Generalized Misner-Sharp quasilocal mass in Einstein-Gauss-Bonnet gravity

Abstract

We investigate properties of a quasi-local mass in a higher-dimensional spacetime having symmetries corresponding to the isomertries of an (n − 2)-dimensional maximally symmetric space in Einstein-Gauss-Bonnet gravity in the presence of a cosmological constant. We assume that the Gauss-Bonnet coupling constant is non-negative. The quasi-local mass was recently defined by one of the authors as a counterpart of the Misner-Sharp quasi-local mass in general relativity. The quasi-local mass is found to be a quasi-local conserved charge associated with a locally conserved current constructed from the generalized Kodama vector and exhibits the unified first law corresponding to the energy-balance law. In the asymptotically flat case, it converges to the Arnowitt-Deser-Misner mass at spacelike infinity, while it does to the Deser-Tekin and Padilla mass at infinity in the case of asymptotically AdS. Under the dominant energy condition, we show the monotonicity of the quasi-local mass for any k, while the positivity on an untrapped hypersurface with a regular center is shown for k = 1 and for k = 0 with an additional condition, where k = ±1, 0 is the constant sectional curvature of each spatial section of equipotential surfaces. Under a special relation between coupling constants, positivity of the quasi-local mass is shown for any k without assumptions above. We also classify all the vacuum solutions by utilizing the generalized Kodama vector. Lastly, several conjectures on further generalization of the quasi-local mass in Lovelock gravity are proposed.

Black Hole Entropy for Two Higher Derivative Theories of Gravity

“…In the last few years, different authors have tried to generalize the Misner-Sharp energy definition to wider classes of gravity theories [49,50]. But even if Cai et al provide a general formula for the generalized MS energy in f (R) gravity, this does not produce any explicit, useful, result for the Clifton-Barrow black hole.…”

Lovelock black holes with a nonlinear Maxwell field

“…In what follows, we only consider the case for which D a R is spacelike since the derivation in the timelike case is quite analogue. In the neutral case, i.e., C = 0, this generalized Birkhoff's theorem was shown under the same assumption, i.e., (D a R)(D a R) = 0 in [17,21,22], while the complete proof including the null case was given in [23].…”

Magnetic black holes with higher-order curvature and gauge corrections in even dimensions

“…For the null case (D a r)(D a r) = 0 [27], on the other hand, there are the Nariai-Bertotti-Robinson type solutions [28] as in the case with or without the Maxwell field in general relativity [29] and in the Einstein-Gauss-Bonnet gravity [24,30,31]. In the case of Θ = 0, the generalized Jebsen-Birkhoff theorem for the vacuum case was shown in [20].…”

“…Although it is difficult to obtain the explicit form of the metric function in the dyonic case with the gauge corrections, this task is render possible in the absence of these terms. The solution in this case is given by 27) where Q e is a constant corresponding to the electric charge.…”