A note on geodesics in inhomogeneous expanding spacetimes

Understand

There are several solutions of Einstein field equations that describe an inhomogeneity in an expanding universe.

• Among these solutions, the McVittie metric and its generalizations have been investigated through decades, though a full understanding of them is still lacking.
• In this note, we explore the trajectories of photons and massive particles in generalized McVittie spacetimes.
• In the case of massless particles, we show that no circular orbits are possible for those models that admit cosmological singularities.