# Does a magnetic field have gravity?

Re-reading http://physics.stackexchange.com/a/33156/5265; I find myself thinking if light, being EM in the humanly visible spectrum, may possess gravity - does a magnetic field also possess gravity?

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## 1 Answer

Per wikipedia, the electromagnetic tensor $F^{\mu \nu}$ contributes to the stress energy tensor $T^{\mu \nu}$ by

$$T^{\mu \nu} = \frac{1}{\mu_0} \left(F^{\mu \alpha} g_{\alpha \beta} F^{\nu \beta} - \frac{1}{4} g^{\mu \nu} F^{\gamma \delta} F_{\gamma \delta} \right)$$

The Einstein equations govern how the stress-energy tensor is coupled to spacetime curvature. Since the magnetic field is entirely captured by the electromagnetic tensor, the answer is yes, magnetic fields contribute to gravitation.

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