Geodesic flows emanating from an arbitrary point $𝒫$ in a manifold $ℳ$ carry important information about the geometric properties of $ℳ$. These flows are characterized by Synge’s world function and van Vleck determinant—important biscalars that also characterize quantum description of physical systems in $ℳ$. If $𝒫$ is a regular point, these biscalars have well-known expansions around their flat space expressions, quantifying local flatness and the equivalence principle. We show that, if $𝒫$ is a singular point, the scaling behavior of these biscalars changes drastically, capturing the nontrivial structure of geodesic flows near singularities. This yields remarkable insights into classical structure of spacetime singularities and provides useful tool to study their quantum structure.

Close

PrevNext

View figure in article

• General relativity
• Singularities In general relativity