Black Hole Spacetime Reconstruction from Galactic Rotation Curves: Thermodynamic Properties and Implications
Abstract
We study how the dark-matter environment of a galaxy, reconstructed directly from its observed rotation curve, affects the black hole at its centre. Using the rotation curve of the spiral galaxy NGC\,5907, we construct a general-relativistic model of its halo. The halo has a positive, outward-decreasing density, satisfies the null energy condition, and reproduces the galaxy's dynamical mass of about 3.3×1011M⊙ within 30\,kpc. We then embed a central black hole in this halo and derive its horizon, Hawking temperature, entropy, heat capacity, photon sphere and shadow. Because the halo's gravitational field is weak, all these quantities differ from those of an isolated Schwarzschild black hole by less than one part in 105. The heat capacity remains negative, so the black hole stays thermodynamically unstable. For a black hole of 108M⊙, the shadow would span about 0.6\,microarcseconds. Archival WISE infrared photometry confirms, as expected, that the black hole leaves no imprint on the galaxy's light on kiloparsec scales.
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BibTeX
@misc{sanyal2026black,
title = {{Black Hole Spacetime Reconstruction from Galactic Rotation Curves: Thermodynamic Properties and Implications}},
author = {Aritra Sanyal and Farook Rahaman},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.17570},
eprint = {2609.17570},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17570},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Black Hole Spacetime Reconstruction from Galactic Rotation Curves: Thermodynamic Properties and Implications
AU - Aritra Sanyal
AU - Farook Rahaman
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2609.17570
UR - https://arxiv.org/abs/2609.17570
AB - We study how the dark-matter environment of a galaxy, reconstructed directly from its observed rotation curve, affects the black hole at its centre. Using the rotation curve of the spiral galaxy NGC\,5907, we construct a general-relativistic model of its halo. The halo has a positive, outward-decreasing density, satisfies the null energy condition, and reproduces the galaxy's dynamical mass of about 3.3×10^11M_⊙ within 30\,kpc. We then embed a central black hole in this halo and derive its horizon, Hawking temperature, entropy, heat capacity, photon sphere and shadow. Because the halo's gravitational field is weak, all these quantities differ from those of an isolated Schwarzschild black hole by less than one part in 10^5. The heat capacity remains negative, so the black hole stays thermodynamically unstable. For a black hole of 10^8M_⊙, the shadow would span about 0.6\,microarcseconds. Archival WISE infrared photometry confirms, as expected, that the black hole leaves no imprint on the galaxy's light on kiloparsec scales.
ER -