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We compute the energy of 2+1 Minkowski space from a covariant action principle. Using Ashtekar and Varadarajan's characterization of 2+1 asymptotic flatness, we first show that the 2+1 Einstein-Hilbert action with Gibbons-Hawking boundary…

High Energy Physics - Theory · Physics 2008-11-26 Donald Marolf , Leonardo Patiño

Hawking's quasi-local energy definition quantifies the energy enclosed by a spacelike 2-sphere in terms of the amount of lightbending on the sphere caused by the energy distribution inside the sphere. This paper establishes for the first…

General Relativity and Quantum Cosmology · Physics 2023-08-16 Dennis Stock , Enea Di Dio , Ruth Durrer

We review Wang-Yau quasi-local definitions along the line of gravitational Hamiltonian. This makes clear the connection and difference between Wang-Yau definition and Brown-York or even global ADM definition. We make a brief comment on…

General Relativity and Quantum Cosmology · Physics 2026-01-06 Bowen Zhao , Lars Andersson , Shing-Tung Yau

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 conditions for the existence of horizons for…

Differential Geometry · Mathematics 2007-05-23 Yuguang Shi , Luen-Fai Tam

In this paper, we prove the following theorem regarding the Wang-Yau quasi-local energy of a spacelike two-surface in a spacetime: Let $\Sigma$ be a boundary component of some compact, time-symmetric, spacelike hypersurface $\Omega$ in a…

Differential Geometry · Mathematics 2011-05-18 Pengzi Miao , Luen-Fai Tam , Naqing Xie

We study a notion of relative entropy for certain hypersurfaces in hyperbolic space. We relate this quantity to the renormalized area introduced by Graham-Witten[RW99]. We also obtain a monotonicity formula for relative entropy applied to…

Differential Geometry · Mathematics 2022-06-28 Junfu Yao

In this note, we compute the limit of the Wang-Yau quasi-local mass on unit spheres at spatial infinity of an asymptotically flat initial data set. Similar to the small sphere limit of the Wang-Yau quasi-local mass, we prove that the…

General Relativity and Quantum Cosmology · Physics 2019-01-23 Po-Ning Chen , Mu-Tao Wang , Ye-Kai Wang , Shing-Tung Yau

Gauge invariant, Hamiltonian formulation of field dynamics within a compact region $\Sigma$ with boundary $\partial \Sigma$ is given for the gravitational field linearized over a Kottler metric. The boundary conditions which make the system…

General Relativity and Quantum Cosmology · Physics 2021-01-18 Jacek Jezierski , Jerzy Kijowski , Piotr Waluk

We provide a space-time covariant Hamiltonian treatment for a finite-range gravitational theory. The Kuchar approach is used to demonstrate the bimetric picture of space-time in its most transparent form. This Hamiltonian formalism is…

General Relativity and Quantum Cosmology · Physics 2011-06-29 V. O. Soloviev , M. V. Tchichikina

In any static spacetime the quasi-local Tolman mass contained within a volume can be reduced to a Gauss-like surface integral involving the flux of a suitably defined generalized surface gravity. By introducing some basic thermodynamics and…

General Relativity and Quantum Cosmology · Physics 2014-11-21 Gabriel Abreu , Matt Visser

We apply the Hawking-Hayward quasi-local energy construct to obtain in a rigorous way the turnaround radius of cosmic structures in General Relativity. A splitting of this quasi-local mass into local and cosmological parts describes the…

General Relativity and Quantum Cosmology · Physics 2015-10-14 Valerio Faraoni , Marianne Lapierre-Léonard , Angus Prain

We extend the quasilocal (metric-based) Hamiltonian formulation of general relativity so that it may be used to study regions of spacetime with null boundaries. In particular we use this generalized Brown-York formalism to study the physics…

General Relativity and Quantum Cosmology · Physics 2009-11-07 Ivan S. Booth

Quasilocal definitions of stress-energy-momentum---that is, in the form of boundary densities (in lieu of local volume densities)---have proven generally very useful in formulating and applying conservation laws in general relativity. In…

General Relativity and Quantum Cosmology · Physics 2021-02-03 Marius Oltean , Hossein Bazrafshan Moghaddam , Richard J. Epp

We investigate measures of distance and redshift in cosmological space-times that admit a shear-free foliation, which we henceforth refer to as `quasi-Newtonian'. Space expands isotropically in this description, and small-scale…

General Relativity and Quantum Cosmology · Physics 2026-04-10 Asta Heinesen , Davide Fontana , Timothy Clifton

Owing to its transformation property under local boosts, the Brown-York quasilocal energy surface density is the analogue of E in the special relativity formula: E^2-p^2=m^2. In this paper I will motivate the general relativistic version of…

General Relativity and Quantum Cosmology · Physics 2009-10-31 Richard J. Epp

We study the aspects of quasi-local energy associated with a $2-$surface $\Sigma$ bounding a space-like domain $\Omega$ of a physical $3+1$ dimensional spacetime in the regime of gravity coupled to a gauge field. The Wang-Yau quasi-local…

General Relativity and Quantum Cosmology · Physics 2022-06-15 Puskar Mondal , Shing-Tung Yau

In any static spacetime the quasilocal Tolman mass contained within a volume can be reduced to a Gauss-like surface integral involving the flux of a suitably defined generalized surface gravity. By introducing some basic thermodynamics, and…

General Relativity and Quantum Cosmology · Physics 2011-09-28 Gabriel Abreu , Matt Visser

We show that the quotient associated to a quasi-Hamiltonian space has a symplectic structure even when 1 is not a regular value of the momentum map: it is a disjoint union of symplectic manifolds of possibly different dimensions, which…

Symplectic Geometry · Mathematics 2017-08-23 Florent Schaffhauser

Physicists believe, with some justification, that there should be a correspondence between familiar properties of Newtonian gravity and properties of solutions of the Einstein equations. The Positive Mass Theorem (PMT), first proved over…

Differential Geometry · Mathematics 2007-05-23 Robert Bartnik

Based on the isoperimetric inequality, G. Huisken proposed a definition of total mass in general relativity that is equivalent to the ADM mass for (smooth) asymptotically flat 3-manifolds of nonnegative scalar curvature, but that is…

Differential Geometry · Mathematics 2020-02-21 Jeffrey L. Jauregui