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Metric Tensor

The metric tensor guhog_{ u ho} is a mathematical object that defines the geometry of spacetime, determining distances and time intervals.
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The statement of the theorem

Define the metric tensor gμνg_{\mu\nu} as the fundamental object determining the spacetime interval ds2ds^2 via the quadratic form:\nds2=gμνdxμdxνds^2 = g_{\mu\nu} dx^{\mu} dx^{\nu} \nIn a local coordinate system, gμνg_{\mu\nu} defines the inner product on the tangent space, allowing the calculation of distances and time intervals.