SPHERICAL-SYMMETRY AND MASS-ENERGY IN HIGHER DIMENSIONS

The components of the Einstein tensor and other relations are given fo r a spherically symmetric metric in null coordinates in higher dimensi ons. These relations arc particularly relevant to the study of gravita tional collapse of a perfect fluid with heat flow but without viscosit y, where the exterior space cannot be considered as vacuum and matchin g to Schwarzschild space-time is not suitable. The analysis generalize s to higher dimensions work of Cahill and McVittie in 4D space-time. U sing the expression for the ''mass function,'' it is observed that pre ssure vanishes at the boundary of the distribution for a perfect fluid in the higher-dimensional case also, but the same is not true when he at flow is considered.