Analytic continuation of Spacetime Metrics

Black holes overview
-for bodies of too large a mass, concentrated in too small a volume, unstoppable collapse
will lead to a singularity in the structure of space-time.
-the term ‘singularity’ refers to a region where the conventional classical picture of spacetime
breaks down
-standard picture of collapse to a BH (Penrose 1978)- the singularities are not visible to
observers at a large distance from the hole, being ‘shielded’ from view by an absolute EH.
solutions of the vacuum field equations of GR (1915) G mn
= 0
BH types
schwarzschild - 1916 (static, neutral)
reissner-nordstrøm - 1918 (static,
electrically charged)
kerr - 1963 (rotating, neutral)
kerr-newman 1965 (rotating, charged)
all are Petrov type-D space-times
BH mass hidden in (point or ring)
singularity