What happens to temperature in a gravitational field?

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Offline jeffreyH

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Time dilation has been experimentally validated on earth so two observers within different gravitational potentials will experience a change in each others passage of time. How would this affect the heat equation.

http://en.wikipedia.org/wiki/Heat_equation

If we are observing the radiation from either a star more massive than the sun or a neutron star, for instance, do we need to correct for time dilation. Could we be interpreting the data wrongly if we do not compensate for the time dilation?
Fixation on the Einstein papers is a good definition of OCD.