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- Title
Spherically Symmetric C 3 Matching in General Relativity.
- Authors
Quevedo, Hernando
- Abstract
We study the problem of matching interior and exterior solutions to Einstein's equations along a particular hypersurface. We present the main aspects of the C 3 matching approach that involve third-order derivatives of the corresponding metric tensors in contrast to the standard C 2 matching procedures known in general relativity, which impose conditions on the second-order derivatives only. The C 3 alternative approach does not depend on coordinates and allows us to determine the matching surface by using the invariant properties of the eigenvalues of the Riemann curvature tensor. As a particular example, we apply the C 3 procedure to match the exterior Schwarzschild metric with a general spherically symmetric interior spacetime with a perfect fluid source and obtain that on the matching hypersurface, the density and pressure should vanish, which is in accordance with the intuitive physical expectation.
- Subjects
EINSTEIN, Albert, 1879-1955; GENERAL relativity (Physics); SCHWARZSCHILD metric; EINSTEIN field equations; SPACETIME; EIGENVALUES; CURVATURE; MATCHING theory
- Publication
Universe (2218-1997), 2023, Vol 9, Issue 9, p419
- ISSN
2218-1997
- Publication type
Article
- DOI
10.3390/universe9090419