On the quantum improved Schwarzschild black hole

TL;DR

This paper explores quantum corrections to Schwarzschild black holes by improving the gravitational action with a running coupling based on curvature invariants, analyzing effects on particle trajectories and thermodynamics.

Contribution

It introduces a method to incorporate quantum effects into black hole solutions using Ricci tensor square for cutoff identification, preserving covariance.

Findings

Modified black hole solutions with quantum corrections

Altered particle trajectories near the black hole

Changes in black hole thermodynamic properties

Abstract

Deriving the gravitational effective action directly from exact renormalization group is very complicated, if not impossible. Hence, to study the effects of running gravitational coupling which tends to a non--Gaussian UV fixed point (as it is supposed by the asymptotic safety conjecture), two steps are usually adopted. Cutoff identification and improvement of the gravitational coupling to the running one. As suggested in [1], a function of all independent curvature invariants seems to be the best choice for cutoff identification of gravitational quantum fluctuations in curved spacetime and makes the action improvement, which saves the general covariance of theory, possible. Here, we choose Ricci tensor square for this purpose and then the equation of motion of improved gravitational action and its spherically symmetric vacuum solution are obtained. Indeed, its effect on the massive particles' trajectory and the black hole thermodynamics are studied.