I guess as a result of the energy-momentum tensor $T_{\mu\nu}$ coupling to a flat Minkowski metric, $\eta_{\mu\nu}$, the flat metric can become that of a curved spacetime, $g_{\mu\nu}$. How can one describe this process mathematically?
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1$\begingroup$ en.wikipedia.org/wiki/Einstein_field_equations $\endgroup$– GhosterCommented Mar 3 at 18:04
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$\begingroup$ Curvature is not a process. It is a local property of the spacetime manifold. $\endgroup$– GhosterCommented Mar 3 at 18:06
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$\begingroup$ I guess my question wasn't too clear. What I meant was how exactly the energy-momentum tensor couples to the metric which as a result the metric changes. $\endgroup$– physics_2015Commented Mar 3 at 18:08
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$\begingroup$ Given an energy-momentum tensor, you solve the Einstein field equations for the metric. This is how you get black holes, Big Bang, gravitational waves, etc. $\endgroup$– GhosterCommented Mar 3 at 18:09
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1$\begingroup$ Here is the action for GR. $\endgroup$– GhosterCommented Mar 3 at 18:12
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