The main outcome of the NSF grant is a complete proof of the nonlinear stability of Black Holes with small angular momentum. Their policies may differ from this site.
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Some full text articles may not yet be available without a charge during the embargo (administrative interval). When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria. The main methodology of the PI is to combine this new method, called Generally Covariant Modulation theory, with the the so called vector-field method. Szeftel in France the PI had proposed a new method to construct these coordinates based on the full covariance properties of the Einstein equations. to show that the perturbations converge to zero for large times. That means, roughly, that one cannot solve the stability problem without finding a specific coordinate system in which one can establish decay of the perturbations, i.e.
At the heart of all these difficulties is the issue of gauge. The high non-linearity of the Einstein equations makes it hard to separate them they are all interconnected. To solve the problem of stability of black holes one has to overcome a large range of difficult issues. Thus all the important features of a unperturbed black hole are preserved by the perturbations. The goal is to show that any small perturbation, at a given time, of a given black hole solution remains small for all later times. This translates to a very difficult, deep and beautiful mathematical conjecture which is the main focus of the proposed research. Chief among them is stability to perturbations. To have physical reality they have to possess properties which make them detectable to observations. Primary Place of Performance Congressional District:Ġ40100 NSF RESEARCH & RELATED ACTIVIT 040100 NSF RESEARCH & RELATED ACTIVIT 040100 NSF RESEARCH & RELATED ACTIVITĪt the most basic level Black Holes are nothing but special, explicit, solutions of the Einstein equations of General Relativity. Sergiu Klainerman (Principal Investigator) Sponsored Research Office:.On the Mathematical Theory of Black Holes NSF Org:
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