No, Einstein did not attempt to prove the equivalence principle using the field equations of general relativity. The equivalence principle, which states that the effects of gravity are indistinguishable from the effects of acceleration, was actually one of the guiding principles that Einstein used to develop his theory of general relativity.
Einstein formulated the equivalence principle based on his insight that an observer in a uniformly accelerated frame of reference cannot distinguish whether the observed effects are due to gravity or acceleration. This principle played a crucial role in the development of general relativity, as it led Einstein to propose that gravity is not a force in the traditional sense but rather the curvature of spacetime caused by mass and energy.
The field equations of general relativity, known as Einstein's field equations, describe how matter and energy generate the curvature of spacetime. These equations relate the distribution of matter and energy to the curvature of spacetime through a set of mathematical equations.
Rather than using the field equations to prove the equivalence principle, Einstein formulated the field equations as a way to mathematically describe the behavior of gravity in the framework of general relativity. The field equations provided a comprehensive and consistent description of gravity, unifying it with the concepts of spacetime curvature and the equivalence principle.
In summary, the equivalence principle was not proven using the field equations of general relativity. Instead, the equivalence principle guided Einstein in formulating his theory, and the field equations of general relativity were developed to describe the gravitational effects predicted by the theory.