Quantum gravitational corrections to the entropy of a Reissner–Nordström black hole

Abstract

Starting from an effective action for quantum gravity, we calculate the quantum gravitational corrections to the Wald entropy of a four dimensional non-extremal Reissner–Nordström (RN) black hole in the limit of small electric charge, generalising a previous calculation carried out by Calmet and Kuipers (Phys Rev D 104(6):066012, 2021) for a Schwarzschild black hole. We show that, at second order in the Ricci curvature, the RN metric receives quantum corrections which shift the classical position of the event horizon. We apply the Wald entropy formula by integrating over the perimeter of the quantum corrected event horizon. We then compute the quantum gravitational corrections to the temperature and the pressure of the black hole.

Noncommutative Correction to the Entropy of Charged BTZ Black Hole

“…One of the simplest ways to achieve this was presented a long time ago by 't Hooft [6,7] using the so-called brick wall method. Alongside the brick wall method, the BH entropy can be described using the entanglement of the degrees of freedom between the two sides of the horizon [80,81] and by using the Wald entropy formula within the effective field theory approach to quantum gravity [21,22,82]. It has been shown [19,83] that all three approaches are related due to the fact that all of them have an almost identical UV divergence of the BH entropy.…”

“…Later, it was argued that the origin of BH entropy is rooted in the statistical mechanics of in-falling particles [5] after a proper regularization of the UV divergence [6,7]. There are many approaches (string theory [8][9][10], quantum geometry [11], conformal field theory [12][13][14][15][16], AdS/CFT duality [17], effective field theory [18][19][20][21][22] and noncommutative geometry [23][24][25], to name a few) toward quantum gravity in which the entropy of BHs coincides with the Bekenstein-Hawking area law in the leading order.…”