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Conservation laws for the wave equation and applications

Initial Data and Evolution Problems in General Relativity November 18, 2013 - November 22, 2013

November 18, 2013 (01:15 PM PST - 02:15 PM PST)
Speaker(s): Stefanos Aretakis (Princeton University)
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC

Abstract We will present recent results regarding conservation laws for the wave equation on null hypersurfaces. We will show that an important example of a null hypersurface admitting such conserved quantities is the event horizon of extremal black holes. We will also show that a global analysis of the wave equation on such backgrounds implies that certain derivatives of solutions to the wave equation asymptotically blow up along the event horizon of such backgrounds. In the second part of the talk we will present a complete characterization of null hypersurfaces admitting conservation laws. For this, we will introduce and study the gluing problem for characteristic initial data and show that the only obstruction to gluing is in fact the existence of such conservation laws.
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