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arXiv · 1312.3466

Almost-Killing conserved currents: a general mass function

Milton Ruiz·Carlos Palenzuela·Carles Bona
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Abstract

A new class of conserved currents, describing non-gravitational energy-momentum density, is presented. The proposed currents do not require the existence of a (timelike) Killing vector, and are not restricted to spherically symmetric spacetimes (or similar ones, in which the Kodama vector can be defined). They are based instead on almost-Killing vectors, which could in principle be defined on generic spacetimes. We provide local arguments, based on energy density profiles in highly simplified (stationary, rigidly-rotating) star models, which confirm the physical interest of these 'almost-Killing currents'. A mass function is defined in this way for the spherical case, qualitatively different from the Hern\'andez-Misner mass function. An elliptic equation determining the new mass function is derived for the Tolman-Bondi spherically symmetric dust metrics, including a simple solution for the Oppenheimer-Schneider collapse. The equations for the non-symmetric case are shown to be of a mixed elliptic-hyperbolic nature.

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Milton Ruiz, Carlos Palenzuela, Carles Bona. 2013-12-12. Almost-Killing conserved currents: a general mass function. https://doi.org/10.1103/physrevd.89.025011

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