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Ergoregions in Magnetised Black Hole Spacetimes

, : Ergoregions in Magnetised Black Hole Spacetimes.

The spacetimes obtained by Ernst's procedure for appending an externalmagnetic field $B$ to a seed Kerr-Newman black hole are commonly believed to beasymptotic to the static Melvin solution. We show that this is not in generaltrue. Unless the electric charge of the black hole satisfies $Q= jB(1+ 1/4 j^2B^4)$, where $j$ is the angular momentum of the original seed solution, anergoregion extends all the way from the black hole horizon to infinity. We givea self-contained account of the solution-generating procedure, includingincluding explicit formulae for the metric and the vector potential. In thecase when $Q= jB(1+ 1/4 j^2 B^4)$, we show that there is an arbitrariness inthe choice of asymptotically timelike Killing field $K_\Omega=\partial/\partial t+ \Omega \partial/\partial \phi$, because there is nocanonical choice of $\Omega$. For one choice, $\Omega=\Omega_s$, the metric isasymptotically static, and there is an ergoregion confined to the neighbourhoodof the horizon. On the other hand, by choosing $\Omega=\Omega_H$, so that$K_{\Omega_H}$ is co-rotating with the horizon, then for sufficiently large $B$numerical studies indicate there is no ergoregion at all. For smaller values,in a range $B_-


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