Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2001-10-31
Acta Phys.Polon.B32:3571-3592,2001
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Latex2e, 10 pages, 2 figures. Submitted to Proc. XXV Int. School of Theor. Phys., Ustron, Poland, 10-16 Sept. 2001
Scientific paper
We discuss the global properties of static, spherically symmetric configurations of a self-gravitating real scalar field $\phi$ in general relativity (GR), scalar-tensor theories (STT) and high-order gravity ($L=f(R)$) in various dimensions. In GR, for fields with arbitrary potentials $V(\phi)$, not necessarily positive-definite, it is shown that the list of all possible types of space-time causal structure in the models under consideration is the same as the one for $\phi = const$. In particular, there are no regular black holes with any asymptotics. These features are extended to STT and $f(R)$ theories, connected with GR by conformal mappings, unless there is a conformal continuation, i.e., a case when a singularity in a solution of GR maps to a regular surface in an alternative theory, and the solution is continued through such a surface. This effect is exemplified by exact solutions in GR with a massless conformal scalar field, considered as a special STT. Necessary conditions for the existence of a conformal continuation are found; they only hold for special choices of STT and high-order theories of gravity.
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