Does anybody know what the electromagnetic field of a charged rotating sphere in five dimensional Maxwell-Chern-Simons theory is?
This theory has action
\begin{equation*} S = - \frac{1}{4} \int d^5 x \sqrt{|g|} F_{\mu\nu}F^{\mu\nu} + \lambda \int A \wedge F \wedge F + \int d^5 x \sqrt{|g|} j^{\mu} A_{\mu} \end{equation*}
The first term is the usual Maxwell action, the second term is the Chern-Simons term, $\lambda$ is a dimensionless constant.
I can write the field as a series in $\lambda$ (see this link for details) , but I do not know if there is a closed form formula if $ \lambda \neq 0$. Any help would be appreciated!
