Abstract
We consider the thermodynamic and stability problem of Kerr black holes arising from the nonextensive/nonadditive nature of the Bekenstein–Hawking entropy formula. Nonadditive thermodynamics is often criticized by asserting that the zeroth law cannot be compatible with nonadditive composition rules, so in this work we follow the so-called formal logarithm method to derive an additive entropy function for Kerr black holes also satisfying the zeroth law’s requirement. Starting from the most general, equilibrium compatible, nonadditive entropy composition rule of Abe, we consider the simplest non-parametric approach that is generated by the explicit nonadditive form of the Bekenstein–Hawking formula. This analysis extends our previous results on the Schwarzschild case, and shows that the zeroth law-compatible temperature function in the model is independent of the mass–energy parameter of the black hole. By applying the Poincaré turning point method, we also study the thermodynamic stability problem in the system.
Highlights
After the finding of the Kerr solution [1], the mathematical and physical properties of the corresponding black hole spacetimes have been widely investigated
In a recent paper [17], we investigated the thermodynamic and stability problem of a Schwarzschild black hole by considering the nonadditive entropy composition rule that is emerging from the Bekenstein–Hawking description
Can describe the Kerr solution, where we have fixed the overall factor of S to reproduce the Schwarzschild result (14) in the a → 0 limit. Comparing this result with the mass–energy parameter of the black hole (19), we can conclude that the new equilibrium- and zeroth law-compatible entropy function of Kerr black holes obtained by the formal logarithm method based on the nonadditive and non-parametric approach arising from the Bekenstein–Hawking model is the same linear function of the energy
Summary
Multidisciplinary Center for Astrophysics & Department of Physics, Instituto Superior Técnico, University of Lisbon, Avenida Rovisco Pais 1, 1049-001 Lisboa, Portugal. Received: 17 December 2016; Accepted: 14 February 2017; Published: 16 February 2017
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