Some globally conserved currents from generalized Killing vectors and scalar test fields

Abstract

In this article, I discuss the construction of some globally conserved currents that one can construct in the absence of a Killing vector. One is based on the Komar current, which is constructed from an arbitrary vector field and has an identically vanishing divergence. I obtain some expressions for Komar currents constructed from some generalizations of Killing vectors which may in principle be constructed in a generic spacetime. I then present an explicit example for an outgoing Vaidya spacetime which demonstrates that the resulting Komar currents can yield conserved quantities that behave in a manner expected for the energy contained in the outgoing radiation. Finally, I describe a method for constructing another class of (non-Komar) globally conserved currents using a scalar test field that satisfies an inhomogeneous wave equation, and discuss two examples; the first example may provide a useful framework for examining the arrow of time and its relationship to energy conditions, and the second yields (with appropriate initial conditions) a globally conserved energy- and momentumlike quantity that measures the degree to which a given spacetime deviates from symmetry.

8 pages. Matches published version

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Cited by in corpus (9)

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• Approximate Killing symmetries in non-perturbative quantum gravity
• Note on conserved currents in static Conformal Killing Gravity
• Thermodynamic stability implies causality
• Hidden Killing Fields, Geometric Symmetries and Black Hole Mergers
• Constructing $p,n$-forms from $p$-forms via the Hodge star operator and the exterior derivative
• Perturbations of the almost Killing equation and their implications
• Generalized Komar currents for vector fields
• Gradient conformal stationarity and the CMC condition in LRS spacetimes