Higher derivative contributions to black hole thermodynamics at NNLO

Abstract

In an effective theory of gravity, thermodynamic quantities of black holes receive corrections from the infinite series of higher derivative terms. At the next to leading order, these can be obtained by using only the leading order solution. In this paper, we push forward this property to the next to next to leading order. We propose a formula which yields the Euclidean action of asymptotically flat black holes at the next to next to leading order using only the solution up to and including the next to leading order. Other conserved quantities are derived from the Euclidean action via standard thermodynamic relation. We verify our formula in examples of D-dimensional pure gravity and Einstein-Maxwell theory extended by 4- and 6-derivative terms. Based on our formula, we also prove that for asymptotically flat black holes, the physical quantities are invariant under field redefinitions.

Force-free higher derivative Einstein-Maxwell theory and multi-centered black holes

“…We verified that force-free combinations of 4-derivative interactions do not modify the MP solution as well as the non-extremal RN black holes. However, the force-free 4-derivative do modify the dyonic black hole solutions whose thermodynamic quantities can be easily computed using the recent results [31,32]. Since Einstein-Maxwell theory also admits magnetically charged objects, out of curiosity, we also studied consequences of force-free condition using the probe limit of 2 magnetic black holes although this seems to be unrelated to our original pursuit about existence of multi-electrically charged black holes.…”