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PreprintCC BY 4.0arXiv

Perturbative solutions for the bumblebee field in a Schwarzschild background

  • Demetre Seturidze
  • Don Colladay
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Abstract

In this paper, we investigate the behavior of a vector field subject to a Lorentz-violating quartic potential on a fixed Schwarzschild background. We analyze the equilibrium configuration of the field and its linear perturbations. We show that the equilibrium solution and spherically symmetric perturbations are governed by a quadratic function whose properties determine their qualitative behavior. By requiring the background field to be real and finite, we derive bounds on the allowed parameters and identify critical cases in which the monopole perturbations become enhanced. We further derive asymptotic expressions for multipole perturbations near the event horizon and at spatial infinity.

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Cite

BibTeXRIS
BibTeX
@misc{seturidze2026perturbative,
  title = {{Perturbative solutions for the bumblebee field in a Schwarzschild background}},
  author = {Demetre Seturidze and Don Colladay},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.15988},
  eprint = {2608.15988},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.15988},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Perturbative solutions for the bumblebee field in a Schwarzschild background
AU  - Demetre Seturidze
AU  - Don Colladay
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2608.15988
UR  - https://arxiv.org/abs/2608.15988
AB  - In this paper, we investigate the behavior of a vector field subject to a Lorentz-violating quartic potential on a fixed Schwarzschild background. We analyze the equilibrium configuration of the field and its linear perturbations. We show that the equilibrium solution and spherically symmetric perturbations are governed by a quadratic function whose properties determine their qualitative behavior. By requiring the background field to be real and finite, we derive bounds on the allowed parameters and identify critical cases in which the monopole perturbations become enhanced. We further derive asymptotic expressions for multipole perturbations near the event horizon and at spatial infinity.
ER  -