# Photon sphere uniqueness in higher-dimensional electrovacuum spacetimes

@article{Jahns2019PhotonSU, title={Photon sphere uniqueness in higher-dimensional electrovacuum spacetimes}, author={Sophia Jahns}, journal={Classical and Quantum Gravity}, year={2019}, volume={36} }

We show a uniqueness result for the n-dimensional spatial Reissner–Nordström manifold: a static, electrovacuum, asymptotically flat system which is asymptotically Reissner–Nordström is a subextremal Reissner–Nordström manifold with positive mass, provided that its inner boundary is a (possibly disconnected) photon sphere that fulfils a suitably defined quasilocal subextremality condition. Our result implies a number of earlier uniqueness results for the Schwarzschild and the Reissner–Nordström…

## 8 Citations

### Photon surfaces with equipotential time slices

- Physics, Mathematics
- 2019

Photon surfaces are timelike, totally umbilic hypersurfaces of Lorentzian spacetimes. In the first part of this paper, we locally characterize all possible photon surfaces in a class of static,…

### A spinorial proof of the rigidity of the Riemannian Schwarzschild manifold

- Mathematics
- 2020

We revisit and generalize a recent result of Cederbaum (Cederbaum in preparation; Cederbaum 2017 Oberwolfach Report) concerning the rigidity of the Schwarzschild manifold for spin manifolds. This…

### Classification of static asymptotically flat spacetimes with a photon sphere in Einstein-multiple-scalar field theory

- Mathematics, PhysicsPhysical Review D
- 2021

In the present paper we consider the Einstein-multiple-scalar field theory. When the target space of the scalar fields is a complete, simply connected Riemannian manifold with non-positive sectional…

### Mean-stable surfaces in Static Einstein-Maxwell theory

- Mathematics
- 2021

In this paper we use the theory of mean-stable surfaces (stable minimal surfaces included) to explore the static Einstein-Maxwell space-time. We ﬁrst prove that the zero set of the lapse function…

### A Minkowski inequality for the static Einstein-Maxwell space-time.

- Mathematics
- 2020

In this paper we prove a Minkowski-like inequality for an asymptotically flat static Einstein-Maxwell (electrostatic) space-time with bounded scalar curvature using as approach the inverse mean…

### Static Einstein–Maxwell space-time invariant by translation

- MathematicsGeneral Relativity and Gravitation
- 2021

In this paper we study the static Einstein-Maxwell space-time when the spatial factor is conformal to an $n$-dimensional pseudo-Euclidean space, which is invariant under the action of an…

### On static manifolds satisfying an overdetermined Robin type condition on the boundary

- Mathematics
- 2022

. In this work, we consider static manifolds M with nonempty boundary ∂M . In this case, we suppose that the potential V also satisﬁes an overdetermined Robin type condition on ∂M . We prove a…

## References

SHOWING 1-10 OF 21 REFERENCES

### Uniqueness of photon spheres in electro-vacuum spacetimes

- Physics
- 2015

In a recent paper (Cederbaum C and Galloway G J 2015 Commun. Analysis Geom. at press), the authors established the uniqueness of photon spheres in static vacuum asymptotically flat spacetimes by…

### Uniqueness of the static Einstein–Maxwell spacetimes with a photon sphere

- Physics, Mathematics
- 2015

We consider the problem of uniqueness of static and asymptotically flat Einstein–Maxwell spacetimes with a photon sphere P3. We are using a naturally modified definition of a photon sphere for…

### Uniqueness of photon spheres via positive mass rigidity

- Mathematics
- 2015

In a recent paper the first author established the uniqueness of photon spheres, suitably defined, in static vacuum asymptotically flat spacetimes by adapting Israel's proof of static black hole…

### The geometry of photon surfaces

- Physics
- 2000

The photon sphere concept in Schwarzschild space–time is generalized to a definition of a photon surface in an arbitrary space–time. A photon sphere is then defined as an SO(3)×R-invariant photon…

### No static bubbling spacetimes in higher dimensional Einstein–Maxwell theory

- Physics, Mathematics
- 2017

We prove that any asymptotically flat static spacetime in higher dimensional Einstein–Maxwell theory must have no magnetic field. This implies that there are no static soliton spacetimes and…

### Event Horizons in Static Vacuum Space-Times

- Physics
- 1967

The following theorem is established. Among all static, asymptotically flat vacuum space-times with closed simply connected equipotential surfaces ${g}_{00}=\mathrm{constant}$, the Schwarzschild…

### A new uniqueness theorem for charged black holes

- Physics
- 1988

It is shown that the unique non-degenerate electrovac static black hole metrics are the Reissner-Nordstrom family. The author does not assume the connectedness of the event horizon. Thus static…

### The classification of static vacuum spacetimes containing an asymptotically flat spacelike hypersurface with compact interior

- Physics, Mathematics
- 1999

We prove non-existence of static, vacuum, appropriately regular, asymptotically flat black hole spacetimes with degenerate (not necessarily connected) components of the event horizon. This finishes…

### Uniqueness of photon spheres in static vacuum asymptotically flat spacetimes

- Physics
- 2014

Adapting Israel's proof of static black hole uniqueness, we show that the Schwarzschild spacetime is the only static vacuum asymptotically flat spacetime that possesses a suitably defined photon…

### Variational and rigidity properties of static potentials

- Mathematics
- 2014

In this paper we study some global properties of static potentials on asymptotically flat $3$-manifolds $(M,g)$ in the nonvacuum setting. Heuristically, a static potential $f$ represents the (signed)…