arXiv subjects

Bibhas Ranjan Majhi

Publications and source records attributed to Bibhas Ranjan Majhi.

At least 91 records · Page 5Linked to original sources

arXiv2019

Detector response along null geodesics in black hole spacetimes and in a Friedmann-Lemaitre-Robertson-Walker Universe

We study the detector's response when moving along an ingoing null geodesic. The backgrounds are chosen to be black hole spacetimes ($(1+1)$ dimensional Schwarzschild metric and near horizon effective metric for any stationary black hole in arbitrary dimensions) as well as Friedmann-Lemaitre-Robertson-Walker (FLRW) Universe. For black holes the trajectories are defined in Schwarzschild coordinates and the field modes are corresponding to {\it Boulware vacuum}. Whereas for FLRW case, the detector is moving along the path defined in original {\it cosmic time} and the field modes are related to {\it conformal vacuum}. The analysis is done for three stages (de-Sitter, radiation dominated and matter dominated) of the Universe. We find that, although the detector is freely falling, it registered particles in the above mentioned respective vacuums. We confirm this by different approaches. The detection probability distributions, in all situations, are thermal in nature.

gr-qc↗

arXiv2019

A general framework to study the extremal phase transition of black holes

We investigate the universality of some features for the extremal phase transition of black holes and unify all the approaches which have been applied in different spacetimes. Unlike the other existing approaches where the information of the spacetime and its dimension is directly used to get various results, we provide a general formulation in which those results are obtained for any arbitrary black hole spacetime having an extremal limit. Calculating the second order moments of fluctuations of some thermodynamic quantities we show that, the phase transition occurs only in the microcanonical ensemble. Without considering any specific black hole we calculate the values of critical exponents for this type of phase transition. These are shown to be in agreement with the values obtained earlier for metric specified cases. Finally we extend our analysis to the geometrothermodynamics (henceforth GTD) formulation. We show that for any black hole, if there is an extremal point, the Ricci scalar for the Ruppeiner metric must diverge at that point.

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arXiv2019

Effective metric in fluid-gravity duality through parallel transport: a proposal

The incompressible Navier-Stokes (NS) equation is known to govern the hydrodynamic limit of essentially any fluid and its rich non-linear structure has critical implications in both mathematics and physics. The employability of the methods of Riemannian geometry to the study of hydrodynamical flows has been previously explored from a purely mathematical perspective. In this work, we propose a bulk metric in $(p+2)$-dimensions with the construction being such that the induced metric is flat on a timelike $r = r_c$ (constant) slice. We then show that the equations of {\it parallel transport} for an appropriately defined bulk velocity vector field along its own direction on this manifold when projected onto the flat timelike hypersurface requires the satisfaction of the incompressible NS equation in $(p+1)$-dimensions. Additionally, the incompressibility condition of the fluid arises from a vanishing expansion parameter $θ$, which is known to govern the convergence (or divergence) of a congruence of arbitrary timelike curves on a given manifold. In this approach Einstein's equations do not play any role and this can be regarded as an {\it off-shell} description of fluid-gravity correspondence. We argue that {\it our metric effectively encapsulates the information of forcing terms in the governing equations as if a free fluid is parallel transported on this curved background}. We finally discuss the implications of this interesting observation and its potentiality in helping us to understand hydrodynamical flows in a probable new setting.

hep-th↗

arXiv2019

How robust is the indistinguishability between quantum fluctuation seen from non-inertial frame and real thermal bath

We re-advocated the conjecture of indistinguishability between the quantum fluctuation observed from a Rindler frame and a real thermal bath, for the case of a free massless scalar field. To clarify the robustness and how far such is admissible, in this paper, we investigate the issue from two different non-inertial observers' perspective. A detailed analysis is being done to find the observable quantities as measured by two non-inertial observers (one is Rindler and another is uniformly rotating) on the real thermal bath and Rindler frame in Minkowski spacetime. More precisely, we compare Thermal-Rindler with Rindler-Rindler and Thermal-rotating with Rindler-rotating situations. In the first model it is observed that although some of the observables are equivalent, all the components of renormalised stress-tensor are not the same. In the later model, we again find that this equivalence is not totally guaranteed. Therefore we argue that the indistinguishability between the real thermal bath and the Rindler frame may not be totally true.

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arXiv2019

Abbott-Deser-Tekin like conserved quantities in Lanczos-Lovelock gravity: beyond Killing diffeomorphisms

We obtain the conserved Abbott-Deser-Tekin (ADT)-{\it like} current for the Lanczos-Lovelock gravity for a diffeomorphism vector, which defines the horizon of a spacetime and, importantly, is not necessarily a Killing vector. As the original ADT current is defined only for the presence of a background Killing vector, one cannot use it extensively for the thermodynamic description of the wide classes of non-Killing horizons which appear in gravity. On the other hand, this general approach can be utilized for those horizons. Here, the conserved current can be written as the derivative of the two-rank anti-symmetric potential, the connection of which is apparent with the conserved Noether potential from our analysis. If one assumes the diffeomorphism vector as the Killing one, the results match to the ADT case, whereas non-trivial result comes for the conformal Killing vectors and other horizon defining diffeomorphism vectors.

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arXiv2018

Fluid description of gravity on a timelike cut-off surface: beyond Navier-Stokes equation

Over the past few decades, a host of theoretical evidence have surfaced that suggest a connection between theories of gravity and Navier-Stokes (NS) equation of fluid dynamics. It emerges out that gravity theory can be treated as some kind of fluid on a particular surface. Motivated by the work carried out by Bredberg et al (JHEP 1207, 146 (2012)) \cite{Bredberg:2011jq}, our paper focuses on including certain modes to the metric which are consistent with the so called hydrodynamic scaling and discuss the consequences, one of which appear in the form of Damour Navier Stokes (DNS) equation with the incompressibility condition. We also present an alternative route to the results by considering the metric as a perturbative expansion in the hydrodynamic scaling parameter $ε$ and with a specific gauge choice, thus modifying the metric. It is observed that the inclusion of certain modes in the metric corresponds to the solution of Einstein's equations in presence of a particular type of matter in the spacetime. This analysis reveals that gravity has both the NS and DNS description not only on a null surface, but also on a timelike surface. So far we are aware of, this analysis is the first attempt to illuminate the possibility of presenting the gravity dual of DNS equation on a timelike surface. In addition, an equivalence between the hydrodynamic expansion and the near-horizon expansion has also been studied in the present context.

hep-th↗

arXiv2018

Universality class of alternative phase space and Van der Waals criticality

A new perspective toward thermodynamic phase space of Reisser-Nordstrom (RN) black holes in an anti-de-Sitter (AdS) spaces was recently proposed [Phys. Lett. B 768 (2017) 235], where the square of the electric charge $(Q^2)$ of black hole was regarded as a thermodynamic variable and the cosmological constant (pressure) as a fixed quantity. In this paper, we address the universality class and critical properties of any AdS black hole in this alternative phase space. We disclose the critical behavior of AdS black hole in the alternative phase space in which a continuous phase transition happens and in a very general framework, independent of the spacetime metric. Based on the expansion of the equation of state and Landau thermodynamic potential in the neighborhood of a critical point in the alternative phase space, we confirm that the set of values for critical exponents for generic black hole is analogous to the Van der Waals fluid system. Finally, we reveal that the scalar curvature in geometry thermodynamic diverges at the critical point of black hole. Our study shows that the approach here is powerful enough to investigate the critical behavior of any black holes and further supports the viability of the alternative viewpoint toward phase space of black holes suggested in [Phys. Lett. B 768 (2017) 235].

hep-th↗

arXiv2018

Presence of horizon makes particle motion chaotic

We analyze the motion of a {\it massless} and {\it chargeless} particle very near to the event horizon. It reveals that the radial motion has exponential growing nature which indicates that there is a possibility of inducing chaos in the particle motion of an integrable system when it comes under the influence of the horizon. This is being confirmed by investigating the Poincar$\acute{e}$ section of the trajectories with the introduction of a harmonic trap to confine the particle's motion. Two situations are investigated: (a) {\it any} static, spherically symmetric black hole and, (b) spacetime represents a stationary, axisymmetric black hole (e.g., Kerr metric). In both cases, the largest Lyapunov exponent has upper bound which is the surface gravity of the horizon. We find that the inclusion of rotation in the spacetime introduces more chaotic fluctuations in the system. The possible implications are finally discussed.

gr-qc↗

arXiv2018

Unruh-DeWitt detector in presence of multiple scalar fields : A Toy Model

Applications of Unruh-Fulling (UF) effect are well studied in literature via the interaction of Unruh-DeWitt (UD) detector and {\it single} scalar field. In this work, we investigate a toy model, where the detector is interacting {\it simultaneously} with the {\it multiple} scalar fields. Our study reveals that the transition rate of the system significantly depends on the acceleration of the detector and the number of scalar fields ($n$). For $n\gg1$, there exists a {\it critical acceleration}, beyond which the transition rate becomes drastically high than the accelerations below the critical point. The appearance of such critical point never occurs in case of the interaction of UD detector and {\it single} scalar field.

hep-th↗

arXiv2018

Noncommutative Heisenberg algebra in the neighbourhood of a generic null surface

We show that the diffeomorphisms, which preserve the null nature for a generic null metric very near to the null surface, provide {\it noncommutative} Heisenberg algebra. This is the generalization of the earlier work (Phys. Rev. D95, 044020 (2017)) \cite{Majhi:2017fua}, done for the Rindler horizon. The present analysis revels that the algebra is very general as it is obtained for a generic null surface and is applicable for any spacetime horizon. Finally using these results, the entropy of the null surface is derived in the form of the Cardy formula. Our analysis is completely {\it off-shell} as no equation of motion is used. We believe present discussion can illuminate the paradigm of `gravity as an emergent phenomenon' and could be a candidate to probe the origin of gravitational entropy.

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arXiv2018

Symmetries near a generic charged null surface and associated algebra: an off-shell analysis

To understand the underlying degrees of freedom, near horizon symmetry analysis of a black has gain significant interest in the recent past. In this paper we generalized those analysis first by taking into account a generic null surface carrying $U(1)$ electromagnetic charge. With the appropriate boundary conditions near the surface under study, we identified the symmetry algebra among the subset of diffeomporphism and gauge generators which preserve the metric of the null surface and the form of the gauge field configuration. With the knowledge of those symmetries we further derived the algebra among the associated charges considering general Lanczos-Lovelock gravity theory and gauge theory. Importantly while computing the charges we not only considered general theory, but also used off-shell formalism which is believed to play crucial role in understanding quantum gravity. Both the non-extremal and extremal cases are addressed here.

gr-qc↗

arXiv2018

Noether and Abbott-Deser-Tekin conserved quantities in scalar-tensor theory of gravity both in Jordan and Einstein frames

We revisit the thermodynamic aspects of the scalar-tensor theory of gravity in the Jordan and in the Einstein frame. Examining the {\it missing links} of this theory carefully, we establish the thermodynamic descriptions from the conserved currents and potentials by following both the Noether and the Abbott-Deser-Tekin (ADT) formalism. With the help of conserved Noether current and potential, we define the thermodynamic quantities, which we show to be {\it conformally invariant}. Moreover, the defined quantities are shown to fit nicely in the laws of (the first and the second) black hole thermodynamics formulated by the Wald's method. We stretch the study of the conformal equivalence of the physical quantities in these two frames by following the ADT formalism. Our further study reveals that there is a connection between the ADT and the Noether conserved quantities, which signifies that the ADT approach provide the equivalent thermodynamic description in the two frames as obtained in Noether prescription. Our whole analysis is very general as the conserved Noether and ADT currents and potentials are formulated {\it off-shell} and the analysis is exempted from any prior assumption or boundary condition.

gr-qc↗

arXiv2018

Fluctuation-dissipation in accelerated frames

An uniformly accelerated (Rindler) observer will detect particles in the Minkowski vacuum, known as Unruh effect. The spectrum is thermal and the temperature is given by that of the Killing horizon, which is proportional to the acceleration. Considering these particles are kept in a thermal bath with this temperature, we find that the correlation function of the random force due to radiation acting on the particles as measured by the accelerated frame, shows the fluctuation-dissipation relation. It is observed that the correlations, in both ($1+1$) spacetime and ($1+3$) dimensional spacetimes, are of Brownian type. We discuss the implications of this new observation at the end.

gr-qc↗

arXiv2018

Interior volume of ($1+D$) dimensional Schwarzschild black hole

We calculate the maximum interior volume, enclosed by the event horizon, of a ($1+D$)-dimensional Schwarzschild black hole. Taking into account the mass change due to Hawking radiation, we show that the volume increases towards the end of the evaporation. This fact is not new as it has been observed earlier for four dimensional case. The interesting point we observe is that this increase rate decreases towards the higher value of space dimensions $D$; i.e. it is a decelerated expansion of volume with the increase of spacial dimensions. This implies that for a sufficiently large $D$, the maximum interior volume does not change. The possible implications of these results are also discussed.

gr-qc↗

arXiv2017

Rainbow Rindler metric and Unruh effect

The energy of a particle moving on a spacetime, in principle, can affect the background metric. The modifications to it depend on the ratio of energy of the particle and the Planck energy, known as rainbow gravity. Here we find the explicit expressions for the coordinate transformations from rainbow Minkowski spacetime to accelerated frame. The corresponding metric is also obtained which we call as rainbow-Rindler metric. So far we are aware of, no body has done it in a concrete manner. Here this is found from the first principle and hence all the parameters are properly identified. The advantage of this is that the calculated Unruh temperature is compatible with the Hawking temperature of the rainbow black hole horizon, obtained earlier. Since the accelerated frame has several importance in revealing various properties of gravity, we believe that the present result will not only fill that gap, but also help to explore different aspects of rainbow gravity paradigm.

gr-qc↗

arXiv2017

Van der Waals criticality in AdS black holes: a phenomenological study

AdS black holes exhibit van der Waals type phase transition. In the {\it extended} phase-space formalism, the critical exponents for any spacetime metric are identical to the standard ones. Motivated by this fact, we give a general expression for the Helmholtz free energy near the critical point which correctly reproduces these exponents. The idea is similar to the Landau model which gives a phenomenological description of the usual second order phase transition. Here two main inputs are taken into account for the analysis: (a) black holes should have van der Waals like isotherms and (b) free energy can be expressed solely as a function of thermodynamic volume and horizon temperature. Resulting analysis shows that the form of Helmholtz free energy correctly encapsulates the features of Landau function. We also discuss the {\it isolated critical point} accompanied by nonstandard values of critical exponents. The whole formalism is then extended to other two criticalities, namely $Y-X$ and $T-S$ (based on the standard; i.e. non-extended phase-space), where $X$ and $Y$ are generalized force and displacement, whereas $T$ and $S$ are horizon temperature and entropy. We observe that in the former case Gibbs free energy plays the role of Landau function, whereas in the later case that role is played by the internal energy (here it is black hole mass). Our analysis shows that, although the existence of van der Waals phase transition depends on the explicit form of the black hole metric, the values of the critical exponents are universal in nature.

gr-qc↗

arXiv2017

P-V criticality of AdS black holes in a general framework

In black hole thermodynamics, it has been observed that AdS black holes behave as van der Waals system if one interprets the cosmological constant as a pressure term. Also the critical exponents for the phase transition of AdS black holes and the van der Waals systems are same. Till now this type of analysis is done by two steps. In the first step one shows that a particular metric allows phase transition and in the second step, using this information, one calculates the exponents. Here, we present a different approach based on two universal inputs (the general forms of the Smarr formula and the first law of thermodynamics) and one assumption regarding the existence of van der Waal like critical point for a metric. We find that the same values of the critical exponents can be obtained by this approach. Thus we demonstrate that, though the existence of van der Waal like phase transition depends on specific metrics, the values of critical exponents are then fixed for that set of metrics.

gr-qc↗

arXiv2017

Hawking evaporation cascade in presence of back reaction effect

We study the cascade of Hawking emission spectrum from the event horizon in presence of one loop back reaction effect in a black hole background. The spacetime is taken here is the modified Schwarzschild one. The analysis shows that it is possible to decrease the sparsity with the decrease in black hole mass. Moreover, at some particular value of mass one has a continuous radiation cascade. This result is completely new and quite different from the usual one. An estimation of the mass for continuous one is also found. We see that the value is of the Planck mass order. In this process it is observed that under a physical background, below a particular value of the mass the Hawking radiation must stop and we have a remnant. This was absent in the earlier analysis.

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