Geometric Inequalities for Quasi-Local Masses
arXiv:1910.07081 · doi:10.1007/s00220-020-03733-0
Abstract
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. In addition, we give a new proof of the positivity property for the Wang-Yau mass which is used to remove the spin condition in higher dimensions. Furthermore, we generalize a recent result of Lu and Miao to obtain a localized version of the Penrose inequality for the static Wang-Yau mass.
arXiv comment37 pages
References in corpus (24)
- Quasilocal Energy and Conserved Charges Derived from the Gravitational Action
- Positivity of Quasilocal Mass
- Quasilocal mass in general relativity
- Isometric embeddings into the Minkowski space and new quasi-local mass
- The area of horizons and the trapped region
- Mass and angular-momentum inequalities for axi-symmetric initial data sets. II. Angular-momentum
- On the Penrose Inequality for Charged Black Holes
- Black hole polarization and new entropy bounds
- Area-charge inequality for black holes
- A comment on Liu and Yau's positive quasi-local mass
- Conserved quantities in general relativity: from the quasi-local level to spatial infinity
- Improved Upper Bound to the Entropy of a Charged System
- Universal Entropy Bound for Rotating Systems
- The Jang equation reduction of the spacetime positive energy theorem in dimensions less than eight
- Convexity of reduced energy and mass angular momentum inequalities
- Proof of the area-angular momentum-charge inequality for axisymmetric black holes
- On a Localized Riemannian Penrose Inequality
- Minimizing properties of critical points of quasi-local energy
- Bekenstein bounds and inequalities between size, charge, angular momentum and energy for bodies
- Bekenstein Bounds, Penrose Inequalities, and Black Hole Formation
- Penrose-like inequality with angular momentum for minimal surfaces
- A Penrose-Like Inequality with Charge
- Size, angular momentum and mass for objects
- A Penrose-Type Inequality with Angular Momentum and Charge for Axisymmetric Initial Data