Penrose-like inequality with angular momentum for minimal surfaces

@article{Anglada2017PenroselikeIW,
  title={Penrose-like inequality with angular momentum for minimal surfaces},
  author={Pablo Anglada},
  journal={Classical and Quantum Gravity},
  year={2017},
  volume={35}
}
  • Pablo Anglada
  • Published 15 August 2017
  • Mathematics, Physics
  • Classical and Quantum Gravity
In axially symmetric spacetimes the Penrose inequality can be strengthened to include angular momentum. We prove a version of this inequality for minimal surfaces, more precisely, a lower bound for the ADM mass in terms of the area of a minimal surface, the angular momentum and a particular measure of the surface size. We consider axially symmetric and asymptotically flat initial data, and use the monotonicity of the Geroch quasi-local energy on 2-surfaces along the inverse mean curvature flow. 
Penrose-like inequality with angular momentum for general horizons
In axially symmetric space-times it is expected that the Penrose inequality can be strengthened to include angular momentum. In a recent work [2] we have proved a weaker version of this inequality
A Penrose-type inequality with angular momentum and charge for axisymmetric initial data
A lower bound for the ADM mass is established in terms of angular momentum, charge, and horizon area in the context of maximal, axisymmetric initial data for the Einstein-Maxwell equations which
Comments on Penrose inequality with angular momentum for outermost apparent horizons
In a recent work we have proved a weaker version of the Penrose inequality with angular momentum, in axially symmetric space-times, for a compact and connected minimal surface. In this previous work
Bekenstein bounds, Penrose inequalities, and black hole formation
A universal geometric inequality for bodies relating energy, size, angular momentum, and charge is naturally implied by Bekenstein's entropy bounds. We establish versions of this inequality for
Geometric Inequalities for Quasi-Local Masses
In this paper lower bounds are obtained for quasi-local masses in terms of charge, angular momentum, and horizon area. In particular we treat three quasi-local masses based on a Hamiltonian approach,
Refined inequalities for a loosely trapped surface and attractive gravity probe surface
where m is the Arnowitt-Deser-Misner (ADM) mass. The inequality for an LTS has also been examined in the Einstein-Maxwell system [3]. This is regarded as an analogy of the Penrose inequality [4]
The Charged Penrose Inequality for Manifolds with Cylindrical Ends and Related Inequalities
of the Dissertation The Charged Penrose Inequality for Manifolds with Cylindrical Ends and Related Inequalities
Desigualdades geométricas para objetos en relatividad general
Fil: Anglada, Pablo Ruben. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnologico Conicet - Cordoba. Instituto de Fisica Enrique Gaviola. Universidad Nacional de
Recent Developments in the Penrose Conjecture
We survey recent developments towards a proof of the Penrose conjecture and results on Penrose-type and other geometric inequalities for quasi-local masses in general relativity.
Extensions of the Mass Angular Momentum Inequality in Mathematical Relativity
of the Dissertation Extensions of the Mass Angular Momentum Inequality in Mathematical Relativity
...
...

References

SHOWING 1-10 OF 40 REFERENCES
Area-angular-momentum inequality for axisymmetric black holes.
TLDR
It is proved that the inequality A≥8π|J| is satisfied for any surface on complete asymptotically flat maximal axisymmetric data and holds for marginal or event horizons of black holes.
The inverse mean curvature flow and the Riemannian Penrose Inequality
Let M be an asymptotically flat 3-manifold of nonnegative scalar curvature. The Riemannian Penrose Inequality states that the area of an outermost minimal surface N in M is bounded by the ADM mass m
On the Penrose inequality for general horizons.
For asymptotically flat initial data of Einstein's equations satisfying an energy condition, we show that the Penrose inequality holds between the Arnowitt-Deser-Misner mass and the area of an
Size, angular momentum and mass for objects
We obtain a geometrical inequality involving the ADM mass, the angular momentum and the size of an ordinary, axially symmetric object. We use the monotonicity of the Geroch quasi-local energy on
Horizon area–angular momentum inequality for a class of axially symmetric black holes
We prove an inequality between horizon area and angular momentum for a class of axially symmetric black holes. This class includes initial conditions with an isometry which leaves fixed a
A Penrose-like inequality with charge
We establish a Penrose-like inequality for general (not necessarily time-symmetric) initial data sets of the Einstein–Maxwell equations, which satisfy the dominant energy condition. More precisely,
A Jang Equation Approach to the Penrose Inequality
We introduce a generalized version of the Jang equation, designed for the general case of the Penrose Inequality in the setting of an asymptotically flat space-like hypersurface of a spacetime
On the Penrose Inequality
We summarize results on the Penrose inequality bounding the ADM-mass or the Bondi mass in terms of the area of an outermost apparent horizon for asymptotically flat initial data of Einstein's
Inequality between size and angular momentum for bodies.
  • S. Dain
  • Physics
    Physical review letters
  • 2014
TLDR
A version of this inequality is proved, as consequence of the Einstein equations, for the case of rotating axially symmetric, constant density, bodies.
The Riemannian Penrose Inequality with Charge for Multiple Black Holes
We present the outline of a proof of the Riemannian Penrose in- equality with charge r ≤ m + m 2 − q 2 ,w hereA =4 πr 2 is the area of the outermost apparent horizon with possibly multiple connected
...
...