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- Title
Nonstaticity with type II, III, or IV matter field in f(Rμνρσ,gμν) gravity.
- Authors
Maeda, Hideki
- Abstract
In all n (≥ 3) -dimensional gravitation theories whose Lagrangians are functions of the Riemann tensor and metric, we show that static solutions are absent unless the total energy-momentum tensor for matter fields is of type I in the Hawking–Ellis classification. In other words, there is no hypersurface-orthogonal timelike Killing vector in a spacetime region with an energy-momentum tensor of type II, III, or IV. This asserts that, if back-reaction is taken into account to give a self-consistent solution, ultra-dense regions with a semiclassical type-IV matter field cannot be static even with higher-curvature correction terms. As a consequence, a static Planck-mass relic is possible as a final state of an evaporating black hole only if the semiclassical total energy-momentum tensor is of type I.
- Subjects
GRAVITATION; TENSOR fields; GRAVITY; BLACK holes; SPACETIME; SEMICLASSICAL limits
- Publication
General Relativity & Gravitation, 2021, Vol 53, Issue 10, p1
- ISSN
0001-7701
- Publication type
Article
- DOI
10.1007/s10714-021-02862-8