Uniqueness of the static Einstein-Maxwell spacetimes with a photon sphere

Abstract

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 ${\iota }_{\xi }F$ 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-Nordström one with mass $M$ and electric charge $Q$ subject to $\frac{Q^2}{M^2}\le \frac{9}{8}$.

13 pages

References in corpus (6)

• Relativistic images of Schwarzschild black hole lensing
• Time delay and magnification centroid due to gravitational lensing by black holes and naked singularities
• Light rings as observational evidence for event horizons: long-lived modes, ergoregions and nonlinear instabilities of ultracompact objects
• Connection between black-hole quasinormal modes and lensing in the strong deflection limit
• Unstable circular null geodesics of static spherically symmetric black holes, Regge poles and quasinormal frequencies
• Thermodynamics of quantum photon spheres

Cited by in corpus (27)

• Calculating black hole shadows: Review of analytical studies
• Uniqueness of photon spheres in electro-vacuum spacetimes
• Observational signatures of strongly naked singularities: image of the thin accretion disk
• Aspherical Photon and Anti-Photon Surfaces
• Extension of photon surfaces and their area: Static and stationary spacetimes
• Transversely trapping surfaces: Dynamical version
• Completing characterization of photon orbits in Kerr and Kerr-Newman metrics
• Metamorphoses of a photon sphere
• Photon trapping in static axially symmetric spacetime
• Uniqueness of static photon surfaces: Perturbative approach
• Classification of the static and asymptotically flat Einstein-Maxwell-dilaton spacetimes with a photon sphere
• Photon regions and umbilic conditions in stationary axisymmetric spacetimes
• Quasi-local photon surfaces in general spherically symmetric spacetimes
• Killing tensors and photon surfaces in foliated spacetimes
• Photon surfaces with equipotential time-slices
• Slice-reducible conformal Killing tensors, photon surfaces and shadows
• Photon sphere uniqueness in higher-dimensional electrovacuum spacetimes
• Classification of static asymptotically flat spacetimes with a photon sphere in Einstein-multiple-scalar field theory
• Geometry and topology of the Kerr photon region in the phase space
• Uniqueness of photon sphere for Reissner-Nordström electric-magnetic system
• Black Hole and Equipotential Photon Surface Uniqueness in 4-dimensional Asymptotically Flat Electrostatic Electro-Vacuum Spacetimes
• Higher-dimensional electric-magnetic photon sphere uniqueness
• Static Einstein-Maxwell space-time invariant by translation
• A Minkowski inequality for the static Einstein-Maxwell space-time
• Uniqueness of electric-magnetic spacetimes with massive particle
• Uniqueness of equipotential photon surfaces in 4-dimensional static vacuum asymptotically flat spacetimes for positive, negative, and zero mass -- and a new partial proof of the Willmore inequality
• A Penrose-type inequality for static spacetimes