Charged Embedded Horizons and their Area Evolution

TL;DR

This paper introduces the concept of charged embedded horizons in black holes, analyzing their area evolution and transition from dynamical to isolated horizons due to charge variance and electric potential effects.

Contribution

It proposes a new model of embedded horizons that evolve dynamically under charge variance, providing a detailed area law evolution and transition to extremality.

Findings

Inner dynamical horizon evolves until reaching isolated horizon radius

Charge variance influences horizon dynamics and evolution

Horizon transitions to extremal isolated state

Abstract

The Embedded Horizon is defined to be a horizon that is in equilibrium with the exterior of the black hole, that is, isolated on the outside, but dynamically evolving on the inside, analogous to the inner and outer event horizons of the Reissner-Nordstrom black hole. This is shown as the result of charge variance on the horizon, which is expressed in electrical angular coordinates. The mass and energy of the black hole are discussed. The intrinsic metric is calculated by taking the electric potential into consideration. An area law evolution law is formulated, which suggests that the inner dynamical horizon evolves until it reaches the radius of the isolated horizon. The dynamical horizon, then, reaches equilibrium with the exterior, turning into an isolated horizon, thus turning extremal.