Absence of an Effective Horizon for Black Holes in Gravity's Rainbow

TL;DR

This paper discusses how the concept of an effective horizon in black holes is affected by Gravity's Rainbow, suggesting that a minimum length scale leads to finite observer times, challenging traditional divergence notions.

Contribution

It introduces the idea that a minimum measurable length scale in Gravity's Rainbow results in finite observer times, countering previous divergence assumptions.

Findings

Divergence in observer time occurs when horizon position is specified beyond the Planck scale.

Accepting a minimum length scale makes the observer times finite.

Both in-going and asymptotic observers experience finite times with the minimum length scale.

Abstract

We argue that the divergence in time for the asymptotic observer occurs because of specifying the position of the Horizon beyond the Planck scale. In fact, a similar divergence in time will also occur for an in-going observer in Gravity's Rainbow, if we again specify the position of the Horizon beyond the Planck scale. On the other hand, if we accept the occurrence of a minimum measurable length scale associated with a universal invariant maximum energy scale in Gravity's Rainbow, then the time taken by both the in-going and asymptotic observers will be finite.