Quantum expansion of geodesic congruences in Schwarzschild anti-De Sitter spacetime

Abstract We evaluate the Raychaudhuri equation for radial ingoing and outgoing null and timelike geodesic congruences in specific families of metrics. Subsequently, we compute the Feynman propagator specifically for the Schwarzschild anti-De Sitter spacetime. Here, we find that the classical expansion scalars diverge at the singularity. Interestingly, while the propagators for null geodesics remain finite ingoing to the singularity, those for timelike geodesics exhibit divergence.