Scalar vacuum structure in general relativity and alternative theories conformal continuations

We discuss the global properties of static, spherically symmetric configurations of a self-gravitating real scalar field ip in General Relativity (GR), scalar-tensor and high-order (curvature-nonlinear) theories of gravity in various dimensions. In GR, for scalar fields with an arbitrary potential V(p), 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 p = const. In particular, there are no regular black holes with any asymptotics. These features are extended to scalartensor and curvature-nonlinear gravity, connected with GR by conformai mappings, unless there is a conformai 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. Such an effect is exemplified by exact solutions in GR with a massless conformai scalar field, considered as a special scalar-tensor theory. Necessary conditions are found for the existence of a conformai continuation; they only hold for special choices of scalar-tensor and high-order theories of gravity.

Authors
Editors
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Publisher
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Number of issue
11
Language
English
Pages
3571-3592
Status
Published
Department
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DOI
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Number
-
Volume
32
Year
2001
Organizations
  • 1 Centre for Gravitation and Fundamental Metrology, VNIIMS, 3-1 M. Ulyanovoy St., Moscow 117313, Russian Federation
  • 2 Institute of Gravitation and Cosmology, PFUR, 6 Miklukho-Maklaya St., Moscow 117198, Russian Federation
Keywords
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Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/287/