Thick self-gravitating plane-symmetric domain walls

Details Thick self-gravitating plane-symmetric domain walls Thick self-gravitating plane-symmetric domain walls

1999-03-15

arxiv.org/abs/gr-qc/9903059v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

10 pages, 9 eps files, talk given at Les Houches '99 Winter School

Scientific paper

We investigate a self-gravitating thick domain wall for a $\lambda \Phi^4$ potential. The system of scalar and Einstein equations admits two types of non-trivial solutions: domain wall solutions and false vacuum-de Sitter solutions. The existence and stability of these solutions depends on the strength of the gravitational interaction of the scalar field, which is characterized by the number $\epsilon$. For $\epsilon \ll 1$, we find a domain wall solution by expanding the equations of motion around the flat spacetime kink. For ``large'' $\epsilon$, we show analytically and numerically that only the de Sitter solution exists, and that there is a phase transition at some $\epsilon_{\rm max}$ which separates the two kinds of solution. Finally, we comment on the existence of this phase transition and its relation to the topology of the domain wall spacetime.

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