Einstein’s later theory of General Relativity. deals with the relative acceleration of different particles under the force of gravity, including the relativistic effects of Special Relativity on these particles. In the small, it reduces to, and must be consistent with, Special Relativity, including the behaviour of light. In the large, when gravitational fields are weaker and spacetime is flat, it must reduce to and be consistent with Newton’s theory of gravity.
General Relativity more accurately describes the interactions of gravity and light.