Normal forces in stationary spacetimes

TL;DR

This paper extends the concept of conserved mechanical energy for particles in stationary spacetimes to include those influenced by normal forces, providing a new perspective on particle dynamics under such forces.

Contribution

It introduces a generalized notion of conserved energy for particles affected by normal forces in stationary spacetimes, expanding the classical understanding.

Findings

Conserved energy concept applies to particles with normal forces.

Illustrative example demonstrates practical usefulness.

Potential applications in gravitational and relativistic physics.

Abstract

For geodesic motion of a particle in a stationary spacetime the $U_0$ component of particle 4-velocity is constant and is considered to be a conserved mechanical energy. We show that this concept of a conserved mechanical energy can be extended to particles that move under the influence of a ``normal force,'' a force that, in the stationary frame, is orthogonal to the motion of the particle. We illustrate the potential usefulness of the concept with a simple example.