Geometric and topological corrections to Schwarzschild black hole
arxiv(2024)
摘要
In this paper, we compute departures in the black hole thermodynamics induced
by either geometric or topological corrections to general relativity.
Specifically, we analyze the spherically symmetric spacetime solutions of two
modified gravity scenarios with Lagrangians ℒ∼ R^1+ϵ
and ℒ∼ R+ϵ 𝒢^2, where 𝒢 is the
Euler density in four dimensions, while 0<ϵ≪ 1 measures the
perturbation around the Hilbert-Einstein action. Accordingly, we find the
expressions of the Bekenstein-Hawking entropy by the Penrose formula, and the
black hole temperature and horizon of the obtained solutions. We then
investigate the heat capacities in terms of the free parameters of the theories
under study. In doing so, we show that healing the problem of negative heat
capacities can be possible under particular choices of the free constants,
albeit with limitations on the masses allowed for the black hole solutions.
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