# Static Black Holes With Back Reaction From Vacuum Energy

## TL;DR

This paper investigates static, spherically symmetric solutions to semi-classical Einstein equations influenced by quantum vacuum energy, revealing horizonless objects that resemble Schwarzschild black holes at a distance.

## Contribution

It introduces new solutions to semi-classical gravity equations showing that horizons can be replaced by horizonless configurations affected by quantum vacuum energy.

## Key findings

- Solutions are small deformations of Schwarzschild metric.
- Horizonless objects are possible due to quantum effects.
- Horizon formation is sensitive to near-horizon quantum energy-momentum.

## Abstract

We study spherically symmetric static solutions to the semi-classical Einstein equation sourced by the vacuum energy of quantum fields in the curved space-time of the same solution. We found solutions that are small deformations of the Schwarzschild metric for distant observers, but without horizon. Instead of being a robust feature of objects with high densities, the horizon is sensitive to the energy-momentum tensor in the near-horizon region.