The nonrelativistic Hamiltonian for a Dirac particle in the Schwarzschild s
pace is compared with that in the frame with a constant acceleration a. The
spin-orbit coupling -s (.) (a x p)/(2mc(2)), in the accelerated frame, tur
ns out to be the Thomas precession. But in the Schwarzschild Hamiltonian, i
n addition to the Thomas precession, there exists a gravitational spin-orbi
t coupling which seems to violate the Einstein's equivalence principle. (C)
2001 Elsevier Science B.V. All rights reserved.