Geodesics and thermodynamics of a κ-deformed anti-de Sitter black hole surrounded by a quintessence field
Abstract
We investigate the geodesic structure and thermodynamics of a κ-deformed Schwarzschild-anti-de Sitter black hole in a Kiselev quintessence field, where dynamics are governed by a mass-dependent lapse deformation. This term produces an inner Cauchy horizon without requiring charge or spin, yet it fails to resolve the central singularity; instead, the Kretschmann scalar diverges more strongly as r−10. Because the deformation amplitude couples to the mass, the standard Bekenstein-Hawking area law violates the first law of thermodynamics. We resolve this by either deriving a modified entropy or rescaling the mass, both of which restore the first law and yield a consistent Smarr relation. Optically, an increasing deformation parameter shrinks both the photon sphere and the critical impact parameter. We also derive a closed-form Joule-Thomson coefficient, revealing that the κ-deformation triggers an inversion curve a feature absent in standard neutral SAdS. Notably, this occurs without generating a van der Waals critical point, demonstrating that Joule-Thomson inversion and van der Waals criticality can be cleanly decoupled. Finally, the deformation suppresses peak Hawking emission by a factor of roughly four and increases flux sparsity, an effect driven almost entirely by a drop in temperature rather than changes to the black hole shadow.
Related
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BibTeX
@misc{ahmed2026geodesics,
title = {{Geodesics and thermodynamics of a $κ$-deformed anti-de Sitter black hole surrounded by a quintessence field}},
author = {Faizuddin Ahmed and Ahmad Al-Badawi and Izzet Sakalli and Erdem Sucu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01704},
eprint = {2609.01704},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01704},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Geodesics and thermodynamics of a κ-deformed anti-de Sitter black hole surrounded by a quintessence field
AU - Faizuddin Ahmed
AU - Ahmad Al-Badawi
AU - Izzet Sakalli
AU - Erdem Sucu
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01704
UR - https://arxiv.org/abs/2609.01704
AB - We investigate the geodesic structure and thermodynamics of a κ-deformed Schwarzschild-anti-de Sitter black hole in a Kiselev quintessence field, where dynamics are governed by a mass-dependent lapse deformation. This term produces an inner Cauchy horizon without requiring charge or spin, yet it fails to resolve the central singularity; instead, the Kretschmann scalar diverges more strongly as r^−10. Because the deformation amplitude couples to the mass, the standard Bekenstein-Hawking area law violates the first law of thermodynamics. We resolve this by either deriving a modified entropy or rescaling the mass, both of which restore the first law and yield a consistent Smarr relation. Optically, an increasing deformation parameter shrinks both the photon sphere and the critical impact parameter. We also derive a closed-form Joule-Thomson coefficient, revealing that the κ-deformation triggers an inversion curve a feature absent in standard neutral SAdS. Notably, this occurs without generating a van der Waals critical point, demonstrating that Joule-Thomson inversion and van der Waals criticality can be cleanly decoupled. Finally, the deformation suppresses peak Hawking emission by a factor of roughly four and increases flux sparsity, an effect driven almost entirely by a drop in temperature rather than changes to the black hole shadow.
ER -