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An intuitive approach to inertial forces and the centrifugal force paradox in general relativity
As the velocity of a rocket in a circular orbit near a black hole increases,
the outwardly directed rocket thrust must increase to keep the rocket in its
orbit. This feature might appear paradoxical from a Newtonian viewpoint, but we
show that it follows naturally from the equivalence principle together with
special relativity and a few general features of black holes. We also derive a
general relativistic formalism of inertial forces for reference frames with
acceleration and rotation. The resulting equation relates the real experienced
forces to the time derivative of the speed and the spatial curvature of the
particle trajectory relative to the reference frame. We show that an observer
who follows the path taken by a free (geodesic) photon will experience a force
perpendicular to the direction of motion that is independent of the observers
velocity. We apply our approach to resolve the submarine paradox, which regards
whether a submerged submarine in a balanced state of rest will sink or float
when given a horizontal velocity if we take relativistic effects into account.
We extend earlier treatments of this topic to include spherical oceans and show
that for the case of the Earth the submarine floats upward if we take the
curvature of the ocean into account.Comment: 14 pages, 21 figure
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