Kinematics of geodesic flows in stringy black hole backgrounds

TL;DR

This paper analyzes the behavior of timelike geodesic flows in stringy black hole backgrounds, revealing new features of their kinematics through analytical and numerical solutions of Raychaudhuri equations.

Contribution

It provides the first detailed analytical and numerical study of geodesic kinematics in stringy black hole spacetimes, introducing new quantifiers to distinguish different flow geometries.

Findings

Differences in geodesic flow evolution between electric and magnetic black holes.

Initial conditions and curvature significantly influence geodesic focusing.

New quantifiers effectively differentiate flow behaviors in various geometries.

Abstract

We study the kinematics of timelike geodesic congruences in two and four dimensions in spacetime geometries representing stringy black holes. The Raychaudhuri equations for the kinematical quantities (namely, expansion, shear and rotation) characterising such geodesic flows are written down and subsequently solved analytically (in two dimensions) and numerically (in four dimensions) for specific geodesics flows. We compare between geodesic flows in dual (electric and magnetic) stringy black hole backgrounds in four dimensions, by showing the differences that arise in the corresponding evolutions of the kinematic variables. The crucial role of initial conditions and the spacetime curvature on the evolution of the kinematical variables is illustrated. Some novel general conclusions on geodesic focusing are obtained from the analytical and numerical findings. We also propose new quantifiers in terms of (a) the time (affine parameter) of approach to a singularity and (b) the location of extrema in the functional evolution of the kinematic variables, which may be used to distinguish between flows in different geometries. In summary, our quantitative findings bring out hitherto unknown features of the kinematics of geodesic flows, which, otherwise, would have remained overlooked, if we confined ourselves to only a qualitative analysis.