General Relativity: An Introduction for Physicists · Problem 6.4

Electromagnetism — Hobson, Efstathiou & Lasenby

Physics · maxwell-equations-covariant

Problem

In a Cartesian inertial coordinate system in Minkowski spacetime the field equations of electromagnetism can be written ∂μFμν=μ0jν,\partial_\mu F^{\mu\nu} = \mu_0 j^\nu, ∂σFμν+∂νFσμ+∂μFνσ=0.\partial_\sigma F_{\mu\nu} + \partial_\nu F_{\sigma\mu} + \partial_\mu F_{\nu\sigma} = 0. Show that these equations are equivalent to the standard form of Maxwell's equations in vacuo.

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