Spherically Symmetric C3 Matching in General Relativity

Hernando Quevedo

doi:10.20944/preprints202306.1880.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 26 June 2023 / Approved: 27 June 2023 / Online: 28 June 2023 (02:13:12 CEST)

We study the problem of matching interior and exterior solutions of Einstein’s equations along a particular hypersuface. We present the main aspects of the C3 matching approach that involves third-order derivatives of the corresponding metric tensors in contrast to the standard matching procedures known in general relativity, which impose conditions on the second-order derivatives only. The C3 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 curvature tensor.

Exact solutions; matching conditions; curvature eigenvalues

Physical Sciences, Astronomy and Astrophysics

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Spherically Symmetric C³ Matching in General Relativity

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