# Electric field and gravitational field

1. Sep 27, 2007

### sterproj

Can a electric field create a gravitational field? I read somewhere that the gravitational field is the gradient of the electric field and a spherical capacitor can create a gravitational field.

2. Sep 27, 2007

### haushofer

According to Einstein, energy is the origin of space-time curvature, and that's what we call a "gravitational field". An electromagnetic field is described by the Maxwell tensor F, and from this tensor one can construct an energy momentum tensor. This tensor is the source of the space time curvature;

$$R_{\mu\nu} - \frac{1}{2}R g_{\mu\nu} = 8\pi T_{\mu\nu}$$

For the electromagnetic field we have that ( I could be wrong with indices here )

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

So, for a given electromagnetic field, we can calculate

$$F_{\mu\nu}[\tex], and with this we can calculate [tex]R_{\mu\nu}-\frac{1}{2}R g_{\mu\nu}$$

from which we can solve

$$g_{\mu\nu}$$.

Last edited: Sep 27, 2007
3. Sep 27, 2007

### OOO

Like every form of energy the electromagnetic field acts as a source for the gravitational field. But usually the created gravitational fields are much weaker than those created by particle masses. This is because it takes a lot of radiation (measured in units typically accessible to ordinary humans, i.e. several electron volt) to aggregate a mass comparable to particle masses.

In this sense a spherical capacitor of course creates a gravitational field (if one accepts general relativity), but this gravitational field is not to be confused with the electric field in the capacitor. The electric field allows to distinguish + from - whereas the additional gravity does not.