Flux of radiation from pointlike sources in general relativity
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Flux of radiation from pointlike sources in general relativity Matej Sárený1 Received: 28 January 2020 / Accepted: 13 August 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In the paper we study propagation of light in general relativity through a spacetime filled with cold plasma with infinite conductivity. We use the geometric optics based on Synge’s approach. As the main result we provide a formula for calculation of spectral flux of radiation emitted from a pointlike source. The formula employs connecting vectors that are obtained by integrating the ray deviation equation along the reference ray connecting the source and observation event. As a byproduct we formulate Etherington’s reciprocity theorem with the inclusion of plasma, interrelating angular size distance and luminosity distance. We also discuss the Liouville theorem and its formulation in terms of connecting vectors. Keywords Relativistic geometric optics · Cold plasma · Flux of radiation · Ray deviation equation · Reciprocity theorem · Relativistic distances · Liouville theorem
Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Flux of radiation based on “intuitive” manipulation of differentials . . 2 Generally relativistic equations for photon propagating through plasma 3 Definition of flux in the kinetic theory . . . . . . . . . . . . . . . . . . 4 Flux coming from √ a pointlike source . . . . . . . . . . . . . . . . . . 5 Expression for h|detV| in terms of connecting vectors . . . . . . . . 6 On the conservation of phase volume . . . . . . . . . . . . . . . . . . 7 Flux of radiation and relativistic distances . . . . . . . . . . . . . . . . 8 Demonstration of the flux calculation . . . . . . . . . . . . . . . . . . 9 Reciprocity theorem with the inclusion of plasma . . . . . . . . . . . . Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix A Utility formula for even-dimensional matrix determinant . . Appendix B Conservation of dtdν . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Matej Sárený [email protected] Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynská dolina F1, 842 48 Bratislava, Slovakia 0123456789().: V,-vol
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M. Sárený
Introduction In astrophysics it is often of great importance to know the specific flux of radiation Fν = d E/dtd
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