A useful expression for relativistic energy conservation of a point mass in an isotropic static gravitational field

By using the symmetry and time-independence properties of Schwarzschild spacetime it is demonstrated that an energy conservation law may be expressed in terms of local velocity. From this form three important results may be derived very concisely. This highlights analogies and differences between relativistic and classical approaches to mechanics and serves as an illustration of the power that the use of particular expressions may provide in solving physical problems.