TITLE:
Surfaces of Revolution in the General Theory of Relativity
AUTHORS:
Taxiarchis Papakostas
KEYWORDS:
General Relativity, Exact Solutions
JOURNAL NAME:
Journal of Modern Physics,
Vol.6 No.14,
November
16,
2015
ABSTRACT: We present a class of axially symmetric and stationary spaces foliated by a congruence of surfaces of revolution. The class of solutions considered is that of Carter’s family [A] of spaces and we try to find a solution to Einstein’s equations in the presence of a perfect fluid with heat flux. This approach is an attempt to find an interior solution that could be matched to a corresponding exterior solution across a surface of zero hydrostatic pressure. The presence of a congruence of surfaces of revolution, described as the quotient space of the commoving observers, can be useful to the determination of the surface of zero pressure. Finally we present two formal solutions representing ellipsoids of revolutions.