Gravity theories, Transverse Doppler and Gravitational Redshifts in Galaxy Clusters

Understand

There is growing interest in testing alternative gravity theories using the subtle gravitational redshifts in clusters of galaxies.

• However, current models all neglect a transverse Doppler redshift of similar magnitude, and some models are not self-consistent.
• An equilibrium model would fix the gravitational and transverse Doppler velocity shifts to be about 6sigma^2/c and 3sigma^2/2c in order to fit the observed velocity dispersion sigma self-consistently.
• This result comes from the Virial Theorem for a spherical isotropic cluster, and is insensitive to the theory of gravity.