Monodromy, Hidden Conformal Symmetry and Entropy Product Formula For Kerr-MOG Black Hole
Abstract
We examine the two-dimensional conformal field theory (2D CFT) dual of the four-dimensional Kerr-MOG (Kerr-modified gravity) black hole using the black hole thermodynamics and monodromy techniques. From these independent procedures, we derive consistent expressions for the left- and right-moving temperatures and the central charge of the dual CFT. Finally, we derive the entropy product using these approaches. We show that the product is \emph{not} universal as well as not quantized. We further explore the hidden conformal symmetry of the non-extremal Kerr-MOG black hole by analyzing the near-region dynamics of a massless scalar field. The resulting Kerr-MOG/CFT correspondence identifies the near-region geometry with a two-dimensional CFT characterized by the temperatures (TL, TR) derived in~(\ref{temperatures}). Moreover, using the Cardy formula, we reproduce the microscopic entropy of the dual CFT and find exact agreement with the Bekenstein-Hawking entropy of the Kerr-MOG black hole. We also show that the low-frequency scalar absorption cross section~(greybody factor) in the near-region Kerr-MOG geometry precisely matches the finite-temperature absorption cross section of the dual 2D CFT. In addition, the near-region scalar wave equation exhibits a hidden (SL(2,ℝ)L × SL(2,ℝ)R) conformal symmetry. These independent results provide strong evidence for the existence of a Kerr/CFT-type holographic duality for the Kerr-MOG black hole, establishing a consistent correspondence between the four-dimensional Kerr-MOG spacetime and a two-dimensional conformal field theory. horizon.
Related
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- Conformal data for the O(2) Wilson-Fisher CFT in (2+1)-dimensional spacetime from exact diagonalization and matrix product states on the fuzzy sphere
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BibTeX
@misc{pradhan2026monodromy,
title = {{Monodromy, Hidden Conformal Symmetry and Entropy Product Formula For Kerr-MOG Black Hole}},
author = {Parthapratim Pradhan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.25205},
eprint = {2607.25205},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.25205},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Monodromy, Hidden Conformal Symmetry and Entropy Product Formula For Kerr-MOG Black Hole
AU - Parthapratim Pradhan
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2607.25205
UR - https://arxiv.org/abs/2607.25205
AB - We examine the two-dimensional conformal field theory (2D CFT) dual of the four-dimensional Kerr-MOG (Kerr-modified gravity) black hole using the black hole thermodynamics and monodromy techniques. From these independent procedures, we derive consistent expressions for the left- and right-moving temperatures and the central charge of the dual CFT. Finally, we derive the entropy product using these approaches. We show that the product is \emph{not} universal as well as not quantized. We further explore the hidden conformal symmetry of the non-extremal Kerr-MOG black hole by analyzing the near-region dynamics of a massless scalar field. The resulting Kerr-MOG/CFT correspondence identifies the near-region geometry with a two-dimensional CFT characterized by the temperatures (T_L, T_R) derived in~(\ref{temperatures}). Moreover, using the Cardy formula, we reproduce the microscopic entropy of the dual CFT and find exact agreement with the Bekenstein-Hawking entropy of the Kerr-MOG black hole. We also show that the low-frequency scalar absorption cross section~(greybody factor) in the near-region Kerr-MOG geometry precisely matches the finite-temperature absorption cross section of the dual 2D CFT. In addition, the near-region scalar wave equation exhibits a hidden (SL(2,ℝ)_L × SL(2,ℝ)_R) conformal symmetry. These independent results provide strong evidence for the existence of a Kerr/CFT-type holographic duality for the Kerr-MOG black hole, establishing a consistent correspondence between the four-dimensional Kerr-MOG spacetime and a two-dimensional conformal field theory. horizon.
ER -