Abstract
The present status of the quasi-local mass, energy-momentum and angular-momentum constructions in general relativity is reviewed. First, the general ideas, concepts, and strategies, as well as the necessary tools to construct and analyze the quasi-local quantities, are recalled. Then, the various specific constructions and their properties (both successes and deficiencies are discussed. Finally, some of the (actual and potential) applications of the quasi-local concepts and specific constructions are briefly mentioned.
Highlights
The present status of the quasi-local mass, energy-momentum and angular-momentum constructions in general relativity is reviewed
PSa and JSa b may be interpreted as the quasi-local energy-momentum and angular momentum of the matter fields associated with the spacelike two-surface S, or, equivalently, to D(Σ)
Let the spacetime be asymptotically flat at future null infinity in the sense of Penrose [413, 414, 415, 426], i.e., the physical spacetime can be conformally compactified by an appropriate boundary I +
Summary
Recent developments of the field are included. A few subsections and more than fifty new references are added, minor improvements and corrections of the text are made at several points, and the bibliography is updated. Page 28: A new paragraph on a candidate for the total mass of closed universes is added. Page 50: A discussion of the monotonicity properties of the quasi-local mass expressions near spatial infinity, motivated by the compatibility with the post Newtonian limit is added. Page 51: A new paragraph on the incompatibility of the monotonicity of the quasi-local mass expressions and two ‘standard’ requirements is added. Page 102: New references on the initial boundary value problem and its potential connection with the quasi-local Hamiltonian approach are added. Page 103: The more detailed discussion of the role of the area 2-form (as a part of the boundary conditions) is given and new references are added. Page 118: A new paragraph on (and the reference to) a recent reformulation and its proof of Thorne’s hoop conjecture for spherically symmetric configurations is given. Page 123: A new Subsection 13.4.3 on a new entropy bound for uncollapsed bodies is added
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