Higher dimensional black holes with a generalized gravitational action

Abstract

We consider the most general higher order corrections to the pure gravity action in $D$ dimensions constructed from the basis of the curvature monomial invariants of order 4 and 6, and degree 2 and 3, respectively. Perturbatively solving the resulting sixth-order equations we analyze the influence of the corrections upon a static and spherically symmetric back hole. Treating the total mass of the system as the boundary condition we calculate location of the event horizon, modifications to its temperature and the entropy. The entropy is calculated by integrating the local geometric term constructed from the derivative of the Lagrangian with respect to the Riemann tensor over a spacelike section of the event horizon. It is demonstrated that identical result can be obtained by integration of the first law of the black hole thermodynamics with a suitable choice of the integration constant. We show that reducing coefficients to the Lovelock combination, the approximate expression describing entropy becomes exact. Finally, we briefly discuss the problem of field redefinition and analyze consequences of a different choice of the boundary conditions in which the integration constant is related to the exact location of the event horizon and thus to the horizon defined mass

Heavy fields and gravity

“…7 we conclude. Finally, we should note that similar ideas have been previously explored in, for instance, [1][2][3][4][5][6] and especially [7] which considers the effects of massive scalars, fermions and vectors on the Reissner-Nordstrom solution. This paper can be viewed as an extension of [7] to spacetimes with non-flat asymptotics.…”

“…After using the identities (2.5) to map their action to ours, we find perfect agreement. Next, [3] generalized the results of [2] to arbitrary d while also including the ∼ R 2 operators in I ∂ 2 EFT (2.3). They calculated the entropy using Wald's formula and their results agree with ours in the d → 4 limit.…”

Entropy of quantum-corrected black holes

“…On the other hand, one can treat the results of Lu and Wise [58] and D = 4 limit of the entropy calculated in Ref. [59] as special cases of present calculations. Indeed, observe that there are similarities between S of the quantized massive fields in a large mass limit and the most general effective action involving all (time-reversal invariant) curvature terms of dimension six considered by Lu and Wise.…”

Stress-energy tensor of the quantized massive fields in Friedman-Robertson-Walker spacetimes

“…If the total stress-energy tensor is known, one can, in principle, construct the selfconsistent solution of the system (19). It should be noted however, that since the general stress-energy tensor, T b a , is constructed from the coincidence limit of a 3 (x, x ′ ), it contains the terms with higher-order derivatives of g ab , and, consequently, there is a real danger that the semiclassical equations may lead to physically unacceptable solutions.…”

“…where t is "ordinary" time coordinate related to η by dt = a(η)dη, c 1/2 1 is some constant and a prime denotes differentiation with respect to t. Transforming the semiclassical equations (19) to (t, w, y, z) coordinates and making use of (20) one obtains…”