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PreprintCC BY 4.0arXiv

On the stability of spherically symmetric relativistic configurations with scalar field

  • Anatolii Tugay
  • Valery Zhdanov
  • Yurii Taistra
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Abstract

Static spherically symmetric asymptotically flat configurations in General Relativity with a minimally coupled scalar field typically possess naked singularities. We study a linear stability of these configurations against radial (monopole) perturbations in case of power-law scalar field potentials. We employ a new shooting method that extracts the eigenvalues corresponding to the exponentially growing modes of the perturbation. The problem is reduced to one second order ``master'' equation in a divergent form with a regularized effective potential. We confirm our previous results showing that instability modes exist for sufficiently small scalar charges of the initial static configurations.

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Cite

BibTeXRIS
BibTeX
@misc{tugay2026stability,
  title = {{On the stability of spherically symmetric relativistic configurations with scalar field}},
  author = {Anatolii Tugay and Valery Zhdanov and Yurii Taistra},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.04360},
  eprint = {2610.04360},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.04360},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On the stability of spherically symmetric relativistic configurations with scalar field
AU  - Anatolii Tugay
AU  - Valery Zhdanov
AU  - Yurii Taistra
PY  - 2026
DA  - 2026/10/03
PB  - arXiv
DO  - 10.48550/arxiv.2610.04360
UR  - https://arxiv.org/abs/2610.04360
AB  - Static spherically symmetric asymptotically flat configurations in General Relativity with a minimally coupled scalar field typically possess naked singularities. We study a linear stability of these configurations against radial (monopole) perturbations in case of power-law scalar field potentials. We employ a new shooting method that extracts the eigenvalues corresponding to the exponentially growing modes of the perturbation. The problem is reduced to one second order ``master'' equation in a divergent form with a regularized effective potential. We confirm our previous results showing that instability modes exist for sufficiently small scalar charges of the initial static configurations.
ER  -