Geodesic motion in the vacuum C-metric

Understand

Geodesic equations of the vacuum C-metric are derived and solved for various cases.

• The solutions describe the motion of timelike or null particles with conserved energy and angular momentum.
• Polar, nearly-circular orbits around weakly accelerated black holes may be regarded as a perturbation of circular Schwarzschild geodesics.
• Results indicate that circular Schwarzschild geodesics of radius $r_0>6m$ are stable under small uniform accelerations along the orbital plane.