Stable photon orbits in stationary axisymmetric spacetimes with an electromagnetic field and a cosmological constant

Abstract

Stable light rings, which are associated with spacetime instabilities, are known to exist in four-dimensional stationary axisymmetric spacetimes that solve the Einstein-Maxwell equations (so-called electrovacuum solutions, with Faraday tensor $F_{\mu \nu }\ne 0$); however, they are not permitted in pure vacuum ($F_{\mu \nu }=0$). In this work, we extend this result to spacetimes with a non-zero cosmological constant $\Lambda$. In particular, we demonstrate that stable light rings are permitted in $\Lambda$-electrovacuum ($F_{\mu \nu }\ne 0$, $\Lambda \ne 0$), but ruled out in $\Lambda$-vacuum ($F_{\mu \nu }=0$, $\Lambda \ne 0$).

arXiv comment6 pages, 1 figure. Minor corrections and improvements. Matches journal version

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