Black Hole Thermodynamics in Fractal Dimension Quantum Gravity

This paper presents the thermodynamic and gravitational-wave predictions of Fractal Dynamical Quantum Gravity (FDQG), a theory in which the effective dimension of spacetime runs with energy scale according to renormalization group flow. By applying FDQG to black hole solutions, we compute corrections to entropy, temperature, and ringdown frequencies arising from a scale-dependent fractal geometry near the horizon. The results show universal ≈1% enhancements in black hole entropy, temperature, and gravitational-wave ringdown frequency for both stellar and supermassive black holes. These corrections originate from an above-four-dimensional effective spacetime structure that increases the phase-space volume near the horizon. The predicted +1.2% shift in ringdown frequency lies within the sensitivity of next-generation gravitational-wave detectors such as the Einstein Telescope and Cosmic Explorer. This work connects astrophysical black hole observables to collider-scale phenomenology through the same running fractal dimension parameter α(μ), demonstrating that FDQG provides a unified, falsifiable framework across more than twenty orders of magnitude in energy.