Slice-reducible conformal Killing tensors, photon surfaces and shadows

Abstract

We generalize our recent method for constructing Killing tensors of the second rank to conformal Killing tensors. The method is intended for foliated spacetimes of arbitrary dimension $m$, which have a set of conformal Killing vectors. It applies to foliations of a more general structure than in previous literature. The basic idea is to start with reducible Killing tensors in slices constructed from a set of conformal Killing vectors and the induced metric, and then lift them to the whole manifold. Integrability conditions are derived that ensure this, and a constructive lifting procedure is presented. The resulting conformal Killing tensor may be irreducible. It is shown that subdomains of foliation slices suitable for the method are fundamental photon surfaces if some additional photon region inequality is satisfied. Thus our procedure also opens the way to obtain a simple general analytical expression for the boundary of the gravitational shadow. We apply this technique to electrovacuum, and $\mathcal{N}=2,4,8$ supergravity black holes, providing a new easy way to establish the existence of exact and conformal Killing tensors.

44 pages, revtex4

References in corpus (25)

• Calculating black hole shadows: Review of analytical studies
• Chaotic lensing around boson stars and Kerr black holes with scalar hair
• Fundamental photon orbits: black hole shadows and spacetime instabilities
• Classification of the Weyl Tensor in Higher Dimensions and Applications
• Gravitational lensing in the Simpson-Visser black-bounce spacetime in a strong deflection limit
• Spherical orbits around a Kerr black hole
• Hidden Symmetries of Dynamics in Classical and Quantum Physics
• Shadows of parametrized axially symmetric black holes allowing for separation of variables
• On conformal Killing-Yano tensors for Plebanski-Demianski family of solutions
• Free motion around black holes with discs or rings: between integrability and chaos - I
• Aspherical Photon and Anti-Photon Surfaces
• Generalized hidden symmetries and the Kerr-Sen black hole
• Black Hole Shadows and Invariant Phase Space Structures
• Gravitational lensing by a photon sphere in a Reissner-Nordström naked singularity spacetime in strong deflection limits
• Completing characterization of photon orbits in Kerr and Kerr-Newman metrics
• Deflection angle of a light ray reflected by a general marginally unstable photon sphere in a strong deflection limit
• Dynamical photon sphere and time evolving shadow around black holes with temporal accretion
• Uniqueness of static photon surfaces: Perturbative approach
• Photon surfaces in less symmetric spacetimes
• Killing tensors and photon surfaces in foliated spacetimes
• On Kerr black hole deformations admitting a Carter constant and an invariant criterion for the separability of the wave equation
• Emissions of photons near the horizons of Kerr-Sen black holes
• Retrolensing by light rays slightly inside and outside of a photon sphere around a Reissner-Nordström naked singularity
• Classification of static asymptotically flat spacetimes with a photon sphere in Einstein-multiple-scalar field theory
• Schouten-Nijenhuis bracket of Killing-Yano tensors for Kimura IIC metric