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I think you're right, except for the spelling of Lorentz factor.

The equation is on Wikipedia. https://en.wikipedia.org/wiki/Lorentz_factor

The terms are: v is the relative velocity between inertial reference frames, c is the speed of light in vacuum, β is the ratio of v to c, t is coordinate time, τ is the proper time for an observer (measuring time intervals in the observer's own frame).

If we could compare the time as we know it (based on the SI unit of seconds using an atomic clock) against the time at the singularity at the centre of the universe, we could figure out whether we're in a black hole, whether we're at the event horizon, or whether we're outside.

But we would have to assume space is a vacuum, which isn't entirely true.



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