Abstract
The nonrelativistic Hamiltonian for a Dirac particle in the Schwarzschild space is compared with that in the frame with a constant acceleration a . The spin–orbit coupling − s ·( a × p )/(2mc 2) , in the accelerated frame, turns out to be the Thomas precession. But in the Schwarzschild Hamiltonian, in addition to the Thomas precession, there exists a gravitational spin–orbit coupling which seems to violate the Einstein's equivalence principle.
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