Information evolution in the interior of an axially symmetric BTZ black hole

TL;DR

This paper investigates the interior information dynamics of an axially symmetric BTZ black hole, analyzing volume growth and scalar entropy increase over time, and deriving an evolution relation linking entropy variation with black hole parameters.

Contribution

It introduces a novel analysis of interior volume and scalar entropy evolution in a (2+1)-dimensional rotating BTZ black hole, extending black hole evaporation concepts to lower dimensions.

Findings

Interior volume increases with time v.

Scalar quantum mode entropy increases with time v.

Derived an evolution relation between entropy variation and Bekenstein-Hawking entropy.

Abstract

In this paper, we consider an axially symmetric $(2+1)-$dimensional rotating Banados-Teitelboim-Zanelli (BTZ) black hole to investigate its interior \textbf{information}. First, we choose a largest space-like hyper-surface at $r_v=0.45$ and calculate the maximal interior volume bound by it. We found the interior volume to increase with advance time $v$. Similarly, the \textbf{scalar} quantum mode entropy \textbf{is} also found to increase with advance time. Next\textbf{,} considering two important assumptions, an evolution relation is obtained between \textbf{the variation of scalar} quantum mode entropy and Bekenstein Hawking entropy \textbf{for an} infinitesimal interval of time. In contrast to the evolution relation of higher dimensional black holes, the characteristic feature of this relation is its increase with extremely large increase in black hole mass. Moreover, this work extends the notion of black hole evaporation idea to lower space-time dimensions.