6533b839fe1ef96bd12a5c05
RESEARCH PRODUCT
Almost-Killing conserved currents: A general mass function
Carles BonaCarlos PalenzuelaMilton Ruizsubject
Physics83C40AstrofísicaNuclear and High Energy PhysicsCollapse (topology)FOS: Physical sciencesFunction (mathematics)General Relativity and Quantum Cosmology (gr-qc)Star (graph theory)General Relativity and Quantum CosmologyNumerical relativityElliptic curveKilling vector fieldGeneral Relativity and Quantum CosmologyClassical mechanicsSimple (abstract algebra)Energy densitydescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2013-12-12 |