What happens to temperature in a gravitational field?

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Online 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?