Analytic continuation of Spacetime Metrics

Formulation of the problem
-BH: regions of space from which nothing, not even light, can escape
because gravity is so strong.
-singularity is “clothed” inside EH where cosmic censorship prevails (we
cannot see inside the event horizon)
-can one See what happens "Inside a Black Hole"?
-is it possible for a distant observer to receive information about the BH interior?
-Can we get information about the region lying inside the apparent horizon?
-investigate the interior of regular axisymmetric and stationary BH
-the occurrence of singularities possible breakdown of GR ->QG??
-what are the possible solutions? Are the solutions stable?
-critical phenomena beyond spherical symmetry? conditions for predictability?
-the final state of gravitational collapse ->spacetime singularities in the causal future of regular initial data,
with divergence of curvature invariants and geodesic incompleteness; we expect continued gravitational
collapse leading to a singularity
-save the situation: spacetime singularities are "invisible" to external observers ->"cosmic censorship
conjecture“ –unproven and the foremost unsolved GR problem.
-under certain physical situations of gravitational collapse spacetime singularities, in the sense of causal
geodesic incompleteness, must occur
-we consider some fundamental questions concerning marginally trapped surfaces (apparent horizons), in
Cauchy data sets for the Einstein equation.
-What is the extension of spacetime beyond the singularity?
Black hole interiors
(a) Trapped surfaces
(b) Singularities and inner horizon instability
(c) Einstein-Rosen bridge on analytic extension