Geometric Inequalities for Quasi-Local Masses

@article{Alaee2019GeometricIF,
  title={Geometric Inequalities for Quasi-Local Masses},
  author={Aghil Alaee and Marcus Khuri and Shing-Tung Yau},
  journal={arXiv: Differential Geometry},
  year={2019}
}
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, namely the Brown-York, Liu-Yau, and Wang-Yau masses. The geometric inequalities are motivated by analogous results for the ADM mass. They may be interpreted as localized versions of these inequalities, and are also closely tied to the conjectured Bekenstein bounds for entropy of macroscopic bodies… 
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References

SHOWING 1-10 OF 81 REFERENCES
A quasi-local Penrose inequality for the quasi-local energy with static references
  • Po-Ning Chen
  • Mathematics, Physics
    Transactions of the American Mathematical Society
  • 2020
The positive mass theorem is one of the fundamental results in general relativity. It states that, assuming the dominant energy condition, the total mass of an asymptotically flat spacetime is
Quasi-Local Mass and the Existence of Horizons
In this paper, we obtain lower bounds for the Brown-York quasilocal mass and the Bartnik quasilocal mass for compact three manifolds with smooth boundaries. As a consequence, we derive sufficient
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
Isometric Embeddings into the Minkowski Space and New Quasi-Local Mass
The definition of quasi-local mass for a bounded space-like region Ω in space-time is essential in several major unsettled problems in general relativity. The quasi-local mass is expected to be a
Convexity of Reduced Energy and Mass Angular Momentum Inequalities
In this paper, we extend the work in Chruściel and Costa (Class. Quant. Grav. 26:235013, 2009), Chruściel et al. (Ann. Phy. 323:2591–2613, 2008), Costa (J. Math. Theor. 43:285202, 2010), Dain (J.
The area-angular momentum-charge inequality for black holes with positive cosmological constant
We establish the conjectured area-angular momentum-charge inequality for stable apparent horizons in the presence of a positive cosmological constant, and show that it is saturated precisely for
On the Penrose inequality for charged black holes
Bray and Khuri (2011 Asian J. Math. 15 557–610; 2010 Discrete Continuous Dyn. Syst. A 27 741766) outlined an approach to prove the Penrose inequality for general initial data sets of the Einstein
Minimizing Properties of Critical Points of Quasi-Local Energy
In relativity, the energy of a moving particle depends on the observer, and the rest mass is the minimal energy seen among all observers. The Wang–Yau quasi-local mass for a surface in spacetime
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
Conserved Quantities in General Relativity: From the Quasi-Local Level to Spatial Infinity
We define quasi-local conserved quantities in general relativity by using the optimal isometric embedding in Wang and Yau (Commun Math Phys 288(3):919–942, 2009) to transplant Killing fields in the
...
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