Exponential Corrections to Black Hole Entropy

Quantum corrections to the thermodynamics of black branes

“…Even though it is not known how such non-perturbative quantum corrections can be explicitly obtained, it is known that they would modify the relation between the area and entropy of black branes. In fact, the perturbative [25][26][27][28] and non-perturbative [31,32] corrections to the relation between area and entropy for any black object have the same functional dependence on the original area and temperature of that black object.…”

“…where α and λ are constants. Furthermore, it has been argued that the non-perturbative correction to the relation between area and entropy is given by [31,32] S c,non-per = ηe − A 4G .…”

“…perturbative [25][26][27][28] and non-perturbative [31,32] quantum corrections to the entropy of any black object is a well defined function of the original area. In fact, as this functional form of the corrected entropy is known it can be used to analyze the quantum corrections to the stability of black branes, without explicitly calculating the corrections to the low energy effective action.…”

“…However, when the size of the black hole is close to the Planck scale, nonperturbative corrections become important, and cannot be neglected. It has been proposed that such non-perturbative corrections can be expressed as the exponential function of the original entropy, for any black object [31]. Such non-perturbative exponential corrections have also been obtained using Kloosterman sums [32].…”

“…These corrections are obtained using AdS/CFT correspondence for massless supergravity fields near the horizon [33,34]. So, these non-perturbative corrections [31,32] have been motivated from string theoretical effects [33,34]. Thus, it is important to analyze their effects on geometries motivated by string theory, such as black branes [35][36][37][38].…”