# Deriving Hubble redshift in closed Universe from Maxwell equations

## Homework Statement

I should derive the Hubble law redshift from Maxwell equations in closed Universe.

## Homework Equations

The metric of closed Universe is $$ds^2 = dt^2 - a^2(t)\left(d\chi^2 + \sin^2 \chi d\theta^2 + \sin^2 \chi \sin^2 \theta d\phi^2\right)$$.
The Hubble law redshift: $$\frac {\lambda(t)} {\lambda(t_0)} = \frac {a(t)} {a(t_0)}$$.
The wave equation for 4-potential is
$$\nabla_\mu F^{\mu\nu} = 0 \Rightarrow \partial_\mu \left(\sqrt{-g}g^{\mu\rho}g^{\nu\sigma}\left(\partial_\rho A _\sigma - \partial_\sigma A_\rho\right)\right)$$

## The Attempt at a Solution

As you can see the wave equation is very difficult to solve. Is there another way to show the Hubble redshift low for electormagnetic waves using Maxwell equations?

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