In this letter, we give two proposals regarding the status of connectivity of entanglement wedges and the associated saturation of mutual information. The first proposal has been given for the scenario before the Page time depicting the fact that the early to late time transition can be obtained from the status of the radiation entanglement wedge. In particular, we compute the time where the mutual information between the regions where the Hawking radiation gets collected vanishes before the formation of the island. We argue that this time is the Hartman-Maldacena time at which the fine-grained entropy of radiation goes as ∼ log(β) where β is the inverse of Hawking temperature of the black hole. On the other hand, the second proposal probes the crucial role played by the mutual information of black hole subsystems in obtaining the correct Page curve of radiation.
We have investigated the black hole thermodynamics and the phase transition for renormalized group improved asymptotically safe Schwarzschild black hole. This geometry takes into account the quantum gravitational correction in the running gravitational constant identifying G(r) ≡ G(k = k(r)). We studied various thermodynamic quantity like the Hawking temperature, specific heat and entropy for the general parameter γ for quantum corrected Schwarzschild metric. We have noticed that the coefficient of the leading quantum correction, that is, the logarithmic correction gets affected by the presence of γ. We further study the local temperature, thermal stability of the black hole and the free energy considering a cavity enclosing the black hole. According to the local specific heat, there exists three black hole states, among them the large and tiny black hole are thermally stable states. We further investigate the on-shell free energy and find that no Hawking-Page phase transition occurs here unlike the ordinary Schwarzschild black hole. The black hole state always prevails for all temperatures. Also, we have found two critical points, T c1 and T c2 , corresponding to the phase transition from one black hole state to another.
In this work we investigate the phenomena of acceleration radiation for a two-level atom falling into the event horizon of a Kerr-Newman black hole. In (Phys. Rev. D 104 (2021) 065006), it has been shown that conformal quantum mechanics has a connection to the generated Planck-like spectrum due to acceleration radiation. In this particular aspect, the near horizon approximation played a significant role. In Phys. Rev. D 106 (2022) 025004, we have used the beyond near horizon approximation to show that the excitation probability attains a Planck-like spectrum irrespective of the non-existence of an underlying conformal symmetry for a general class of static spherically symmetric black holes. In our analysis we have gone beyond the near horizon approximation for the rotating and charged case and even without the consideration of the conformal symmetry we observe a similar Planck-like spectrum. However, the coefficient of the spectrum is significantly different from the near horizon case. We have then considered a different scenario where a two-level atom emits multiple photons while freely falling into the event horizon of the Kerr-Newman black hole. It is observed that the Planck factor in the excitation probability is significantly small than that of the case of single-photon emission (for large number of simultaneously emitted photons from the two-level atom). Finally, we have computed the von-Neumann entropy which is also known as the horizon brightened acceleration radiation entropy or the HBAR entropy. We have carried out our analysis for a scalar field only to see the effect of the charge and rotation of the black hole in this particular scenario.
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