Pencilvester

## Main Question or Discussion Point

Can someone tell me how we know that our physical universe is geodesically complete? In response to a question I had about why we assign any meaning to the other side of a black hole’s event horizon (or its interior), I got an answer prompting me to look into the concept of geodesic completeness. I found a little bit about it in a book titled “Semi-Riemannian Geometry with Applications to Relativity” by O’Neill. I found the definition of a geodesically complete manifold and a few examples of complete and incomplete manifolds (the Schwarzschild half-plane being of the incomplete variety). So I now understand what geodesic completeness means, and I understand that considering our physical spacetime to end at the event horizon of a black hole implies the manifold we live on is geodesically incomplete, but I still don’t understand why I should have a problem with that. Is there some physical evidence that tells us that we should?

Related question: If we consider a black hole’s mass to be concentrated beneath the event horizon (at a singularity or otherwise), and gravitational effects propagate through space with speed c, and anything with a speed less than or equal to c cannot cross an event horizon from below, how does a black hole affect any other mass gravitationally?

Related question: If we consider a black hole’s mass to be concentrated beneath the event horizon (at a singularity or otherwise), and gravitational effects propagate through space with speed c, and anything with a speed less than or equal to c cannot cross an event horizon from below, how does a black hole affect any other mass gravitationally?