The extremal Kerr entropy in higher-derivative gravities

Abstract

We investigate higher derivative corrections to the extremal Kerr black hole in the context of heterotic string theory with α′ corrections and of a cubic-curvature extension of general relativity. By analyzing the near-horizon extremal geometry of these black holes, we are able to compute the Iyer-Wald entropy as well as the angular momentum via generalized Komar integrals. In the case of the stringy corrections, we obtain the physically relevant relation S(J) at order α′2. On the other hand, the cubic theories, which are chosen as Einsteinian cubic gravity plus a new odd-parity density with analogous features, possess special integrability properties that enable us to obtain exact results in the higher-derivative couplings. This allows us to find the relation S(J) at arbitrary orders in the couplings and even to study it in a non-perturbative way. We also extend our analysis to the case of the extremal Kerr-(A)dS black hole.

Boundary terms and conserved charges in higher-derivative gauged supergravity

“…where σ's are the left-invariant Maurer-Cartan one-forms of SU(2), given in terms of Euler angles on S 3 (ψ, θ, φ) as, σ 1 = cos ψdθ + sin ψ sin θdφ, σ 2 = − sin ψdθ + cos ψ sin θdφ, σ 3 = dψ + cos θdφ, (5.2) 13 The same approach has been followed recently in [82] to study corrections to the extremal Kerr entropy in the context of the heterotic string and cubic gravities. For an analysis in the ungauged case see [83].…”

Higher derivative contributions to black hole thermodynamics at NNLO

“…Finally, our results can also be applied to compute the charge to mass ratio of extremal black holes, providing constraints on the low effective theory of quantum gravity at NNLO. In this regard, it would be useful to compare with other approach specific for extremal black holes [25].…”