The spatial relation between the event horizon and trapping horizon

TL;DR

This paper explores the relationship between event horizons and trapping horizons in black holes, focusing on their thermodynamic roles, localizability, and behavior during accretion and evaporation, with new models and definitions introduced.

Contribution

It introduces a local method to locate event horizons, models trapping horizons outside the event horizon before evaporation, and proposes a conformally invariant definition of trapping horizons.

Findings

Difference in horizon areas can be large during accretion

Trapping horizons can appear outside the event horizon before evaporation

A conformally invariant definition of trapping horizons is proposed

Abstract

The relation between event horizons and trapping horizons is investigated in a number of different situations with emphasis on their role in thermodynamics. A notion of constant change is introduced that in certain situations allows the location of the event horizon to be found locally. When the black hole is accreting matter the difference in area between the two different horizons can be many orders of magnitude larger than the Planck area. When the black hole is evaporating the difference is small on the Planck scale. A model is introduced that shows how trapping horizons can be expected to appear outside the event horizon before the black hole starts to evaporate. Finally a modified definition is introduced to invariantly define the location of the trapping horizon under a conformal transformation. In this case the trapping horizon is not always a marginally outer trapped surface.