Higher dimensional Bondi energy with a globally specified background structure**KEK-Cosmo-3 KEK/TH/1213.

Abstract

A higher (even spacetime) dimensional generalization of the Bondi energy has recently been proposed (Hollands and Ishibashi 2005 J. Math. Phys. 46 022503) within the framework of conformal infinity and Hamiltonian formalism. The gauge condition employed in Hollands and Ishibashi to derive the Bondi-energy expression is, however, peculiar in the sense that cross sections of null infinity specified by that gauge are anisotropic and in fact non-compact. For this reason, that gauge is difficult to use for explicit computation of the Bondi energy in general, asymptotically flat radiative spacetimes. Also it is not clear, under that gauge condition, whether an apparent difference between the expressions of higher dimensional Bondi energy and the four-dimensional one is due to the choice of gauges or a qualitatively different nature of higher dimensional gravity from four-dimensional gravity. In this paper, we consider instead, the Gaussian null conformal gauge as one of the more natural gauge conditions that admit a global specification of background structure with compact, spherical cross sections of null infinity. Accordingly, we modify the previous definition of higher dimensional news tensor so that it becomes well defined in the Gaussian null conformal gauge and derive, for vacuum solutions, an expression for the Bondi energy–momentum in the new gauge choice, which takes a universal form in arbitrary (even spacetime) dimensions greater than or equal to 4.