Sachs equations for light bundles in a cold plasma

Abstract

We study the propagation of light bundles in non-empty spacetime, as most of the Universe is filled by baryonic matter in the form of a (dilute) plasma. Here we restrict to the case of a cold (i.e., pressureless) and non-magnetised plasma. Then the influence of the medium on the light rays is encoded in the spacetime dependent plasma frequency. Our result for a general spacetime generalises the Sachs equations to the case of a cold plasma Universe. We find that the reciprocity law (Etherington theorem), the relation that connects area distance with luminosity distance, is modified. Einstein's field equation is not used, i.e., our results apply independently of whether or not the plasma is self-gravitating. As an example, our findings are applied to a homogeneous plasma in a Robertson-Walker spacetime. We find small modifications of the cosmological redshift of frequencies and of the Hubble law.

minor reformulations; 26 pages, 3 figures

References in corpus (7)

• Light propagation in a plasma on Kerr spacetime: Separation of the Hamilton-Jacobi equation and calculation of the shadow
• Frequency-dependent effects of gravitational lensing within plasma
• Gravitational lensing in a non-uniform plasma
• Gravitational radiospectrometer
• Escape and Trapping of Low-Frequency Gravitationally Lensed Rays by Compact Objects within Plasma
• Gravitational Lensing of Rays through the Levitating Atmospheres of Compact Objects
• Dispersion by pulsars, magnetars, fast radio bursts and massive electromagnetism at very low radio frequencies

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