Analytic continuation of Spacetime Metrics

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Historical note The first public use of the term "black hole". - appeared in the Phi Beta Kapper journal "The American Scholar" (Vol.37, No.2, Spring 1968, pp.248) and in the Sigma Xi journal, "American Scientist" Vol.56 No.l Spring 1968, pp. 1- 20. This page was sent to the authors by John Wheeler with his handwritten notes. -first postulated in 1783 by John Michell -the term “black hole” coined in 1969 -observational evidence starting in 1970s
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
Page 1: Analytic continuation of Spacetime
Page 5 and 6: Exact solutions any space-time metr
Page 7 and 8: Beyond the Event Horizon (M′, g
Page 9 and 10: Closed trapped surfaces Cauchy hori
Page 11 and 12: Compacted conformal infinity by cho
Page 13 and 14: Revisiting the problem Time slices,
Page 15 and 16: The Schwarzschild black hole The me
Page 17 and 18: Cross-section of a Kerr black hole
Page 19 and 20: Maximal extension diagrams Penrose
Page 21 and 22: Where are we? -if singularities can

Analytic continuation of Spacetime Metrics

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