Boundedness and decay of scalar waves at the Cauchy horizon of the Kerr spacetime
Adapting and extending the techniques developed in recent work with Vasy for the study of the Cauchy horizon of cosmological spacetimes, we obtain boundedness, regularity and decay of linear scalar waves on subextremal Reissner–Nordström and (slowly rotating) Kerr spacetimes, without any symmetry as...
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Veröffentlicht in: | Commentarii mathematici Helvetici 2017-01, Vol.92 (4), p.801-837 |
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description | Adapting and extending the techniques developed in recent work with Vasy for the study of the Cauchy horizon of cosmological spacetimes, we obtain boundedness, regularity and decay of linear scalar waves on subextremal Reissner–Nordström and (slowly rotating) Kerr spacetimes, without any symmetry assumptions; in particular, we provide simple microlocal and scattering theoretic proofs of analogous results by Franzen. We show polynomial decay of linear waves relative to a Sobolev space of order slightly above 1/2. This complements the generic $H_{\mathrm {loc}}^1$ blow-up result of Luk and Oh. |
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Math. Helv</addtitle><date>2017-01-01</date><risdate>2017</risdate><volume>92</volume><issue>4</issue><spage>801</spage><epage>837</epage><pages>801-837</pages><issn>0010-2571</issn><eissn>1420-8946</eissn><abstract>Adapting and extending the techniques developed in recent work with Vasy for the study of the Cauchy horizon of cosmological spacetimes, we obtain boundedness, regularity and decay of linear scalar waves on subextremal Reissner–Nordström and (slowly rotating) Kerr spacetimes, without any symmetry assumptions; in particular, we provide simple microlocal and scattering theoretic proofs of analogous results by Franzen. We show polynomial decay of linear waves relative to a Sobolev space of order slightly above 1/2. This complements the generic $H_{\mathrm {loc}}^1$ blow-up result of Luk and Oh.</abstract><cop>Zuerich, Switzerland</cop><pub>European Mathematical Society Publishing House</pub><doi>10.4171/CMH/425</doi><tpages>37</tpages></addata></record> |
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source | European Mathematical Society Journals; E-Periodica Journals; Free E-Journal (出版社公開部分のみ) |
subjects | Global analysis, analysis on manifolds Partial differential equations Relativity and gravitational theory |
title | Boundedness and decay of scalar waves at the Cauchy horizon of the Kerr spacetime |
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