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Is Light Affected by the Gravitational Field of a Black Hole?

Question:
Is light affected by time dilation around black holes? That is to say, if light were to pass by a black hole and become redshifted and then reached us, would we be seeing light that took longer to get to us than if it just traveled at light speed the entire time? If this isn’t the case, then why not?
Answer:
Yes. Light is redshifted to longer wavelengths when it interacts with a black hole. This redshifted light, though, travels at the same speed when traveling from the black hole to us. The speed of light is unchanged.