arXiv subjects

Abhishek Majhi

Publications and source records attributed to Abhishek Majhi.

25 records · Page 2Linked to original sources

arXiv2015

Black Hole Entropy from indistinguishable quantum geometric excitations

In loop quantum gravity, the quantum geometry of a black hole horizon consist of discrete non-perturbative quantum geometric excitations (or punctures) labeled by spins, which are responsible for the quantum area of the horizon. If these punctures are compared to a gas of particles, then the spins associated with the punctures can be viewed as single puncture area levels analogous to single particle energy levels. Consequently, if we {\it assume} these punctures to be {\it indistinguishable}, the microstate count for the horizon resembles that of Bose-Einstein counting formula for gas of particles. For the Bekenstein-Hawking area law(BHAL) to follow from the entropy calculation in the large area limit, the Barbero-Immirzi parameter($\g$) approximately takes a constant value.

gr-qc↗

arXiv2014

Quantum Hairs and Entropy of Quantum Isolated Horizon from Chern-Simons Theory

We articulate the fact that the loop quantum gravity description of the quantum macrostates of black hole horizons, modeled as Quantum Isolated Horizons (QIHs), is completely characterized in terms of two independent integer-valued `quantum hairs', viz,. the coupling constant $(k)$ of the quantum $SU(2)$ Chern-Simons theory describing QIH dynamics, and the number of punctures $(N)$ produced by the bulk spin network edges piercing the isolated horizon (which act as pointlike sources for the Chern- Simons fields). We demonstrate that the microcanonical entropy of macroscopic (both parameters assuming very large values) QIHs can be obtained directly from the microstates of this Chern-Simons theory, using standard statistical mechanical methods, without having to additionally postulate the horizon as an ideal gas of punctures, or incorporate any additional classical or semi-classical input from general relativity vis-a-vis the functional dependence of the IH mass on its area, or indeed, without having to restrict to any special class of spins. Requiring the validity of the Bekenstein-Hawking area law relates these two parameters (as an equilibrium `equation of state') and consequently allows the Barbero-Immirzi parameter to take any real and positive value depending on the value of $k/N$. The logarithmic correction to the area law obtained a decade ago by R. Kaul and one of us (P.M.), ensues straightforwardly, with precisely the coefficient -3/2, making it a signature of the loop quantum gravity approach to black hole entropy.

gr-qc↗

arXiv2014

Thermodynamics of Quantum Isolated Horizons with model Hamiltonians

Following a recent proposal, we consider the most general structure possible for the Hamiltonian operator associated with the Quantum Isolated Horizon(QIH) with explanations of the underlying physical motivations. An extensive thermodynamic analysis with this model Hamiltonian is presented. Considering {\it fixed} number of punctures, the canonical partition function can now be written in the usual energy ensemble. Arguing that the known classical results must follow in the correspondence limit (viz. the equilibrium temperature as observed by a local observer) the model is fixed, yielding the energy spectrum of the QIH.

gr-qc↗

arXiv2014

The Microcanonical Entropy of Quantum Isolated Horizon, `quantum hair' $N$ and the Barbero-Immirzi parameter fixation

{\it If} the total number of punctures($N$) of a quantum isolated horizon is considered to be a macroscopic parameter alongside the Chern-Simons level($k$) or equivalently classical area$(A_{cl})$ a strict analysis of the {\it microcanonical} ensemble reveals that the {\it microcanonical} entropy has the form $S_{MC}=A_{cl}/4\ell_p^2+Nσ(γ)$, only for values of the Barbero-Immirzi(BI) parameter$(γ)$ greater than a certain number. It is argued that the term $Nσ(γ)$ must be negative definite, which leads to the bound on the BI parameter.

gr-qc↗

arXiv2013

Comment on `Black hole entropy and isolated horizon thermodynamics'

There is a deep underlying problem in the model dependent thermodynamic analysis of black holes shown in the above quoted paper. In this method one can only find out the canonical entropy of the black hole but not the `microcanonical' entropy. Besides this crucial issue a few other problems are also discussed.

gr-qc↗

arXiv2013

Stability of Quantum Isolated Horizon : A Local Observer's View

It is shown that a Quantum Isolated Horizon(QIH), as observed by a local observer, is locally unstable as a thermodynamic system. The result is derived in two different ways. Firstly, the specific heat of the QIH is shown to be negative definite through a quantum statistical analysis. Then, it is shown, in the thermal holographic approach, that the canonical partition function of the QIH diverges under Gaussian thermal fluctuations of such energy spectrum, implying local instability of such a QIH as a thermodynamic system.

gr-qc↗

arXiv2012

Charged Quantum Black Holes : Thermal Stability Criterion

A criterion of thermal stability is derived for electrically charged quantum} black holes having large horizon area (compared to Planck area), as an inequality between the mass of the black hole and its microcanonical entropy. The derivation is based on key results of Loop Quantum Gravity and equilibrium statistical mechanics of a grand canonical ensemble, with Gaussian fluctuations around an equilibrium thermal configuration assumed here to be a quantum isolated horizon. No aspect of classical black hole geometry is used to deduce the stability criterion. Since, no particular form of the mass function is used a priori, our stability criterion provides a platform to test the thermal stability of a black hole with a given mass function. The mass functions of the two most familiar charged black hole solutions are tested as a fiducial check. We also discuss the validity of the saddle point approximation used to incorporate thermal fluctuations. Moreover, the equilibrium Hawking temperature is shown to have an additional quantum correction over the semiclassical value.

gr-qc↗