On the Stability of Spherically Symmetric Space-Times in Scalar-Tensor Gravity

We study the linear stability of vacuum static, spherically symmetric solutions to the gravitational field equations of the Bergmann–Wagoner–Nordtvedt class of scalar-tensor theories (STT) of gravity, restricting ourselves to nonphantom theories, massless scalar fields and configurations with positi...

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Bibliographic Details
Published in:Gravitation & cosmology 2023-12, Vol.29 (4), p.374-386
Main Authors: Bronnikov, K. A., Bolokhov, S. V., Skvortsova, M. V., Badalov, K., Ibadov, R.
Format: Article
Language:English
Subjects:
Astronomy
Astrophysics and Astroparticles
Boundary conditions
Classical and Quantum Gravitation
Gravitational fields
Mathematical analysis
Observations and Techniques
Perturbation
Physics
Physics and Astronomy
Quantum Physics
Relativity
Relativity Theory
Scalars
Stability
Tensors
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Summary:We study the linear stability of vacuum static, spherically symmetric solutions to the gravitational field equations of the Bergmann–Wagoner–Nordtvedt class of scalar-tensor theories (STT) of gravity, restricting ourselves to nonphantom theories, massless scalar fields and configurations with positive Schwarzschild mass. We consider only small radial (monopole) perturbations as the ones most likely to cause an instability. The problem reduces to the same Schrödinger-like master equation as is known for perturbations of Fisher’s solution of general relativity (GR), but the corresponding boundary conditions that affect the final result of the study depend on the choice of the STT and a particular solution within it. The stability or instability conclusions are obtained for the Brans–Dicke, Barker and Schwinger STT as well as for GR nonminimally coupled to a scalar field with an arbitrary parameter .
ISSN:0202-2893
1995-0721
DOI:10.1134/S0202289323040059