Geometrical origin of the Kodama vector
arXiv:2402.16484 · doi:10.1103/PhysRevD.110.044056
Abstract
It has been known that warped-product spacetimes such as spherically symmetric ones admit the Kodama vector. This vector provides a locally conserved current made by contraction of the Einstein tensor, even though there is no Killing vector. In addition, a quasilocal mass, Birkhoff's theorem and various properties are closely related to the Kodama vector. Recently, it is shown that the notion of the Kodama vector can be extended to three-dimensional axisymmetric spacetimes even if the spacetimes are not warped product. This implies that warped product may not be a necessary condition for a spacetime to admit the Kodama vector. We show properties of the Kodama vector originate from the conformal Killing-Yano 2-form. In particular, the well-known spacetimes that admit the Kodama vector have a closed conformal Killing-Yano 2-form. Furthermore, we show the Kodama vector provides local conserved currents for each order of the Lovelock tensor as well as the Einstein tensor.
arXiv comment10 pages; v2: minor changes, appendix B and references added; v3: published in PRD
References in corpus (30)
- Gravitational Energy in Spherical Symmetry
- Smarr Formula and an Extended First Law for Lovelock Gravity
- Lanczos-Lovelock models of gravity
- Black holes, hidden symmetries, and complete integrability
- Generalized Misner-Sharp quasi-local mass in Einstein-Gauss-Bonnet gravity
- Holography of Gravitational Action Functionals
- Birkhoff's theorem in Lovelock gravity
- Komar Integrals in Higher (and Lower) Derivative Gravity
- Lovelock black holes with maximally symmetric horizons
- Characterization of the Lovelock gravity by Bianchi derivative
- Generalized Killing-Yano equations in D=5 gauged supergravity
- Generalized hidden symmetries and the Kerr-Sen black hole
- Conserved gravitational charges from Yano tensors
- Birkhoff for Lovelock Redux
- Conformal Yano-Killing tensor for the Kerr metric and conserved quantities
- CYK Tensors, Maxwell Field and Conserved Quantities for Spin-2 Field
- Birkhoff's Theorem in Lovelock Gravity for General Base Manifolds
- Lovelock black holes with non-constant curvature horizon
- New approach to conserved charges of generic gravity in AdS
- Conserved current for the Cotton tensor, black hole entropy and equivariant Pontryagin forms
- New currents with Killing-Yano tensors
- Extension of Kodama vector and quasilocal quantities in three-dimensional axisymmetric spacetimes
- Warped Product Space-times
- Killing-Yano forms and Killing tensors on a warped space
- Killing-Yano Cotton Currents
- Fully constrained, high-resolution shock-capturing, formulation of the Einstein-fluid equations in dimensions
- Field-theoretical construction of currents and superpotentials in Lovelock gravity
- Geometry, conformal Killing-Yano tensors and conserved "currents"
- Birkhoff theorem and conformal Killing-Yano tensors
- A Systematic Construction of Kastor-Traschen Currents and their Extensions to Generic Powers of Curvature
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