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Photon surfaces with equipotential time-slices
Carla Cederbaum, Gregory J. Galloway
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 cla…
A flow approach to Bartnik's static metric extension conjecture in axisymmetry
Carla Cederbaum, Oliver Rinne, Markus Strehlau
We investigate Bartnik's static metric extension conjecture under the additional assumption of axisymmetry of both the given Bartnik data and the desired static extensions. To do s…
A survey on extensions of Riemannian manifolds and Bartnik mass estimates
Armando J. Cabrera Pacheco, Carla Cederbaum
Mantoulidis and Schoen developed a novel technique to handcraft asymptotically flat extensions of Riemannian manifolds , with satisfying $λ_1 = λ_1(-Δ_…
Geometry and topology of the Kerr photon region in the phase space
Carla Cederbaum, Sophia Jahns
We study the set of trapped photons of a subcritical (a<M) Kerr spacetime as a subset of the phase space. First, we present an explicit proof that the photons of constant Boyer--Li…
Asymptotically flat extensions with charge
Aghil Alaee, Armando J. Cabrera Pacheco, Carla Cederbaum
The Bartnik mass is a notion of quasi-local mass which is remarkably difficult to compute. Mantoulidis and Schoen [2016] developed a novel technique to construct asymptotically fla…
Asymptotically hyperbolic extensions and an analogue of the Bartnik mass
Armando J. Cabrera Pacheco, Carla Cederbaum, Stephen McCormick
The Bartnik mass is a quasi-local mass tailored to asymptotically flat Riemannian manifolds with non-negative scalar curvature. From the perspective of general relativity, these mo…