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 ($T_{L}, T_{R}$) 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 $(SL(2,\mathbb{R})_L \times SL(2,\mathbb{R})_R)$ 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.