The curvature on a black hole boundary

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Read the full article for free* in Classical and Quantum Gravity:
On the Bartnik mass of apparent horizons
Christos Mantoulidis and Richard Schoen 2015 Class. Quantum Grav. 32 205002
arXiv:1412.0382
*until 04/11/15

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Christos Mantoulidis is a graduate student in Mathematics at Stanford University.

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):

1. Apparent horizons are topologically equivalent to (one or more) two-dimensional spheres.⁽¹⁾
2. 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:

The return of Newton-Cartan geometry

Jelle Hartong is a postdoctoral researcher at the Université Libre de Bruxelles. His research concerns the foundations and applications of various non-AdS holographies and non-relativistic gravity.

Non-relativistic field theories defined on Newton-Cartan Geometry and its extension called Torsional Newton-Cartan Geometry, have (re-)appeared in recent studies of non-AdS holography and condensed matter physics.

Relativistic, Poincaré invariant, field theories are defined on Minkowski space-time. This flat background can be turned into a curved geometry by coupling the theory to a Lorentzian metric as one does when adding matter to Einstein’s theory of gravity. There are many areas of physics, notably