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This question is about the ementary notions about the physics of General Relativity. So, consider then the Einstein Field Equation (EFE):

$$G_{\mu \nu} = \frac{8 \pi G}{c^{4}} T_{\mu \nu}$$

The fundamental notion about this formula lies about that the matter encoded by the energy-momentum tensor $T_{\mu \nu}$ constrain the geometry of spacetime (and then the motion of particles and photons etc..)

But is said very often in the introductory courses the phrase:

"The mass distribuition, like Earth, curves the spacetime"

Consider then the electromagnetic energy-momentum tensor:

$$T_{\mu \nu} = F_{\mu \sigma}F^{\sigma}_{\nu}-g_{\mu \nu}\frac{1}{4}F_{\rho \sigma}F^{\rho \sigma}$$

But to see how the eletromagnetism interacts with EFE beyond the classical exemple of Reissner metric the students must deal with GR beyond the elementary level, and then the notion of the "mass curves the spacetime" prevail and the fundamental concept of energy density curving the spacetime get lost.

I'm a undergraduate student and maybe I found a simple non-orthodoxal exemple to conveince the students that in fact energy density of a eletrostatic potential curves the spacetime.

Consider then two planet-sized parallel metal plates. If we charge the system, then we create a capacitor, a huge capacitor. The energy density stored by the eletrostatic field indeed curves the spacetime. If we look just to the energy density of the field and disconsider the curvature due to the giant metal plates i.e. a mass distribuition, the curvature of spacetime in the interior of the capacitor is just due to the energy density.

M.N.Raia
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