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Are there any equations that show the curvature of space around a black hole?

Yes. The gravitational field around a non-rotating, uncharged black hole is described by Schwarzschild Metric. There are solutions available for more exotic black holes but one should learn the simplest case first. You can find a description of Schwarzschild geometry in most books on relativity, you can choose one which suits your level.

Jasjeet S Balga

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