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Register a new userBarrows black hole entropy and the equipartition theorem
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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.
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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.
If general relativity is spontaneously induced, the black hole limit is governed by a phase transition which occurs precisely at the would have been horizon. The exterior Schwarzschild solution then connects with a novel core of vanishing spatial volume. The Kruskal structure, admitting the exact Hawking imaginary time periodicity, is recovered, with the conic defect defused at the origin, rather than at the horizon. The entropy stored inside textbf{any} interior sphere is universal, equal to a quarter of its surface area, thus locally saturating the t Hooft-Susskind holographic bound. The associated Komar mass and material energy functions are non-singular.
We review aspects of the thermodynamics of black holes and in particular take into account the fact that the quantum entanglement between the degrees of freedom of a scalar field, traced inside the event horizon, can be the origin of black hole entropy. The main reason behind such a plausibility is that the well-known Bekenstein-Hawking entropy-area proportionality -- the so-called `area law of black hole physics -- holds for entanglement entropy as well, provided the scalar field is in its ground state, or in other minimum uncertainty states, such as a generic coherent state or squeezed state. However, when the field is either in an excited state or in a state which is a superposition of ground and excited states, a power-law correction to the area law is shown to exist. Such a correction term falls off with increasing area, so that eventually the area law is recovered for large enough horizon area. On ascertaining the location of the microscopic degrees of freedom that lead to the entanglement entropy of black holes, it is found that although the degrees of freedom close to the horizon contribute most to the total entropy, the contributions from those that are far from the horizon are more significant for excited/superposed states than for the ground state. Thus, the deviations from the area law for excited/superposed states may, in a way, be attributed to the far-away degrees of freedom. Finally, taking the scalar field (which is traced over) to be massive, we explore the changes on the area law due to the mass. Although most of our computations are done in flat space-time with a hypothetical spherical region, considered to be the analogue of the horizon, we show that our results hold as well in curved space-times representing static asymptotically flat spherical black holes with single horizon.
In this article we compute the black hole entropy by finding a classical central charge of the Virasoro algebra of a Liouville theory using the Cardy formula. This is done by performing a dimensional reduction of the Einstein Hilbert action with the ansatz of spherical symmetry and writing the metric in conformally flat form. We obtain two coupled field equations. Using the near horizon approximation the field equation for the conformal factor decouples. The one concerning the conformal factor is a Liouville equation, it posses the symmetry induced by a Virasoro algebra. We argue that it describes the microstates of the black hole, namely the generators of this symmetry do not change the thermodynamical properties of the black hole.
In this work we derive a generalized Newtonian gravitational force and show that it can account for the anomalous galactic rotation curves. We derive the entropy-area relationship applying the Feynman-Hibbs procedure to the supersymmetric Wheeler-DeWitt equation of the Schwarzschild black hole. We obtain the modifications to the Newtonian gravitational force from the entropic formulation of gravity.
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