On gravitational shock waves in curved spacetimes |
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| Affiliation: | 1. Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russian Federation;2. Universidad de Buenos Aires, Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET), National Institute of Plasma Physics (INFIP), Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, Buenos Aires 1428, Argentina;3. Dzhelepov Laboratory of Nuclear Problems, Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russian Federation;1. Department of Mathematics and Statistics, University of Hyderabad, Hyderabad-500046, India;2. Department of Mathematics, IIT Bombay, Powai, Mumbai-400076, India;1. Kishine Koen, 222-0034 Yokohama, Japan;2. Mathematisches Institut der Universität Heidelberg, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany;3. Ludwig-Maximilians-Universität München, Fakultät für Physik, Theresienstraße 37, 80333 München, Germany;4. School of Mathematics, University of Edinburgh, Edinburgh, UK |
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| Abstract: | Some years ago Dray and 't Hooft found the necessary and sufficient conditions to introduce a gravitational shock wave in a particular class of vacuum solutions to Einstein's equations. We extend this work to cover cases where non-vanishing matter fields and a cosmological constant are present. The sources of gravitational waves are massless particles moving along a null surface such as a horizon in the case of black holes. After we discuss the general case we give many explicit examples. Among them are the d-dimensional charged black hole (that includes the 4-dimensional Reissner-Nordström and the d-dimensional Schwarzschild solution as subcases), the 4-dimensional De Sitter and anti-De Sitter spaces (and the Schwarzschild-De Sitter black hole), the 3-dimensional anti-De Sitter black hole, as well as backgrounds with a covariantly constant null Killing vector. We also address the analogous problem for string-inspired gravitational solutions nd give a few examples. |
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