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On the Bartnik mass of apparent horizons
Christos Mantoulidis and Richard Schoen 2015 Class. Quantum Grav. 32 205002
In our latest CQG paper we study the geometry (i.e. curvature) of apparent horizons and its relationship with ADM mass.
We were motivated by the following two foundational results in the theory of black holes in asymptotically flat initial data sets (slices of spacetime) satisfying the dominant energy condition (DEC):
- Apparent horizons are topologically equivalent to (one or more) two-dimensional spheres.(1)
- When the initial data set is additionally time symmetric (totally geodesic in spacetime), the apparent horizon’s total area is bounded from above by the slice’s ADM mass per . This is called the Penrose inequality.(2) Equality is only achieved on Schwarzschild data, whose apparent horizon is a single sphere with constant Gauss curvature.
One then naturally wonders: Continue reading