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PreprintCC BY 4.0arXiv

Exact solution of the Klein-Gordon equation in a Kiselev black hole background

  • Matheus. D. de Oliveira
  • Alexandre G. M. Schmidt
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Abstract

In this work, we investigate exactly the dynamics of a relativistic spinless particle influenced by a static and uncharged black hole surrounded by a quintessence-like anisotropic fluid or Kiselev black hole. Considering two quintessence-like models as examples, we calculate the radial wave function and determine, in both cases, the quasispectrum of energy, as well as the Hawking radiation and temperature. We find that the stronger the influence of quintessence-like anisotropic fluid, the smaller the radiation observed outside the event horizon. Furthermore, the temperatures obtained in both cases are directly influenced by the quintessence-like anisotropic fluid, and we recover the values obtained in other contexts, such as those derived using the surface gravity. Finally, in the absence of quintessence, we recover in both cases the Hawking temperature TH = 1/(8πkB M) corresponding to the Schwarzschild black hole.

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Cite

BibTeXRIS
BibTeX
@misc{oliveira2026exact,
  title = {{Exact solution of the Klein-Gordon equation in a Kiselev black hole background}},
  author = {Matheus. D. de Oliveira and Alexandre G. M. Schmidt},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.04467},
  eprint = {2609.04467},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.04467},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Exact solution of the Klein-Gordon equation in a Kiselev black hole background
AU  - Matheus. D. de Oliveira
AU  - Alexandre G. M. Schmidt
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.04467
UR  - https://arxiv.org/abs/2609.04467
AB  - In this work, we investigate exactly the dynamics of a relativistic spinless particle influenced by a static and uncharged black hole surrounded by a quintessence-like anisotropic fluid or Kiselev black hole. Considering two quintessence-like models as examples, we calculate the radial wave function and determine, in both cases, the quasispectrum of energy, as well as the Hawking radiation and temperature. We find that the stronger the influence of quintessence-like anisotropic fluid, the smaller the radiation observed outside the event horizon. Furthermore, the temperatures obtained in both cases are directly influenced by the quintessence-like anisotropic fluid, and we recover the values obtained in other contexts, such as those derived using the surface gravity. Finally, in the absence of quintessence, we recover in both cases the Hawking temperature T_H = 1/(8πk_B M) corresponding to the Schwarzschild black hole.
ER  -