- #1
Pouramat
- 28
- 1
- Homework Statement
- Let ##K## be a Killing vector field. Show that an electromagnetic field with potential ##A_\mu = K_\mu## solves Maxwell's eqs if the metric is a vacuum solution to Einstein's Eqs.
- Relevant Equations
- N/A
Einstein's vacuum solution metric:
$$
ds^2 = -(1-\frac{2GM}{r})dt^2 +(1-\frac{2GM}{r})^{-1}dr^2+r^2 d\Omega^2
$$
which ##g_{\mu \nu}## can be read off easily.
metric Killing vectors are:
$$
K = \partial_t
$$$$
R = \partial_\phi
$$
How can I relate these to Maxwell equation?
$$
ds^2 = -(1-\frac{2GM}{r})dt^2 +(1-\frac{2GM}{r})^{-1}dr^2+r^2 d\Omega^2
$$
which ##g_{\mu \nu}## can be read off easily.
metric Killing vectors are:
$$
K = \partial_t
$$$$
R = \partial_\phi
$$
How can I relate these to Maxwell equation?
Last edited: