# Trapping Horizon and Negative Energy

## TL;DR

This paper demonstrates that near a trapping horizon, the vacuum energy-momentum tensor universally exhibits an ingoing negative energy flux responsible for black hole mass loss, independent of matter composition.

## Contribution

It proves the universality of negative energy flux at trapping horizons using semi-classical Einstein equations under spherical symmetry.

## Key findings

- Negative energy flux at trapping horizons is universal and independent of matter details.
- The energy density of the flux is approximately -1/(2κa^2).
- This flux causes black hole mass decrease over time.

## Abstract

Assuming spherical symmetry and the semi-classical Einstein equation, we prove that, for the observers on top of the trapping horizon, the vacuum energy-momentum tensor is always that of an ingoing negative energy flux at the speed of light with a universal energy density ${\cal E} \simeq - 1/(2\kappa a^2)$, (where $a$ is the areal radius of the trapping horizon), which is responsible for the decrease in the black hole's mass over time. This result is independent of the composition of the collapsing matter and the details of the vacuum energy-momentum tensor. The physics behind the universality of this quantity ${\cal E}$ and its surprisingly large magnitude will be discussed.