Perihelion Advance and Trajectory of Charged Test Particles in Reissner-Nordstrom Field via the Higher-Order Geodesic Deviations

Figure 1

Deviation of two nearby geodesics in a gravitational field. Lines (a) and (b) represent the central geodesic and the nearby geodesic , respectively; lines (c) and (d) show the corresponding first and second-order approximations to the nearby geodesic (b). Also, is the unit tangent vector to the central world-line, is the separation vector to the curve , and is the second-order geodesic deviation [24].