Phenomenology of Rotating GEUP Black Holes

TL;DR

This paper explores how quantum gravity effects, modeled via the Generalized Extended Uncertainty Principle, influence rotating black holes' properties, thermodynamics, and gravitational wave signatures, with implications for observational constraints.

Contribution

It introduces a metric-based model of rotating black holes with GEUP corrections, analyzes their thermodynamics, perturbations, and quasinormal modes, and constrains parameters using observational data.

Findings

Infrared corrections prolong black hole lifetimes.

QNM spectrum shifts depend on minimal length and large-scale parameters.

Observational data tightly constrain the EUP parameter.

Abstract

We investigate the phenomenological implications of quantum gravity on rotating black holes within the framework of the Generalized Extended Uncertainty Principle (GEUP), which incorporates both minimal length (ultraviolet) and large-scale (infrared) corrections. Lacking a full non-perturbative formulation of quantum gravity, we adopt a metric-based approach. We construct a stationary, axisymmetric ansatz via the Newman-Janis algorithm to model the kinematic features of a rotating black hole subject to Generalized Extended Uncertainty Principle (GEUP) corrections. The thermodynamic analysis reveals that in the infrared-dominated regime, the Hawking temperature scales as $T_H \sim M^{-3}$, leading to a rapid cooling phase that significantly prolongs the lifetime of supermassive black holes. We derive the modified Teukolsky Master Equation for gravitational perturbations and demonstrate that the background geometry preserves the isospectrality between axial and polar modes. In the eikonal limit, the quasinormal mode (QNM) spectrum exhibits orthogonal shifts: the minimal length parameter $\beta$ induces a spectral blueshift and enhanced damping, while the large-scale parameter $\alpha$ induces a spectral redshift and suppressed damping. Finally, we constrain the theory using observational data from LIGO/Virgo and the Event Horizon Telescope. We establish that the shadow of M87* is approximately $10^6$ times more sensitive to large-scale corrections than Sgr A*, placing stringent bounds on the EUP parameter, while gravitational wave spectroscopy provides complementary constraints on the GUP sector.