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For a spacelike 2-surface in spacetime, we propose a new definition of quasi-local angular momentum and quasi-local center of mass, as an element in the dual space of the Lie algebra of the Lorentz group. Together with previous defined…

Differential Geometry · Mathematics 2014-01-30 Po-Ning Chen , Mu-Tao Wang , Shing-Tung Yau

A new generalization of the Hawking-Hayward quasilocal energy to scalar-tensor gravity is proposed without assuming symmetries, asymptotic flatness, or special spacetime metrics. The procedure followed is simple but powerful and consists of…

General Relativity and Quantum Cosmology · Physics 2016-02-10 Valerio Faraoni

We modify previous quasi-local mass definition. The new definition provides expressions of the quasi-local energy, the quasi-local linear momentum and the quasi-local mass. And they are equal to the ADM expressions at spatial infinity.…

General Relativity and Quantum Cosmology · Physics 2009-12-15 Xiao Zhang

A new notion of quasilocal mass is defined for generic, compact, two dimensional, spacelike surfaces in four dimensional spacetimes with negative cosmological constant. The definition is spinorial and based on work for vanishing…

General Relativity and Quantum Cosmology · Physics 2025-09-09 Virinchi Rallabhandi

We construct a Hamiltonian formulation of quasilocal general relativity using an extended phase space that includes boundary coordinates as configuration variables. This allows us to use Hamiltonian methods to derive an expression for the…

General Relativity and Quantum Cosmology · Physics 2008-11-26 Ivan S. Booth , Stephen Fairhurst

We analyse the definition of quasi-local energy in GR based on a Hamiltonian analysis of the Einstein-Hilbert action initiated by Brown-York. The role of the constraint equations, in particular the Hamiltonian constraint on the timelike…

General Relativity and Quantum Cosmology · Physics 2010-11-11 Michael T. Anderson

We study the limit of quasilocal energy defined in [7] and [8] for a family of spacelike 2-surfaces approaching null infinity of an asymptotically flat spacetime. It is shown that Lorentzian symmetry is recovered and an energy-momentum…

Differential Geometry · Mathematics 2015-05-18 PoNing Chen , Mu-Tao Wang , Shing-Tung Yau

The popular Hamilton-Jacobi method first proposed by Brown and York for defining quasilocal quantities such as energy for spatially bound regions assumes that the spatial boundary is orthogonal to the foliation of the spacetime. Such a…

General Relativity and Quantum Cosmology · Physics 2010-11-19 I. S. Booth , R. B. Mann

Consider the definition E of quasilocal energy stemming from the Hamilton-Jacobi method as applied to the canonical form of the gravitational action. We examine E in the standard "small-sphere limit," first considered by Horowitz and…

General Relativity and Quantum Cosmology · Physics 2016-08-25 J. D. Brown , S. R. Lau , J. W. York

We show that in a generic scalar-tensor theory of gravity, the ``referenced'' quasilocal mass of a spatially bounded region in a classical solution is invariant under conformal transformations of the spacetime metric. We first extend the…

General Relativity and Quantum Cosmology · Physics 2009-10-31 Sukanta Bose , Daksh Lohiya

We derive an expression for effective gravitational mass for any closed spacelike 2-surface. This effective gravitational energy is defined directly through the geometrical quantity of the freely falling 2-surface and thus is well adapted…

General Relativity and Quantum Cosmology · Physics 2015-06-25 Keita Ikumi , Tetsuya Shiromizu

A key test for any quasi-local energy in general relativity is that it be nonnegative and satisfy a rigidity property; if it vanishes, the region enclosed is flat. We show that the Hawking energy, when evaluated on its natural…

Mathematical Physics · Physics 2025-08-12 Alejandro Peñuela Diaz

In this article, we survey recent developments in defining the quasi-local mass in general relativity. We discuss various approaches and the properties and applications of the different definitions. Among the expected properties, we focus…

Differential Geometry · Mathematics 2014-11-25 Po-Ning Chen , Mu-Tao Wang

We present the gravitational action and Hamiltonian for a spatially bounded region of an eternal black hole. The Hamiltonian is of the general form $H=H_{+} - H_{-}$, where $H_{+}$ and $H_{-}$ are respectively the Hamiltonians for the…

General Relativity and Quantum Cosmology · Physics 2007-05-23 Valeri Frolov , Erik A. Martinez

We define a quasilocal energy of a compact manifold-with-boundary, relative to a background manifold. The construction uses spinors on one manifold and the pullback of dual spinors from the other manifold. We prove positivity results for…

Differential Geometry · Mathematics 2023-12-05 John Lott

A generalization of the Hawking-Hayward quasilocal mass to scalar-tensor gravity is compared, in vacuo and for asymptotically flat stationary geometries, with a recent multipole expansion of the gravitational field. The quasilocal mass seen…

General Relativity and Quantum Cosmology · Physics 2019-10-16 Valerio Faraoni , Jeremy Coté

In this paper we would have a brief overview of several proposals of quasilocal mass which are based on Hamiltonian formulation. We also show the positivity of the Wang-Yau energy under a more general condition. We then further study the…

Differential Geometry · Mathematics 2024-04-16 Tin-Yau Tsang

With the aid of a simple family of examples, we show that the quasi-local mass defined by Kijowski and Liu and Yau, and shown by Liu and Yau to be positive, may be strictly positive for space-like, topologically spherical 2-surfaces in flat…

General Relativity and Quantum Cosmology · Physics 2013-05-29 N. O'Murchadha , L. B. Szabados , K. P. Tod

We have proposed a program for determining the reference for the quasi-local energy defined in the covariant Hamiltonian formalism. Our program has been tested by applying it to the spherically symmetric spacetimes. With respect to…

General Relativity and Quantum Cosmology · Physics 2014-11-20 Chiang-Mei Chen , Jian-Liang Liu , James M. Nester , Ming-Fan Wu

We derive the gravitational Hamiltonian starting from the Gauss-Bonnet action, keeping track of all surface terms. This is done using the language of orthonormal frames and forms to keep things as tidy as possible. The surface terms in the…

General Relativity and Quantum Cosmology · Physics 2009-11-10 Antonio Padilla