Can we use Lorentz Transformations to understand the space-time curvature around a black hole? To my understanding, the Lorentz Transformations enable us to understand time dilation, as in the case of the Twins Paradox. So can we apply these same equations to black holes? If not, why?
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1No. The Lorentz Transformations have nothing to say about spacetime curvature. – m4r35n357 Dec 17 '19 at 16:41
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No. The Lorentz transformation is something that applies to a flat spacetime. A black hole spacetime isn't a flat spacetime. This is basically because there are no global frames of reference in GR: How do frames of reference work in general relativity, and are they described by coordinate systems?
If you want to predict things like gravitational effects on time, the tool you want is the metric.
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But we can still measure the time delay using the transformations falling into the black hole within line of sight, using a light signal? – Gareth Meredith Dec 17 '19 at 17:46
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If so what would that tell us about the slice of geometry it is going through? – Gareth Meredith Dec 17 '19 at 17:48