Symmetry analysis of wave equation on physically significant spacetimes

The currently accepted theory of gravitation is General Relativity. It is at present the most accurately tested physical theory on account of the observations of the Taylor-Hulse binary pulsar, for which Taylor and Hulse were awarded the Nobel Prize. The theory, originally propounded by Einstein, regards the motion of objects not as being due to some driving force (as in Newtons theory) but as due to the curvature of spacetime, where the usual 3-dimensional space and 1-dimensional time are inextricably tied together as an indivisible whole spacetime. Since one sees the Universe at present only by electromagnetic radiation emitted by stars (and other sources such as hot gasses and matter accreting into black holes), the distribution of matter can only be deduced by analyzing the radiation and seeing how it was scattered off different sources. For this purpose, it is useful to be able to solve the wave equation in the background of some gravitational sources. This work is part of a research program to investigate the wave equation on physically significant spacetimes with different background metrics. Symmetry analysis of wave equation on static spherically symmetric spacetimes with higher symmetries has been recently carried out by the LPI et al. The proposed work in this project deals with study of wave equation on following spacetimes which have great physical relevance. Schwarzschild metric Reissner-Nordstrm metric Kerr metric Schwarzschild-de Sitter metric Reissner-Nordstrm -de Sitter metric Kerr-de Sitter metric The holographic screen metric C-metrics representing accelerating black holes Vaidya's radiating Schwarzschild solution Precisely we consider the wave equation on each metric under study, and aim to investigate Lie and Noether symmetries, carry out a classification of symmetries into conjugacy classes, provide examples of exact solutions and conservation laws, physically interpret results and draw physically significant conclusions. An analysis of the inclusion relations between Lie symmetries, Noether symmetries and isometries of spacetimes is also carried out. A final physically significant comparative analysis of the findings of different cases will also be presented.