Geodesic congruences in quantum improved spacetimes

TL;DR

This paper explores how quantum improvements to spacetime geometry affect geodesic behavior, deriving modified equations that challenge classical energy conditions and influence gravitational focusing.

Contribution

It introduces a quantum improved Raychaudhuri equation and analyzes its implications on geodesic convergence, highlighting deviations from classical predictions.

Findings

Quantum improvements alter geodesic convergence conditions

Classical strong energy condition does not guarantee geodesic convergence in quantum spacetimes

Modified equations suggest new gravitational focusing behaviors

Abstract

We investigate the geodesic deviation equation in the context of quantum improved spacetimes. The improved Raychaudhuri equation is derived, and it is shown that the classical strong energy condition does not necessarily lead to the convergence of geodesics in a congruence in the quantum improved spacetime.