2018/11/21 by Justin C. Feng · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Black Holes and Theoretical Physics #Classical mechanics #Conserved quantity #Cosmology and Gravitation Theories #Current (fluid) #Divergence (linguistics) #Geometry #Killing vector field #Mathematical physics #Mathematics #Physics #Quantum mechanics #Scalar (mathematics) #Scalar field #Spacetime #Theoretical physics #Vector field #gr-qc
paper · pdf · doi:10.1103/physrevd.98.104035
published as Phys. Rev. D 98, 104035 (2018) · 8 pages. Matches published version
openalex publication_date 2018/11/21 · arxiv created 2018/11/22 · arxiv updated 2018/11/26 · openalex created_date 2018/11/29 · openalex updated_date 2026/08/06
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.