A covariant approach to LRS-II spacetime matching.
Paul, Erwin Roderic.
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In this thesis we examine the spacetime matching conditions covariantly for Locally Rotationally Symmetric class II (LRS-II) spacetimes, of which spherical symmetry is a special case. We use the semi-tetrad 1+1+2 covariant formalism and look at two general spacetime regions in LRS-II and match them across a timelike hypersurface using the Israel-Darmois matching conditions. This gives a new and unique result which is transparently presented in terms of the matching of various geometrical quantities (e.g. the expansion, shear, acceleration). Thereafter we apply the new result to the case involving a general spherically symmetric spacetime, representing for instance the interior of a star, and the Schwarzschild spacetime, which could represent the exterior. It is shown that the matching conditions make the Misner-Sharp and Schwarzschild masses exactly the same at the boundary, and the pressure is zero on the boundary.