# Does the actual curvature of spacetime hold energy?

My understanding of GR is that curvature of spacetime reflects the density of energy-matter. Does the curvature itself have energy? Or if energy is assigned to curvature it simply reflects the energy density at that point?

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The gravitational field can indeed be assigned an energy. Unfortunately though whereas for, say, the EM field you can define an energy density at a point ($\bf{E}^2+\bf{B}^2$), for the gravitational field you can't do this. - Whichever way you define the energy in terms of the Christoffel symbols, you run into the problem that you can make them, and hence the energy, vanish at a point be choosing an appropriate frame.