Journal
CLASSICAL AND QUANTUM GRAVITY
Volume 32, Issue 16, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/0264-9381/32/16/165021
Keywords
photon sphere; Einstein; Maxwell; uniqueness
Categories
Funding
- Research Group Linkage Programme of the Alexander von Humboldt Foundation
- COST Action [MP1304]
- Bulgarian NSF [DFNI T02/6]
- Sofia University Research Grant [N70/2015]
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We consider the problem of uniqueness of static and asymptotically flat Einstein-Maxwell spacetimes with a photon sphere P-3. We are using a naturally modified definition of a photon sphere for electrically charged spacetimes with the additional property that the one-form t(xi) F is normal to the photon sphere. For simplicity we are restricting ourselves to the case of zero magnetic charge and assume that the lapse function regularly foliates the spacetime outside the photon sphere. With this information we prove that P-3 has constant mean curvature and constant scalar curvature. We also derive a few equations which we later use to prove the main uniqueness theorem, i.e. the static asymptotically flat Einstein-Maxwell spacetimes with a non-extremal photon sphere are isometric to the Reissner-Nordstrom one with mass M and electric charge Q subject to Q(2)/M-2 <= 9/8.
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