In the general theory of relativity the equation of motion for a particle with mass m and charge e , moving in a space with metric tensor g a b and electromagnetic field F a b , is given as m d u c d s − − m 1 2 g a b , c u a u b = e F c b u b , where u a = d x a / d s ( d x a is taken along the trajectory), g a b , c = ∂ ∂ g a b / ∂ ∂ x c , and d s 2 = g a b d x a d x b .