Abstract
The thermodynamic formalism for rotating black holes, characterized by noncommutative and quantum corrections, is constructed. From a fundamental thermodynamic relation, the equations of state and thermodynamic response functions are explicitly given, and the effect of noncommutativity and quantum correction is discussed. It is shown that the well-known divergence exhibited in specific heat is not removed by any of these corrections. However, regions of thermodynamic stability are affected by noncommutativity, increasing the available states for which some thermodynamic stability conditions are satisfied.
Highlights
It is known that the classical thermodynamics formalism can be applied to explore the physical entropy of a black hole, using semiclassical approaches to general relativity
Response functions contain valuable information about the thermodynamic behavior of systems; this topic must be addressed in order to study the changes, if any, introduced to black hole thermodynamic properties by noncommutativity and quantum correction to its entropy
Equations [32] are completely analogous to their magnetic counterparts [18]. And following this resemblance with magnetic systems, thermodynamic response functions are defined in this work without any weight factor except for heat capacities, defined with such a factor given by the inverse of temperature
Summary
It is known that the classical thermodynamics formalism can be applied to explore the physical entropy of a black hole, using semiclassical approaches to general relativity. Starting from the fact that Equation (14) is correct, whatever be the expression for the non-approximated entropy for the quantum noncommutative Kerr black hole, it is clear that our proposed entropy will be a good approximation for small values of J when compared to the values of U 2 In this approximation in the vicinity of small values of angular momentum, the coordinates of the minisuperspace, namely λ and γ, are the same as in the Schwarzschild case. Equation (15) will be assumed as a fundamental thermodynamic relation for Kerr black holes when noncommutative and quantum corrections are considered It is well known from classical thermodynamics that fundamental thermodynamic relations contain all thermodynamic information of the system under study [31]; as a consequence, modifications on thermodynamic information originated by the introduced corrections to entropy are carried through all thermodynamic quantities.
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