# Deriving Hubble redshift in closed Universe from Maxwell equations

1. Oct 24, 2011

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1. The problem statement, all variables and given/known data
I should derive the Hubble law redshift from Maxwell equations in closed Universe.
2. Relevant 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
$$\nabla_\mu F^{\mu\nu} = 0 \Rightarrow \partial_\mu \left(\sqrt{-g}g^{\mu\rho}g^{\nu\sigma}\left(\partial_\rho A _\sigma - \partial_\sigma A_\rho\right)\right)$$
3. 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?

Last edited: Oct 24, 2011
2. Oct 24, 2011