Analytic continuation of Spacetime Metrics

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Black Hole interiors -over the last 30 years, BH have been shown to have a number of surprising properties - directions for further research? -unforeseen relations between distinct areas of GR, quantum physics and statistical mechanics. -> deep puzzles at the foundations of physics -theoretical investigations of BH interiors aim to understand the geometry of spacetime inside generic BH - significant progress in the last decade. -singularities inside spherical, (non-)charged BH: null singularity along the Cauchy horizon precedes a spacelike, central singularity. The singularity along the Cauchy horizon is weak (tidal distortion of extended bodies is finite there). The nature of the Cauchy horizon singularity inside rotating BH: the divergence of curvature dominated by the propagating modes of the gravitational field leading to an intuitive picture of the singularity as a singular shock wave propagating along the Cauchy horizon. Proposed BH definition = missing piece of the spacetime that disrupts the predictability of the laws of physics and whose interior structure depends on the conditions on the event horizon at very distant future (infinite future) of an observer. The presence of a Cauchy horizon (light-like signals propagating from the future infinity), generated by infalling matter hitting the singularity and feeding the BH with information represents the minimal condition for forming a realistic BH. BH existence condition - possible only if the spacetime possesses inextendible curves with finite affine length.
Where are we? -if singularities can be observed from the rest of spacetime causality may break down -> physics loses its predictive power. The existence of BH = conundrum -facts: matter reaches the speed of light, hits the singularity, feeds the BH with information that can be used to create conditions of predictability of the infinite past. It may be possible to “feed” the initial conditions of the spacetime metric to be primarily created. We may possess the current conditions to “predict” the past initial conditions of the spacetime topology. Which comes first? (circular cause and consequence): singularity as a necessary condition of the metric or matter reaching the singularity causes the spacetime fabric to break. Our hypothesis could answer the question and close the circle. – infinite forces are acting – laws of physics break down – “The stability of EH require exotic matter violating the average null energy condition” - quantum gravity/string theory may help ? -no problem as long as a singularity is shielded from the outside world by an EH. Accept CCC? -unpredictability created by the presence of singularities -censorship proposal doesn’t eliminate the possibility of as thunderbolts (Hawking 1993, Penrose 1978). -‘wave of singularity’ -what forms first, singularity or apparent horizon (trapped surface)?
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 and 16: The Schwarzschild black hole The me
Page 17 and 18: Cross-section of a Kerr black hole
Page 19: Maximal extension diagrams Penrose

Analytic continuation of Spacetime Metrics

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