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1. The statistical mechanics of near-BPS black holes

   https://doi.org/10.1088/1751-8121/ac3be9  

   Heydeman, Matthew; Iliesiu, Luca V; Turiaci, Gustavo J; Zhao, Wenli (December 2021, Journal of Physics A: Mathematical and Theoretical)

   Abstract Due to the failure of thermodynamics for low temperature near-extremal black holes, it has long been conjectured that a ‘thermodynamic mass gap’ exists between an extremal black hole and the lightest near-extremal state. For non-supersymmetric near-extremal black holes in Einstein gravity with an AdS 2 throat, no such gap was found. Rather, at that energy scale, the spectrum exhibits a continuum of states, up to non-perturbative corrections. In this paper, we compute the partition function of near-BPS black holes in supergravity where the emergent, broken, symmetry is PSU (1, 1|2). To reliably compute this partition function, we show that the gravitational path integral can be reduced to that of a N = 4 supersymmetric extension of the Schwarzian theory, which we define and exactly quantize. In contrast to the non-supersymmetric case, we find that black holes in supergravity have a mass gap and a large extremal black hole degeneracy consistent with the Bekenstein–Hawking area. Our results verify a plethora of string theory conjectures, concerning the scale of the mass gap and the counting of extremal micro-states. 

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2. Thermodynamics of the near-extremal Kerr spacetime

   https://doi.org/10.1007/JHEP06(2024)011  

   Rakic, Ilija; Rangamani, Mukund; Turiaci, Gustavo J (June 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> We examine the thermodynamics of a near-extremal Kerr black hole, and demonstrate that the geometry behaves as an ordinary quantum system with a vanishingly small degeneracy at low temperatures. This is in contrast with the classical analysis, which instead predicts a macroscopic entropy for the extremal Kerr black hole. Our results follow from a careful analysis of the gravitational path integral. Specifically, the low temperature canonical partition function behaves as$$ Z\sim {T}^{\frac{3}{2}}\ {e}^{S_0+c\log {S}_0} $$ $Z\sim T^{\frac{3}{2}}{e}^{S_0+clog{S}_0}$, withS₀the classical degeneracy andca numerical coefficient we compute. This is in line with the general expectations for non-supersymmetric near-extremal black hole thermodynamics, as has been clarified in the recent past, although cases without spherical symmetry have not yet been fully analyzed until now. We also point out some curious features relating to the rotational zero modes of the near-extremal Kerr black hole background that affects the coefficientc. This raises a puzzle when considering similar black holes in string theory. Our results generalize to other rotating black holes, as we briefly exemplify. 

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3. Spin-refined partition functions and $$ \mathcal{CRT} $$ black holes

   https://doi.org/10.1007/JHEP12(2024)013  

   Grabovsky, David; Kolanowski, Maciej (December 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> We investigate spin-refined partition functions in AdS/CFT using Euclidean gravitational path integrals. We construct phase diagrams forZ_X= Tr(e^−βHX) in various dimensions and for different choices of discrete isometryX, discovering rich structures at finite temperature. WhenXis a reflection,Z_Xcounts the difference between the number of even- and odd-spin microstates. The high-temperature regime is universally dominated by$$ \mathcal{CRT} $$ $\mathrm{CRT}$-twisted black holes in any dimension, and in odd spacetime dimensions we examine whether complex rotating black hole solutions can contribute to spin-refined observables or potentially dominate at finite temperature. We also analyze the microcanonical ensemble. There the leading contribution almost always comes from rotating black holes, showing that the two ensembles are not necessarily equivalent. 

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4. Null states and time evolution in a toy model of black hole dynamics

   https://doi.org/10.1007/JHEP08(2024)199  

   Dong, Xi; Kolanowski, Maciej; Liu, Xiaoyi; Marolf, Donald; Wang, Zhencheng (August 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> Spacetime wormholes can provide non-perturbative contributions to the gravitational path integral that make the actual number of statese^Sin a gravitational system much smaller than the number of states$$ {e}^{S_{\textrm{p}}} $$ $e^{S_p}$predicted by perturbative semiclassical effective field theory. The effects on the physics of the system are naturally profound in contexts in which the perturbative description actively involvesN=O(e^S) of the possible$$ {e}^{S_{\textrm{p}}} $$ $e^{S_p}$perturbative states; e.g., in late stages of black hole evaporation. Such contexts are typically associated with the existence of non-trivial quantum extremal surfaces. However, by forcing a simple topological gravity model to evolve in time, we find that such effects can also have large impact forN≪e^S(in which case no quantum extremal surfaces can arise). In particular, even for smallN, the insertion of generic operators into the path integral can cause the non-perturbative time evolution to differ dramatically from perturbative expectations. On the other hand, this discrepancy is small for the special case where the inserted operators are non-trivial only in a subspace of dimensionD≪e^S. We thus study this latter case in detail. We also discuss potential implications for more realistic gravitational systems. 

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5. Black hole wavefunctions and microcanonical states

   https://doi.org/10.1007/JHEP06(2024)054  

   Chua, Wan Zhen; Hartman, Thomas (June 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> We consider the problem of defining a microcanonical thermofield double state at fixed energy and angular momentum from the gravitational path integral. A semiclassical approximation to this state is obtained by imposing a mixed boundary condition on an initial time surface. We analyze the corresponding boundary value problem and gravitational action. The overlap of this state with the canonical thermofield double state, which is interpreted as the Hartle-Hawking wavefunction of an eternal black hole in a mini-superspace approximation, is calculated semiclassically. The relevant saddlepoint is a higher-dimensional, rotating generalization of the wedge geometry that has been studied in two-dimensional gravity. Along the way we discuss a new corner term in the gravitational action that arises at a rotating horizon. 

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