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Let $M$ be a locally rotationally symmetric spacetime, and $\xi^a$ a conformal Killing vector for the metric on $M$, lying in the subspace spanned by the unit timelike direction and the preferred spatial direction, and with non-constant…

General Relativity and Quantum Cosmology · Physics 2024-02-02 Abbas M. Sherif

In this short note, we verify explicitly in static coordinates that the non trivial asymptotic Killing vectors at spatial infinity for anti-de Sitter space-times correspond one to one to the conformal Killing vectors of the conformally flat…

General Relativity and Quantum Cosmology · Physics 2009-11-10 Glenn Barnich , Friedemann Brandt , Kim Claes

We study N=2 superconformal theories on Euclidean and Lorentzian four-manifolds with a view toward applications to holography and localization. The conditions for supersymmetry are equivalent to a set of differential constraints including a…

High Energy Physics - Theory · Physics 2015-06-16 Claudius Klare , Alberto Zaffaroni

Koutras has proposed some methods to construct reducible proper conformal Killing tensors and Killing tensors (which are, in general, irreducible) when a pair of orthogonal conformal Killing vectors exist in a given space. We give the…

General Relativity and Quantum Cosmology · Physics 2009-11-10 Raffaele Rani , S. Brian Edgar , Alan Barnes

Killing vectors play a crucial role in characterizing the symmetries of a given spacetime. However, realistic astrophysical systems are in most cases only approximately symmetric. Even in the case of an astrophysical black hole, one might…

General Relativity and Quantum Cosmology · Physics 2021-04-21 Sumanta Chakraborty , Justin C. Feng

We introduce Sinyukov-like tensors, a special kind of conformal Killing tensors. In Robertson-Walker space-times they have the perfect-fluid form and only depend on two constants and the scale factor. They are the candidate for the dark…

General Relativity and Quantum Cosmology · Physics 2024-09-13 Carlo Alberto Mantica , Luca Guido Molinari

It is well known that any 4-dimensional hyperkahler metric with two commuting Killing fields may be obtained explicitly, via the Gibbons-Hawking Ansatz, from a harmonic function invariant under a Killing field on R^3. In this paper, we find…

Differential Geometry · Mathematics 2007-05-23 David M. J. Calderbank , Henrik Pedersen

In this paper I show that the Newman-Tamburino spherical metrics always admit a Killing vector, correcting a claim by Collinson and French, (1967 J. Math. Phys. 8 701) and also admit a homothety. A similar calculation is given for the limit…

General Relativity and Quantum Cosmology · Physics 2007-05-23 John D. Steele

The existence of symmetries in asymptotically flat space-times are studied from the point of view of initial value problems. General necessary and sufficient (implicit) conditions are given for the existence of Killing vector fields in the…

General Relativity and Quantum Cosmology · Physics 2009-10-31 Janos Kannar

We consider the problem of picking a physically motivated vacuum state on a spherically symmetric spacetime with an extra conformal Killing vector, as opposed to an extra Killing vector as in the Schwarzschild case. Considering a conformal…

General Relativity and Quantum Cosmology · Physics 2014-03-07 Alex Venditti , Charles Dyer

We introduce the notion of metric Lie algebras of Killing type, which are characterized by the fact that all conformal Killing symmetric tensors are sums of Killing tensors and multiples of the metric tensor. We show that if a Lie algebra…

Differential Geometry · Mathematics 2023-05-02 Viviana del Barco , Andrei Moroianu

A covariant algorithm for deriving the conserved quantities for natural Hamiltonian systems is combined with the non-relativistic framework of Eisenhart, and of Duval, in which the classical trajectories arise as geodesics in a higher…

Mathematical Physics · Physics 2015-06-19 M. Cariglia , G. W. Gibbons , J. -W. van Holten , P. A. Horvathy , P. -M. Zhang

It is commonly known that Killing vectors and tensors are in one-to-one correspondence with polynomial first integrals of the geodesic equation. In this work, metrics admitting nonpolynomial first integrals of the geodesic equation are…

General Relativity and Quantum Cosmology · Physics 2021-06-30 Anton Galajinsky

The Killing equation for a general Finsler space is set up. It is showed that the Killing equation of $(\alpha,\beta)$ space can be divided into two parts. One is the same with Killing equation of a Riemannian metric, another equation can…

General Relativity and Quantum Cosmology · Physics 2010-04-08 Xin Li , Zhe Chang , Xiaohuan Mo

The integrals of the motion associated with conformal Killing vectors of a curved space-time with an additional electromagnetic background are studied for massive particles. They involve a new term which might be non-local. The difficulty…

General Relativity and Quantum Cosmology · Physics 2025-05-20 K. Andrzejewski , N. Dimakis , M. Elbistan , P. A. Horvathy , P. Kosinski , P. -M. Zhang

We derive the equations corresponding to twisting type-N vacuum gravitational fields with one Killing vector and one homothetic Killing vector by using the same approach as that developed by one of us in order to treat the case with two…

General Relativity and Quantum Cosmology · Physics 2009-10-31 F. J. Chinea , F. Navarro-Lerida

We prove that every conformal vector field on the complex hyperbolic space $\mathbb{C}H^n$ is Killing for all $n\ge 2$. Although this rigidity is classically known, our proof is entirely different in nature: it is local, analytic, and fully…

Differential Geometry · Mathematics 2026-02-23 Hiroyasu Satoh , Hemangi Madhusudan Shah

We give a complete local classification of all Riemannian 3-manifolds $(M,g)$ admitting a nonvanishing Killing vector field $T$. We then extend this classification to timelike Killing vector fields on Lorentzian 3-manifolds, which are…

Differential Geometry · Mathematics 2023-09-06 Amir Babak Aazami , Robert Ream

We study the Killing vectors of the quantum ground-state manifold of a parameter-dependent Hamiltonian. We find that the manifold may have symmetries that are not visible at the level of the Hamiltonian and that different quantum phases of…

Statistical Mechanics · Physics 2023-11-15 Diego Liska , Vladimir Gritsev

We discuss the existence of Killing tensors for certain (physically motivated) stationary and axially symmetric vacuum space-times. We show nonexistence of a nontrivial Killing tensor for a Tomimatsu-Sato metric (up to valence 7), for a…

Differential Geometry · Mathematics 2017-04-12 Andreas Vollmer