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Gravitational Correction to Hyperfine Structure

The effective Hamiltonian of a fermion with spin-spin coupling to another fermion is derived from the non-relativistic approximation of the generally covariant Dirac equation in a weak gravitational field. This makes hyperfine structure of s-state of atomic hydrogen to be triplet other than the doublet in fiat spacetime. The difference is large enough to be measured for the atomic hydrogen on the earth and the sun.