Analytic continuation of Spacetime Metrics

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Schwarzschild maximal extension 1. Connection (bridge) in the sense of Einstein-Rosen between 2 otherwise euclidean spaces 2. Wormhole in the sense of Wheeler connecting 2 regions in 1 euclidean space multiple asymptotic regions and BH regions that contain timelike singularities Curves of constant r = hyperbolas asymptotic to the lines r=2m In the (u, v) plane, the spacetime is regular If a test particle crosses r=2m into the interior, it can never get back out but must hit inevitably the singularity r=0 (curvature invariants infinite) ->guarantee of causality non-violation (no signals sent through the wormhole faster than c)
Cross-section of a Kerr black hole Event horizon at (∆=0) and angular momentum between 0≤a all stationary BH solutions of Einstein-Maxwell equations are uniquely determined by 3 parameters: M, Q, and J with for extreme BH. -solutions for which have no EH; exposed singularities (naked) -subsitute solution. ->Kerr-Newman metric. for a=0 ->Reissner-Nordstrom
Page 1 and 2: Analytic continuation of Spacetime
Page 3 and 4: Formulation of the problem -BH: reg
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: The Schwarzschild black hole The me
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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