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Solutions to the linear wave equation:

[itex]

\large\frac{\partial \Psi}{\partial t} = \frac{1}{c^{2}}\frac{\partial \Psi}{\partial x^{i}}

[/itex]

are sinusoidal waves of constant wavelength, i.e. they describe light

traveling in a flat space. But when light enters a region that is curved,

it is blue shifted, meaning that the above equation doesn't model

the light wave correctly. So my question is, if the wavelength of the light

becomes variable in a curved spacetime, is there a different more elaborate wave equation that models this? and if so, can it be arrived at from the metric, say for instance for a space with a Schwartzchild geometry?

Thank you for any replies.

P.S. I am not really sure what the relationship or even if one exists between Minkowski's metric and the wave equation is, but they seem to

have a very similar form, that is what prompted the question.