Abstract
Abstract
Gauge invariant, Hamiltonian formulation of field dynamics within a compact region Σ with boundary ∂Σ is given for the gravitational field linearized over a Kottler metric. The boundary conditions which make the system autonomous are discussed. The corresponding Hamiltonian functional
H
Inv
uniquely describes the energy carried by the (linearized) gravitational field. It is shown that, under specific boundary conditions, the quasi-local Hawking mass
H
Haw
reduces to
H
Inv
in the weak field approximation. This observation is a quasi-local version of the classical Brill–Deser result (Brill and Deser 1968 Ann.Phys.(N.Y.)
50 3) and enables us to declare Hawking mass as the correct expression (at least up to quadratic terms in the Taylor expansion) for the quasi-local mass, which correctly describes energy carried by the gravitational field.
Subject
Physics and Astronomy (miscellaneous)
Cited by
3 articles.
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