A pedagogical note claims that parallel forces in cosmology and scalar-tensor gravity can be reparametrized away, but its claim that such forces occur generally in Einstein frame scalar-tensor gravity relies on an invalid assumption.
Normal forces in stationary spacetimes
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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.
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Forces parallel to particle trajectories in relativistic gravity
A pedagogical note claims that parallel forces in cosmology and scalar-tensor gravity can be reparametrized away, but its claim that such forces occur generally in Einstein frame scalar-tensor gravity relies on an invalid assumption.