Energy Transformation in Gravitational Fields: A New Perspective on Four-Velocity

Incorporating the effective speed of light, rather than the conventional constant c, into the four-velocity vector leads to a more physically meaningful expression for the momentum and energy of stationary objects in Schwarzschild spacetime. This indicates that free-falling objects do not gain any energy in the gravitational field; instead, they experience a conversion of rest energy into kinetic energy within the specific spacetime structure. This innovative approach allows us to dispense with the traditional concept of gravitational potential energy, simplifying energy transformations within gravitational fields.