The original expectation was that generic black holes would terminate in a spacelike singular boundary where the geometry of spacetime is completely destroyed. The second major objective of this proposal concerns the analysis of black hole interiors.
#Information about blackhole series#
A series of projects is outlined, of increasing difficulty, culminating in a complete resolution of the Kerr stability conjecture in the fully nonlinear setting, the statement that small perturbations of Kerr initial states stay close to the Kerr family in the black hole exterior and asymptote back to it as time goes to infinity. At a more technical level, the first objective of the proposal concerns the dynamic stability of the Kerr metrics, a two parameter family of explicit solutions to the celebrated Einstein equations that represent the simplest black hole solutions. The subject of black holes and spacetime singularities has inspired the popular imagination well beyond the confines of the scientific community, and work on this proposal will strengthen the ties between scientific research and the general public. This project will thus contribute to this long tradition of rigorous mathematics making fundamental statements about our physical world. Both the above objectives can be formulated as conjectures in pure mathematics concerning the governing equations of general relativity, the celebrated Einstein equations, and thus can be addressed by modern techniques of mathematical analysis. The project will strive to show, based in part on previous work of the proposer, that a portion of this singularity is not as "ferocious" as previously thought. It has long been expected that observers entering black hole regions eventually encounter "ferocious singularities", where the very structure of spacetime breaks down. The second major objective concerns understanding what generic black holes look like from the inside. If they are not, then much of our astrophysical world-picture will need to be revised. The first major objective to be addressed is to resolve the question of whether the simplest examples of black holes are indeed stable objects as observed from the outside.
This project strives to better understand two basic predictions of Einstein's theory of gravity: black holes and spacetime singularities. Primary Place of Performance Congressional District: Mihalis Dafermos (Principal Investigator) Sponsored Research Office:.
Justin Holmer DMS Division Of Mathematical Sciences MPS Direct For Mathematical & Physical Scien The mathematical analysis of black holes and spacetime singularities in general relativity NSF Org:
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