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On static solutions of the Einstein - Scalar Field equations · Around

2015

On static solutions of the Einstein - Scalar Field equations

Reiris, Martin

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In this article we study self-gravitating static solutions of the Einstein-ScalarField system in arbitrary dimensions.

We discuss the existence and the non-existence of geodesically complete solutions depending on the form of the scalar field potential $V(\phi)$, and provide full global geometric estimates when the solutions exist.
Our main results are summarised as follows.
For the Klein-Gordon field, namely when $V(\phi)=m^{2}|\phi|^{2}$, it is proved that geodesically complete solutions have Ricci-flat spatial metric, have constant lapse and are vacuum, (that is $\phi$ is constant and equal to zero if $m\neq 0$).

Built on

On the non-existence of regular stationary solutions of relativistic field equations
W. Pauli A. Einstein · 1943
Earlier work this paper cites.
Theories relativiste de la gravitation et de l electromagnetisme
A Lichnerowicz · 1955
Earlier work this paper cites.
Particle - Like Solutions of the Einstein Yang-Mills Equations
R. Bartnik and J. Mckinnon · 1988
Earlier work this paper cites.
On stationary vacuum solutions to the Einstein equations
Michael T. Anderson · 2000
Earlier work this paper cites.

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