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Register a new userOn the equipartition theorem and black holes nongaussian entropies
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In this Letter we have shown that, from the standard thermodynamic functions, the mathematical form of an equipartition theorem may be related to the algebraic expression of a particular entropy initially chosen to describe the black hole thermodynamics. Namely, we have different equipartition expressions for distinct statistics. To this end, four different mathematical expressions for the entropy have been selected to demonstrate our objective. Furthermore, a possible phase transition is observed in the heat capacity behavior of the Tsallis and Cirto entropy model.
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The Barrow entropy appears from the fact that the black hole surface can be modified due to quantum gravitational outcome. The measure of this perturbation is given by a new exponent $Delta$. In this letter we have shown that, from the standard mathematical form of the equipartition theorem, we can relate it with Barrow entropy. From this equivalence, we have calculated precisely the value of the exponent for the equipartition law. After that, we tested the thermodynamical coherence of the system by calculating the heat capacity which established an interval of the possible thermodynamical coherent values of Barrow entropic exponent and corroborated our first result.
Bopp-Podolsky electrodynamics is generalized to curved space-times. The equations of motion are written for the case of static spherically symmetric black holes and their exterior solutions are analyzed using Bekensteins method. It is shown the solutions split-up into two parts, namely a non-homogeneous (asymptotically massless) regime and a homogeneous (asymptotically massive) sector which is null outside the event horizon. In addition, in the simplest approach to Bopp-Podolsky black holes, the non-homogeneous solutions are found to be Maxwells solutions leading to a Reissner-Nordstrom black hole. It is also demonstrated that the only exterior solution consistent with the weak and null energy conditions is the Maxwells one. Thus, in light of energy conditions, it is concluded that only Maxwell modes propagate outside the horizon and, therefore, the no-hair theorem is satisfied in the case of Bopp-Podolsky fields in spherically symmetric space-times.
All known stationary black hole solutions in higher dimensions possess additional rotational symmetries in addition to the stationary Killing field. Also, for all known stationary solutions, the event horizon is a Killing horizon, and the surface gravity is constant. In the case of non-degenerate horizons (non-extremal black holes), a general theorem was previously established [gr-qc/0605106] proving that these statements are in fact generally true under the assumption that the spacetime is analytic, and that the metric satisfies Einsteins equation. Here, we extend the analysis to the case of degenerate (extremal) black holes. It is shown that the theorem still holds true if the vector of angular velocities of the horizon satisfies a certain diophantine condition, which holds except for a set of measure zero.
We prove a uniqueness theorem for stationary $D$-dimensional Kaluza-Klein black holes with $D-2$ Killing fields, generating the symmetry group ${mathbb R} times U(1)^{D-3}$. It is shown that the topology and metric of such black holes is uniquely determined by the angular momenta and certain other invariants consisting of a number of real moduli, as well as integer vectors subject to certain constraints.
Recent results of arXiv:1907.08788 on universal black holes in $d$ dimensions are summarized. These are static metrics with an isotropy-irreducible homogeneous base space which can be consistently employed to construct solutions to virtually any metric theory of gravity in vacuum.
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