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L is a (4D) distance. Its useful to talk about because knowing distances between points in a space allows you to derive almost anything else you might be interested in (there are important exceptions though).
dL is always a quadratic function in the four coordinates, even with gravity. It is a solution of Einstein's equation, which is a nonlinear partial differential equation.
Most of this falls under differential geometry. Tensor calculus is also very useful.
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