Existence of gradient CKV and gradient conformally stationary LRS spacetimes
arXiv:2305.05148 · doi:10.1140/epjc/s10052-024-12425-1
Abstract
In this work, we study the existence of gradient (proper) CKVs in locally rotationally symmetric spacetimes (LRS), those CKVs in the space spanned by the tangent to observers' congruence and the preferred spatial direction, allowing us to provide a (partial) characterization of gradient conformally static (GCSt) LRS solutions. Irrrotational solutions with non-zero spatial twist admit an irrotational timelike gradient conformal Killing vector field and hence are GCSt. In the case that both the vorticity and twist vanish, that is, restricting to the LRS II subclass, we obtain the necessary and sufficient condition for the spacetime to admit a gradient CKV. This is given by a single wave-like PDE, whose solutions are in bijection to the gradient CKVs on the spacetime. We then introduce a characterization of these spacetimes as GCSt using the character of the divergence of the CKV, provided that the metric functions of the spacetimes obey certain inequalities.
arXiv comment15 pages, no figure, moderate modifications of the Introduction and Discussion sections for clarity, additional references provided and discussed, accepted for publication in Eur. Phys. J. C
References in corpus (14)
- Generalized Robertson-Walker space times, a survey
- A covariant approach for perturbations of rotationally symmetric spacetimes
- Covariant Perturbations of Schwarzschild Black Holes
- Marginally trapped tubes and dynamical horizons
- Killing Initial Data
- Killing Tensors and Conformal Killing Tensors from Conformal Killing Vectors
- Symmetries of Bianchi I space-times
- Exact solutions of Bianchi I spacetimes which admit Conformal Killing vectors
- New class of LRS spacetimes with simultaneous rotation and spatial twist
- Conformal Killing Initial Data
- Constructing the CKVs of Bianchi III and V spacetimes
- Rotating and twisting locally rotationally symmetric imperfect fluids
- What makes a shear-free spherical perfect fluid be inhomogeneous with tidal effects?
- Closed conformal Killing-Yano initial data