The Oppenheimer-Volkoff Equations, Astrophysical Shock Waves, and Axially Symmetric Yang-Mills Theory in General Relativity

Details The Oppenheimer-Volkoff Equations, Astrophysical Shock Waves, and Axially Symmetric Yang-Mills Theory in General Relativity The Oppenheimer-Volkoff Equations, Astrophysical Shock Waves, and Axially Symmetric Yang-Mills Theory in General Relativity

Sep 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998phdt........24w&link_type=abstract

Thesis (PHD). THE UNIVERSITY OF MICHIGAN , Source DAI-B 59/07, p. 3489, Jan 1999, 188 pages.

Mathematics

Logic

2

Black Holes

Scientific paper

This dissertation begins by formulating the Oppenheimer-Volkoff equations (OV-Λ) in the case where Einstein's equations include a cosmological term. Properties of solutions to OV-Λ are determined. The major result is that (under mild assumptions on the equation of state) black holes cannot form as smooth solutions of OV-Λ. Complete solutions are constructed. These consist of a solution to OV-Λ and the static, spherically symmetric solution to Einstein's equations for the vacuum. The boundary is a contact discontinuity. The criteria for a C1 matching is that the pressure and density of the OV-Λ solution fall to zero at the contact discontinuity. Astrophysical shock wave solutions are constructed for the Einstein's equations with cosmological term. The solutions consist of a solution to OV-Λ matched Lipschitz continuously to an FRW solution across a fluid-dynamical shock wave. An explicit example of such a shock wave solution is calculated. The form of the rotationally invariant connection on an SU(2) bundle over a four dimensional real Lorentzian manifold is determined. Gauge transformations are derived that simplify the pullback of the connection to the base manifold. The axially symmetric Einstein-Yang-Mills equations are formulated, and existence of solutions is demonstrated for the gauge groups U(1) and SU(2).

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