arXiv subjects

Bibhas Ranjan Majhi

Publications and source records attributed to Bibhas Ranjan Majhi.

At least 109 records · Page 6Linked to original sources

arXiv2017

Entropy corresponding to the interior of a Schwarzschild black hole

Interior volume within the horizon of a black hole is a non-trivial concept which turns out to be very important to explain several issues in the context of quantum nature of black hole. Here we show that the entropy, contained by the {\it maximum} interior volume for massless modes, is proportional to the Bekenstein-Hawking expression. The proportionality constant is less than unity implying the horizon bears maximum entropy than that by the interior. The derivation is very systematic and free of any ambiguity. To do so the precise value of the energy of the modes, living in the interior, is derived by constraint analysis. Finally, the implications of the result are discussed.

gr-qc↗

arXiv2017

Thermogeometric description of the van der Waals like phase transition in AdS black holes

It is well known that interpreting the cosmological constant as the pressure, the AdS black holes behave as the van der Waals thermodynamic system. In this case, like a phase transition from vapor to liquid in a usual van der Waals system, black holes also changes phases about a critical point in the $P$-$V$ picture, where $P$ is the pressure and $V$ is the thermodynamic volume. Here, we give a geometrical description of this phase transition. Defining the relevant Legendre invariant thermogeometrics corresponding to the two criticality conditions, which determine the critical values of respective thermodynamical entities, we show that the critical point refers to the divergence of the Ricci scalars calculated from these metrics. The similar descriptions are also provided for the other two pictures of the van der Waals like phase transition: one is $T$-$S$ and the other one is $Y$-$X$ where $T$, $S$, $X$ and $Y$ are temperature, entropy, generalized force and generalized displacement; i.e. potential corresponding to external charge, respectively. The whole discussion is very general as no specific black hole metric is being used.

gr-qc↗

arXiv2017

Fresh look at the scalar-tensor theory of gravity in Jordan and Einstein frames from undiscussed standpoints

We study the scalar-tensor theory of gravity profoundly in the action level as well as in the thermodynamic level. Contrary to the usual description in the literature about the equivalence in the two conformally connected frames, this paper addresses several incomplete inferences regarding it and mentions some inequivalences which were not pointed out earlier. In the thermodynamic level, our analysis shows the two frames are equivalent. In that process, we identify the entropy, the energy and the temperature for the thermodynamic description, and we find these quantities are conformally invariant even without any prior assumption. The same conclusion is reached from the gravitational action as well as from the Gibbons-Hawking-York boundary term, establishing the result in a more convincing manner.

gr-qc↗

arXiv2017

Noncomutativity in near horizon symmetries in gravity

We have a new observation that near horizon symmetry generators, corresponding to diffeomorphisms which leave the horizon structure invariant, satisfy noncommutative Heisenberg algebra. The results are valid for any null surfaces (which has Rindler structure in the near null surface limit) and in any spacetime dimensions. Using Sugawara construction technique the central charge is identified. It is shown that the horizon entropy is consistent with the standard form of Cardy formula. Therefore we feel that the noncommutative algebra might leads to quantum mechanics of horizon and also can probe into the microscopic description of entropy.

gr-qc↗

arXiv2017

Thermogeometric phase transition in a unified framework

Using geomterothermodynamics (GTD), we investigate the phase transition of black hole in a metric independent way. We show that for any black hole, curvature scalar (of equilibrium state space geometry) is singular at the point where specific heat diverges. Previously such a result could only be shown by taking specific examples on a case by case basis. A different type of phase transition, where inverse specific heat diverges, is also studied within this framework. We show that in the latter case, metric (of equilibrium state space geometry) is singular instead of curvature scalar. Since a metric singularity may be a coordinate artifact, we propose that GTD indicates that it is the singularity of specific heat and not inverse specific heat which indicates a phase transition of black holes.

gr-qc↗

arXiv2016

Gravitational surface Hamiltonian and entropy quantization

The surface Hamiltonian corresponding to the surface part of a gravitational action has $xp$ structure where $p$ is conjugate momentum of $x$. Moreover, it leads to $TS$ on the horizon of a black hole. Here $T$ and $S$ are temperature and entropy of the horizon. Imposing the hermiticity condition we quantize this Hamiltonian. This leads to an equidistant spectrum of its eigenvalues. Using this we show that the entropy of the horizon is quantized. This analysis holds for any order of Lanczos-Lovelock gravity. For general relativity, the area spectrum is consistent with Bekenstein's observation. This provides a more robust confirmation of this earlier result as the calculation is based on the direct quantization of the Hamiltonian in the sense of usual quantum mechanics.

gr-qc↗

arXiv2016

Phase transition and critical phenomena of black holes: A general approach

We present a general framework to study the phase transition of a black hole. Assuming that there is a phase transition, it is shown that without invoking any specific black hole, the critical exponents and the scaling powers can be obtained. We find that the values are exactly same which were calculated by taking explicit forms of different black hole spacetimes. The reason for this universality is also explained. The implication of the analysis is -- one does not need to investigate this problem case by case, what the people are doing right now. We also observe that these, except two such quantities, are independent of the details of the spacetime dimensions.

gr-qc↗

arXiv2016

A Boundary Term for the Gravitational Action with Null Boundaries

Constructing a well-posed variational principle is a non-trivial issue in general relativity. For spacelike and timelike boundaries, one knows that the addition of the Gibbons-Hawking-York (GHY) counter-term will make the variational principle well-defined. This result, however, does not directly generalize to null boundaries on which the 3-metric becomes degenerate. In this work, we address the following question: What is the counter-term that may be added on a null boundary to make the variational principle well-defined? We propose the boundary integral of $2 \sqrt{-g} \left( Θ+κ\right)$ as an appropriate counter-term for a null boundary. We also conduct a preliminary analysis of the variations of the metric on the null boundary and conclude that isolating the degrees of freedom that may be fixed for a well-posed variational principle requires a deeper investigation.

gr-qc↗

arXiv2016

Temperature and thermodynamic structure of Einstein's equations for a cosmological black hole

It is expected that the cosmological black holes are the closest realistic solutions of gravitational theories and they evolve with time. Moreover, the natural way of defining thermodynamic entities for the stationary ones is not applicable in the case of a time dependent spacetime. Here we confine our discussion within the Sultana-Dyer metric which is a cosmological black hole solution of Einstein's gravity. In literature, there exists two expressions of horizon temperature -- one is time dependent and the other does not depend on time. To single out the correct one we find the temperature by studying the Hawking effect in the tunnelling formalism. This leads to time dependent structure. After identifying the correct one, the Einstein's equations are written on the horizon and we show that this leads to the first law of thermodynamics. In this process the expressions for horizon entropy and energy, obtained earlier by explicit calculations, are being used. This provides the evidence that Einstein's equations have thermodynamic structure even for a cosmological black hole spacetime. Moreover, this study further clarifies the correctness of the expressions for the thermodynamic quantities; like temperature, entropy and internal energy.

gr-qc↗

arXiv2015

Gravitational anomalies and one dimensional behaviour of black holes

It has been pointed out by Bekenstein and Mayo that the behavior of the Black hole's entropy or information flow is similar to that through one-dimensional channel. Here I analyse the same issue with the use of gravitational anomalies. The rate of the entropy change ($\dot{S}$) and the power ($P$) of the Hawking emission are calculated from the relevant components of the anomalous stress-tensor under the Unruh vacuum condition. I show that the dependence of $\dot{S}$ on power is $\dot{S}\propto P^{1/2}$ which is identical to that for the information flow in one dimensional system. This is established by using the ($1+1$) dimensional gravitational anomalies first. Then the fact is further bolstered by considering the ($1+3$) dimensional gravitational anomalies. It is found that in the former case, the proportionality constant is exactly identical to one dimensional situation, known as Pendry's formula, while in later situation its value decreases.

gr-qc↗

arXiv2015

Entropy function from the gravitational surface action for an extremal near horizon black hole

It is often argued that {\it all the information of a gravitational theory is encoded in the surface term of the action}; which means one can find several physical quantities just from the surface term without incorporating the bulk part of the action. This has been observed in various instances; e.g. derivation of the Einstein's equations, surface term calculated on the horizon leads to entropy, etc. Here I investigate the role of it in the context of entropy function and entropy of extremal near horizon black holes. Considering only the Gibbons-Hawking-York (GHY) surface term to define an entropy function for the extremal near horizon black hole solution, it is observed that the extremization of such function leads to the exact value of the horizon entropy. This analysis again supports the previous claim that there exists a ``{\it holographic}'' nature in the gravitational action -- surface term contains the information of the bulk.

gr-qc↗

arXiv2015

Tolman temperature once again: A derivation from gravitational surface action

The temperature distribution in presence of gravity, as measured by a local observer, is given by the Tolman expression. Here I derive the same only from the Gibbon's-Hawking-York surface term. In this process no explicit use of Einstein's equations of motion is done. Therefore, the present one is an off-shell analysis. Finally I discuss the importance and various implications of the derivation.

gr-qc↗

arXiv2015

Near horizon hidden symmetry and entropy of Sultana-Dyer black hole: A time dependent case

The non-extremal stationary black holes do have "{\it hidden}" conformal symmetry in which case the generators form $SL(2,\mathbb{R})$ group. Here, I explicitly show that the Sultana-Dyer black hole solution also possesses the similar near horizon conformal symmetry. This is the first example of time dependent case which also exhibits such feature. Moreover, using the corresponding generators I find the expression of the horizon entropy in the context of Virasoro algebra and Cardy formula. The result matches with the earlier findings. The present analysis is important since in reality the metric is not stationary and hence one must look into these realistic situations to obtain more information about our universe. I expect that the analysis will illuminate certain features of the time dependent situations.

gr-qc↗

arXiv2015

Entropy current in two dimensional anomalous hydrodynamics and a bound on the sum of the response parameters

The exact expression for the entropy current of a fluid in presence of two dimensional gravitational anomalies is given. To make it compatible with the second law of thermodynamics; i.e. positivity of the entropy production rate of a system (which is considered to be fundamental), we find a bound on the sum of the two response parameters ($\bar{C}_1$ and $\bar{C}_2$), in terms of the trace and diffeomorphism anomaly coefficients ($c_w$ and $c_g$). The precise expression, we obtain here, is $\bar{C}_1 + \bar{C}_2\leq 4π^2c_w + 8π^2 c_g$. Interestingly, when the bound is saturated corresponding to a reversible process, the result reproduces earlier findings obtained by either studying field theory on the cone or using the {\it Israel-Hartle-Hawking} boundary condition. Finally, possible physical implications and connections with the existing approaches are addressed.

hep-th↗

arXiv2015

Free-fall energy density and flux in the Schwarzschild black hole

In the four-dimensional background of Schwarzschild black hole, we investigate the energy densities and fluxes in the freely falling frames for the Boulware, Unruh, and Israel-Hartle-Hawking states. In particular, we study their behaviors near the horizon and asymptotic spatial infinity by using the trace anomaly of a conformally invariant scalar field. In the Boulware state, both the energy density and flux are negative divergent when the observer is dropped at the horizon, and asymptotically vanish. In the Unruh state, the energy density is also negative divergent at the horizon while it is positive finite asymptotically. The flux in the Unruh state is always positive and divergent at the horizon. In the Israel-Hartle-Hawking state, the energy density depends on the angular motion of free fall, and fluxes vanish at the horizon and the spatial infinity. Finally, we discuss the role of the negative energy density near the horizon in the evaporating black hole.

gr-qc↗

arXiv2014

Is the principle of least action a must?

The least action principle occupies a central part in contemporary physics. Yet, as far as classical field theory is concerned, it may not be as essential as generally thought. We show with three detailed examples of classical interacting field theories that it is possible, in cases of physical interest, to derive the correct field equations for all fields from the action (which we regard as defining the theory), some of its symmetries, and the conservation law of energy-momentum (this last regarded as ultimately coming from experiment)

hep-th↗

arXiv2014

Vacuum condition and the relation between response parameter and anomaly coefficient in (1+3) dimensions

The role of Israel-Hartle-Hawking vacuum is discussed for anomalous fluid in presence of both the gauge and gravitational anomalies in ($1+3$) dimensions. I show that imposition of this vacuum condition leads to the relation $\tilde{c}_{4d}=-8π^2c_m$ between the response parameter ($\tilde{c}_{4d}$) and the anomaly coefficient ($c_m$). This establishes a connection between the coefficients appearing in a first order and a third order derivative terms in the constitutive relation.

gr-qc↗

arXiv2014

Conformal Transformation, Near Horizon Symmetry, Virasoro Algebra and Entropy

There are certain black hole solutions in general relativity (GR) which are conformally related to the stationary solutions in GR. It is not obvious that the horizon entropy of these spacetimes is also one quarter of the area of horizon, like the stationary ones. Here I study this topic in the context of Virasoro algebra and Cardy formula. Using the fact that the conformal spacetime admits conformal Killing vector and the horizon is determined by the vanishing of the norm of it, the diffemorphisms are obtained which keep the near horizon structure invariant. The Noether charge and a bracket among them corresponding to these vectors are calculated in this region. Finally, they are evaluated for the Sultana-Dyer (SD) black hole, which is conformal to the Schwarzschild metric. It is found that the bracket is identical to the usual Virasoro algebra with the central extension. Identifying the zero mode eigenvalue and the central charge, the entropy of the SD horizon is obtained by using Cardy formula. Interestingly, this is again one quarter of the horizon area. Only difference in this case is that the area is modified by the conformal factor compared to that of the stationary one. The analysis gives a direct proof of the earlier assumption.

gr-qc↗