Black holes are exotic thermodynamic systems where the entropy scales with the area rather than volume. This brings in interesting features such as non-extensivity, i.e., the black hole entropy does not scale linearly with the energy content of the spacetime. However, a strong analogy between the thermodynamics of black holes and that of hydrostatic systems (such as the van der Waals' fluid) exists, including the presence of phase transitions and the appearance of the mean-field critical exponents.
The fact that black holes should have an entropy (otherwise, the second law of thermodynamics would be violated) brings in a fascinating motivation towards quantum gravity -- because of the no-hair theorem, the microscopic origin of the black hole entropy can only be explained by counting the states associated with the degrees of freedom of quantum gravity. One of the great feats of string theory is the exact determination of the black hole entropy via microscopic counting of states, with the final result being in agreement with the macroscopic result expected from semiclassical black hole thermodynamics. An intriguing feature of the black hole entropy is its scaling with the area (not volume) which can now be understood via the holographic principle, the best known example of which is the AdS/CFT correspondence in which gravity is formulated in anti-de Sitter (AdS) spacetimes that are Lorentzian spacetimes with negative curvature.
Thermodynamic features of black holes become all-the-more interesting in AdS spacetimes in which intriguing phase structures emerge. A further development in which the cosmological constant of the AdS spacetime is taken to vary and is interpreted as a pressure brings in further interesting features -- one observes the emergence of fluid-like critical behavior, triple points, re-entrant phase transitions, etc.
During my stint as a graduate student in IIT Bhubaneswar, I and my coworkers (including my thesis advisor) spent a great deal of time trying to understand fluctuation properties of black holes in AdS spacetimes within frameworks where the cosmological constant is regarded as a pressure. From the viewpoint of the geometrical approach to thermodynamics, spaces of equilibrium states within the thermodynamic phase space can be associated with the notion of metric structures whose curvature properties are believed to encode some empirical information about the nature of microscopic interactions of the system, and therefore may reveal early insights into the microscopics of black holes. In a series of papers [1-4], we made several such explorations in which we computed explicitly the scalar curvatures of the spaces of equilbrium states of black holes in different gravity theories and analyzed how the curvature varies as a function of different thermodynamic variables, possibly revealing insights into an effective microscopic description of the black hole thermodynamics; an equipartition theorem akin to hydrostatic systems was reported by us in [5]. The general framework that we developed and employed was later presented in the review paper [6].
As a part of my PhD thesis, I worked on computing logarithmic corrections to the entropy of black holes in AdS spacetimes within frameworks where the cosmological constant is regarded as a pressure. In fact, we were the first to apply the framework of fixed-pressure ensembles to compute corrections to the black hole entropy, the preliminary results of which were reported in [7,8], and then later refined in [9,10] wherein the AdS/CFT correspondence was taken as a benchmark to validate the corrections.
I was also a part of two short investigations on the area quantization (as advanced by Bekenstein in the 70s), one involving the pseudo-Hermitian representation of the black hole area [11] and the other in which we showed that under a certain area spacing between consecutive levels of the area spectrum, Hawking radiation occuring as transitions between the levels saturates Landauer's principle from information theory [12]. In both of the studies, logarithmic corrections due to quantum effects were computed.
Collaborators:
1) Chandrasekhar Bhamidipati (IIT-BBS)
2) Sudipta Mukherji (IOPB)
3) Bijan Bagchi (Brainware University)
5) Sauvik Sen (Shiv Nadar University)
6) Sandip Mahish (IIT-BBS)
7) Aditya Singh (IIT-BBS)
Related publications:
[1] A. Ghosh and C. Bhamidipati, Phys. Rev. D 101, 046005 (2020) [arXiv].
[2] A. Ghosh and C. Bhamidipati, Phys. Rev. D 101, 106007 (2020) [arXiv].
[3] S. Mahish, A. Ghosh, and C. Bhamidipati, Phys. Lett. B 811, 135958 (2020) [arXiv].
[4] A. Singh, A. Ghosh, and C. Bhamidipati, Front. Phys. 9, 631471 (2021) [arXiv].
[5] A. Ghosh and C. Bhamidipati, Proceedings of the XXV DAE-BRNS High Energy Physics (HEP) Symposium 2022.
[6] A. Ghosh and C. Bhamidipati, Front. Phys. 11, 1132712 (2023) [arXiv].
[7] A. Ghosh, S. Mukherji, and C. Bhamidipati, Class. Quant. Grav. 39, 225011 (2022) [arXiv].
[8] A. Ghosh, S. Mukherji, and C. Bhamidipati, Nucl. Phys. B 982, 115902 (2022) [arXiv].
[9] A. Ghosh, Class. Quant. Grav. 40, 155013 (2023) [arXiv].
[10] A. Ghosh, C. Bhamidipati, and S. Mukherji, arXiv:2207.02820.
[11] B. Bagchi, A. Ghosh, and S. Sen, Grav. Cosm. 30, 481 (2024) [arXiv].
[12] B. Bagchi, A. Ghosh, and S. Sen, Gen. Relativ. Gravit. 56, 108 (2024) [arXiv].