# Quantum Corrections to Schwarzschild Black Hole

## TL;DR

This paper uses effective field theory to analyze quantum corrections to Schwarzschild black holes, finding that they remain solutions with no corrections at quadratic order, while massive stars do receive quantum modifications.

## Contribution

It introduces a covariant non-local effective action approach to compute quantum corrections to spherically symmetric solutions in Einstein's gravity.

## Key findings

- Eternal Schwarzschild black holes are unaffected by quantum corrections at this order.
- Quantum corrections significantly modify the field of a massive star.
- The approach accounts for both local and non-local quantum effects.

## Abstract

Using effective field theory techniques, we compute quantum corrections to spherically symmetric solutions of Einstein's gravity and focus in particular on the Schwarzschild black hole. Quantum modifications are covariantly encoded in a non-local effective action. We work to quadratic order in curvatures simultaneously taking local and non-local corrections into account. Looking for solutions perturbatively close to that of classical general relativity, we find that an eternal Schwarzschild black hole remains a solution and receives no quantum corrections up to this order in the curvature expansion. In contrast, the field of a massive star receives corrections which are fully determined by the effective field theory.