The most accurate description possible of the behavior of a spin $\frac{1}{2}$ particle in Earth’s gravitational field is obtained by writing the Dirac equation in Kerr spacetime. Approximate methods, such as the use of rotating frames in Schwarzschild spacetime and accelerated and rotating frames in Minkowski spacetime, can also be used and will in general give different results. In this paper the orders of magnitude of energies are determined at which the Hamiltonian in the above cases become distinct, thus enabling one to choose the appropriate spacetime for the interpretation of experimental results.

• Received 8 October 1999

DOI:https://doi.org/10.1103/PhysRevD.62.024016