a unitary evolution. The exterior metric of the collapsing shell is described by the global monopole (GM) metric. The analysis is performed using the Wheeler-deWitt formalism which gave rise to a Schrödinger-like wave equation. Existence of unitarity is confirmed from two independent lines of approach. Firstly, by showing that the trace of the square of the density matrix, of the outgoing radiation, from a quantized massless scalar field, is unity. Secondly, by proving that the conservation of probability holds for the wave function of the system.
We have shown analytically that radiation from a collapsing shell which leads to a charged black hole, whose exterior is described by the RN (Reissner-Nordström) metric (and hence the background spacetime is non-globally hyperbolic), is processed with a unitary evolution. For the analysis, we have used the Wheeler-deWitt formalism which in turn gave rise to a Schrödinger-like wave equation. We showed the existence of unitarity by proving that the trace of the squared density matrix of the outgoing radiation, from a quantized massless scalar field, is unity and that the conservation of probability holds for the wave function of the system.
In the present work we investigate the stability of the k-essence models allowing upto quadratic terms of the kinetic energy. The system of field equations is written as an autonomous system in terms of dimensionless variables and the stability criteria of the equilibria have been extensively investigated. The results strongly indicate that cosmologically consistent models dynamically evolve towards the quintessence model, a stable solution with a canonical form of the dark energy.
A new strategy for the reconstruction of $f(R)$ gravity models have been attempted using Raychaudhuri equation. Two examples, one for an eternally accelerating universe and the other for one that mimics a $Λ$CDM expansion history have been worked out. For both the cases, the relevant $f=f(R)$ could be found out analytically. In the first case, $f(R)$ is found to be a combination of power-law terms and in the expression for the second case involves hypergeometric functions. The evolution history of the universe, given as specific values of the kinematical quantities like the jerk or the deceleration parameter, serve as the input. It is found that the corresponding $f(R)$ gravity models, in both the examples, are not viable options.
The present work deals with holographic dark energy models with Hubble horizon as the infra-red cut-off. The interaction rate between dark energy and dark matter has been reconstructed with three different choices of the interaction term. It is shown that the coupling parameter of the interaction term should evolve with redshift to allow the successful transition from decelerated to accelerated phase of expansion. Constraints on the model parameters are obtained from Markov Chain Monte Carlo (MCMC) analysis using the supernova distance modulus data and observational measurements of the Hubble parameter. Results show that the model with the coupling parameter increasing with redshift (z) or equivalently decreasing with the evolution, are ruled out. On the other hand, coupling parameters, increasing or slowly varying with the evolution, are consistent with the observed evolution scenario. A Bayesian evidence calculation has been carried out for statistical selection of the reconstructed models. Though the kinematical parameters are well behaved for these models, the physical variables which determine the nature of the components in the matter sector, are not at all realistic. We have concluded that the existence of spatial curvature is essential for this particular type of dark energy models.
A comparative study of thawing and tracking models of dark energy is carried out with the help of a dynamical systems analysis. It is found that both of them have stable solutions which are consistent with the requirement of a dark energy. So none of them is actually favored from the consideration of stability. The trackers have the interesting possibility that the present acceleration is a transient phenomenon.
The present work includes an analytical investigation of a collapsing spherical star in f (R) gravity. The interior of the collapsing star admits a conformal flatness. Information regarding the fate of the collapse is extracted from the matching conditions of the extrinsic curvature and the Ricci curvature scalar across the boundary hypersurface of the star. The radial distribution of the physical quantities such as density, anisotropic pressure and radial heat flux are studied. The inhomogeneity of the collapsing interior leads to a non-zero acceleration. The divergence of this acceleration and the loss of energy through a heat conduction forces the rate of the collapse to die down and the formation of a zero proper volume singularity is realized only asymptotically.