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Register a new userEntropy in the interior of a Kerr black hole
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Christodoulou and Rovelli have shown that the maximal interior volume of a Schwarzschild black hole linearly grows with time. Recently, their conclusion has been extended to the Reissner{-}Nordstr$ddot{text{o}}$m and Kerr black holes. Meanwhile, the entropy of interior volume in a Schwarzschild black hole has also been calculated. Here, a new method calculating the entropy of interior volume of the black hole is given and it can be used in more general cases. Using this method, the entropy associated with the volume of a Kerr black hole is calculated and it is found that the entropy is proportional to the Bekenstein-Hawking entropy in the early stage of black hole evaporation. Using the differential form, the entropy of interior volume in a Schwarzschild black hole is recalculated. It is shown that the proportionality coefficient between the entropy and the Bekenstein-Hawking entropy is half of that given in the previous literature. Moreover, the black hole information paradox is brought up again and discussed.
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The investigation about the volume of a black hole is closely related to the quantum nature of the black hole. The entropy is a significant concept for this. A recent work by Majhi and Samanta [Phys. Lett. B 770 (2017) 314] after us presented a similar conclusion that the entropy associated with the volume is proportional to the surface area of the black hole, but the proportionality coefficient is different from our earlier result. In this paper, we clarify the difference and show that their calculation is unrelated to the interior of the black hole.
Based on the consideration that the black hole horizon and the cosmological horizon of Kerr-de Sitter black hole are not independent each other, we conjecture the total entropy of the system should have an extra term contributed from the correlations between the two horizons, except for the sum of the two horizon entropies. By employing globally effective first law and effective thermodynamic quantities, we obtain the corrected total entropy and find that the region of stable state for kerr-de Sitter is related to the angular velocity parameter $a$, i.e., the region of stable state becomes bigger as the rotating parameters $a$ is increases.
We study the interior of a Reissner-Nordstrom Black-Hole (RNBH) using Relativistic Quantum Geometry, which was introduced in some previous works. We found discrete energy levels for a scalar field from a polynomial condition for the Heun Confluent functions expanded around the effective causal radius $r_*$. From the solutions it is obtained that the uncertainty principle is valid for each energy level of space-time, in the form: $E_n, r_{*,n}=hbar/2$, and the charged mass is discretized and distributed in a finite number of states. The classical RNBH entropy is recovered as the limit case where the number of states is very large, and the RNBH quantum temperature depends on the number of states in the interior of the RNBH. This temperature, depending of the number of states of the RNBH, is related with the Bekeinstein-Hawking (BH) temperature: $T_{BH} leq T_{N} < 2,T_{BH}$.
We find strong numerical evidence for a new phenomenon in a binary black hole spacetime, namely the merger of marginally outer trapped surfaces (MOTSs). By simulating the head-on collision of two non-spinning unequal mass black holes, we observe that the MOTS associated with the final black hole merges with the two initially disjoint surfaces corresponding to the two initial black holes. This yields a connected sequence of MOTSs interpolating between the initial and final state all the way through the non-linear binary black hole merger process. In addition, we show the existence of a MOTS with self-intersections formed immediately after the merger. This scenario now allows us to track physical quantities (such as mass, angular momentum, higher multipoles, and fluxes) across the merger, which can be potentially compared with the gravitational wave signal in the wave-zone, and with observations by gravitational wave detectors. This also suggests a possibility of proving the Penrose inequality mathematically for generic astrophysical binary back hole configurations.
The spacetime in the interior of a black hole can be described by an homogeneous line element, for which the Einstein--Hilbert action reduces to a one-dimensional mechanical model. We have shown in [SciPost Phys. 10, 022 (2021), [2010.07059]] that this model exhibits a symmetry under the $(2+1)$-dimensional Poincare group. Here we explain how this can be understood as a broken infinite-dimensional BMS$_3$ symmetry. This is done by reinterpreting the action for the model as a geometric action for BMS$_3$, where the configuration space variables are elements of the algebra $mathfrak{bms}_3$ and the equations of motion transform as coadjoint vectors. The Poincare subgroup then arises as the stabilizer of the vacuum orbit. This symmetry breaking is analogous to what happens with the Schwarzian action in AdS$_2$ JT gravity, although in the present case there is no direct interpretation in terms of boundary symmetries. This observation, together with the fact that other lower-dimensional gravitational models (such as the BTZ black hole) possess the same broken BMS$_3$ symmetries, provides yet another illustration of the ubiquitous role played by this group.
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