General relativistic plasma in higher dimensional space time

TL;DR

This paper generalizes Einstein-Maxwell and plasma equations to higher-dimensional spacetimes, analyzing wave propagation, redshift, and Faraday rotation effects in an expanding universe with implications for cosmology.

Contribution

It extends plasma physics and electromagnetic wave analysis to higher dimensions within a cosmological context, providing new dispersion relations and insights into wave behavior.

Findings

Maximum redshift for photons varies with dimension.

Wave propagation restricted to specific frequency ranges depending on dimensions.

Dielectric constant remains constant despite universe expansion.

Abstract

The well known (3+1) decomposition of Thorne and Macdonald is invoked to write down the Einstein-Maxwell equations generalised to (d+1) dimensions and also to formulate the plasma equations in a flat FRW like spacetime in higher dimensions (HD). Assuming an equation of state for the background metric we find solutions as also dispersion relations in different regimes of the universe in a unified manner both for magnetised(un) cold plasma. We find that for a free photon in expanding background we get maximum redshift in 4D spacetime, while for a particular dimension it is so in pre recombination era. Further wave propagation in magnetised plasma is possible for a restricted frequency range only, depending on the number of dimensions. Relevant to point out that unlike the special relativistic result this allowed range evolves with time. Interestingly the dielectric constant of the plasma media remains constant, not sharing the expansion of the background, which generalises a similar 4D result of Holcomb-Tajima in radiation background to the case of higher dimensions with cosmic matter obeying an equation of state . Further, analogous to the flat space static case we observe the phenomenon of Faraday rotation in higher dimensional case also.