Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.556239
Title: Linear waves on higher dimensional Schwarzschild black holes and Schwarzschild de Sitter spacetimes
Author: Schlue, Volker
Awarding Body: University of Cambridge
Current Institution: University of Cambridge
Date of Award: 2012
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Abstract:
I study linear waves on higher dimensional Schwarzschild black holes and Schwarzschild de Sitter spacetimes. In the first part of this thesis two decay results are proven for general finite energy solutions to the linear wave equation on higher dimensional Schwarzschild black holes. I establish uniform energy decay and improved interior first order energy decay in all dimensions with rates in accordance with the 3 + 1-dimensional case. The method of proof departs from earlier work on this problem. I apply and extend the new physical space approach to decay of Dafermos and Rodnianski. An integrated local energy decay estimate for the wave equation on higher dimensional Schwarzschild black holes is proven. In the second part of this thesis the global study of solutions to the linear wave equation on expanding de Sitter and Schwarzschild de Sitter spacetimes is initiated. I show that finite energy solutions to the initial value problem are globally bounded and have a limit on the future boundary that can be viewed as a function on the standard cylinder. Both problems are related to the Cauchy problem in General Relativity.
Supervisor: Dafermos, Mihalis. Sponsor: Engineering and Physical Sciences Research Council ; Cambridge European Trust ; European Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.556239  DOI: Not available
Keywords: Mathematical general relativity ; Wave equations on black hole spacetimes
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