# Gravitational redshift +blackbody spectrum

1. Jul 7, 2005

### virtual

Hi,

How can I prove that gravitational redshift preserves the characteristic shape of a blackbody spectrum?

2. Jul 7, 2005

### hellfire

From the Stefan-Boltzmann Law you have a relation e ~ T4. On the other hand, a gas of photons has an energy density e ~ v N, with N a number density and v the frequency, integrated over the whole spectrum. Since the frequency v evolves with redshift z as v = v0(1 + z) and N as N = N0 (1 + z)3 you get that T = T0(1 + z). If you insert this and v = v0(1 + z) in the Planck function for the energy distribution the (1 + z) terms will cancel.