(Alpha) General relativity violates the equivalence principle


Valued Senior Member
(The “Alpha” in the title indicates that the Alpha rules apply to this thread.)

In another thread I proved that general relativity (GR) is self-inconsistent. Here I will prove that the inconsistency leads to a violation of the equivalence principle. First see the supporting info in the other thread, which includes the equivalence principle as stated by Einstein. (For the record, this is my second attempt. The first was refuted by Pete here.)

Now the proof:

Let X be an inertial frame falling through the horizon of a black hole. Since the spacetime throughout an inertial frame is flat, it must be possible to set up an inertial frame Y that extends throughout X and in which a free test particle, that is above the horizon and moves away from the black hole indefinitely, stays at rest. But GR predicts that nothing may pass outward through a horizon. Then Y cannot extend below the horizon (if only because otherwise a latticework of synchronized clocks, that is spread throughout Y and stays at rest with respect to Y, would be passing outward through the horizon), and so the spacetime cannot be flat throughout X. The equivalence principle says that X is equivalent to an inertial frame J in an idealized, gravity-free universe. Yet the spacetime throughout J is flat. Then X and J are nonequivalent, and so GR violates the equivalence principle.

Note that:
  • The definitions of flat spacetime and inertial frame in the supporting info account for the tidal force. The tidal force in X need not be nonexistent.
  • X can be arbitrarily small and its duration can be arbitrarily short. Then the tidal force in X can be nonexistent in the limit.
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