Geodesic flows around charged black holes in two dimensions

TL;DR

This paper investigates the behavior of timelike geodesics around two-dimensional charged black holes, analyzing how charge and cosmological constant influence geodesic focusing and defocusing through the Raychaudhuri equation.

Contribution

It provides a detailed analysis of geodesic evolution in 2D black hole spacetimes, highlighting the effects of charge and cosmological constant on geodesic focusing.

Findings

Charge affects geodesic focusing behavior.

Cosmological constant influences expansion scalar evolution.

Critical expansion scalar values are computed for different parameters.

Abstract

We study the evolution of timelike geodesics for two dimensional black hole spacetimes arising in string theory and general theory of relativity by solving the Raychaudhuri equation for expansion scalar as an initial value problem. The possibility of geodesic focusing/defocusing is then examined accordingly with different settings of black hole parameters. In view of the geodesic focusing/defocusing, the critical value of expansion scalar is also calculated in each case. The effect of the charge and the cosmological constant on the evolution of expansion scalar for timelike geodesics is discussed in detail.