Generalized MisnerSharp quasilocal mass in EinsteinGaussBonnet gravity
Abstract
We investigate properties of a quasilocal mass in a higherdimensional spacetime having symmetries corresponding to the isomertries of an (n2)dimensional maximally symmetric space in EinsteinGaussBonnet gravity in the presence of a cosmological constant. We assume that the GaussBonnet coupling constant is nonnegative. The quasilocal mass was recently defined by one of the authors as a counterpart of the MisnerSharp quasilocal mass in general relativity. The quasilocal mass is found to be a quasilocal conserved charge associated with a locally conserved current constructed from the generalized Kodama vector and exhibits the unified first law corresponding to the energybalance law. In the asymptotically flat case, it converges to the ArnowittDeserMisner mass at spacelike infinity, while it converges to the DeserTekin and Padilla mass at infinity in the case of asymptotically antide Sitter. Under the dominant energy condition, we show the monotonicity of the quasilocal 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 quasilocal 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 quasilocal mass in Lovelock gravity are proposed.
 Publication:

Physical Review D
 Pub Date:
 March 2008
 DOI:
 10.1103/PhysRevD.77.064031
 arXiv:
 arXiv:0709.1199
 Bibcode:
 2008PhRvD..77f4031M
 Keywords:

 04.20.Cv;
 04.20.Ha;
 04.50.h;
 Fundamental problems and general formalism;
 Asymptotic structure;
 Higherdimensional gravity and other theories of gravity;
 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 13 pages, no figures, 1 table