Killing tensors in pp-wave spacetimes

Keane, A.; Tupper, B. O. J.

doi:10.1088/0264-9381/27/24/245011

Cited by 13 publications

(11 citation statements)

References 29 publications

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“…In [36] the authors calculated the Killing tensors for a number of pp-wave spacetimes along with their conformal Killing vector fields. The metric tensor G for the type Biv pp-wave spacetime admits the form…”

Section: Determination Of Geodesicsmentioning

confidence: 99%

Variational contact symmetries of constrained Lagrangians

Terzis

Dimakis

Christodoulakis

et al. 2016

Journal of Geometry and Physics

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The investigation of contact symmetries of re-parametrization invariant Lagrangians of finite degrees of freedom and quadratic in the velocities is presented. The main concern of the paper is those symmetry generators which depend linearly in the velocities. A natural extension of the symmetry generator along the lapse function N (t), with the appropriate extension of the dependence inṄ (t) of the gauge function, is assumed; this action yields new results. The central finding is that the integrals of motion are either linear or quadratic in velocities and are generated, respectively by the conformal Killing vector fields and the conformal Killing tensors of the configuration space metric deduced from the kinetic part of the Lagrangian (with appropriate conformal factors). The freedom of re-parametrization allows one to appropriately scale N (t), so that the potential becomes constant; in this case the integrals of motion can be constructed from the Killing fields and Killing tensors of the scaled metric. A rather interesting result is the non-necessity of the gauge function in Noether's theorem due to the presence of the Hamiltonian constraint.

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Section: Determination Of Geodesicsmentioning

confidence: 99%

Variational contact symmetries of constrained Lagrangians

Terzis

Dimakis

Christodoulakis

et al. 2016

Journal of Geometry and Physics

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“…This satisfies L ψ g ab = 2g ab . More extensive discussions of the symmetries of plane wave spacetimes may be found in [36,37].…”

Section: A Symmetriesmentioning

confidence: 99%

Caustics and wave propagation in curved spacetimes

Harte

Drivas

2012

Phys. Rev. D

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The term "Green function" as used here coincides with the standard definition of a fundamental solution. For the model equation (1.1), a Green function is any solution to LG(p, p ) = −4πIδ(p, p ), where I denotes an appropriate identity operator (needed for non-scalar fields) and δ(p, p ) the Dirac distribution. By contrast, some authors define Green functions somewhat more restrictively. See, e.g., [1].2 Distributions like θ(p ≥ p )δ(σ) appearing here are not a priori, well-defined. They are to be interpreted as, e.g., lim →0 + θ(p ≥ p )δ(σ + ). See Sect. 4.1 of [2].

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“…Note that KS and KY tensors on 4-dimensional pp-wave spacetimes have been investigated before, see e.g. [39,40]. Although the probe (5) admits an infinite number of symmetries propagating on a pp-wave background, it does not immediately imply that the dynamics is completely integrable.…”

Section: M-theory Pp-wavesmentioning

confidence: 99%

TCFHs, hidden symmetries and M-theory backgrounds

Papadopoulos¹,

Pérez-Bolaños²

2022

Preprint

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We present the TCFH of 11-dimensional supergravity and so demonstrate that the form bilinears of supersymmetric solutions satisfy a generalisation of the conformal Killing-Yano equation with resepct to the TCFH connection. We also compute the Killing-Stäckel, Killing-Yano and closed conformal Killing-Yano tensors of all spherically symmetric M-branes that include the M2-brane, M5-brane, KK-monopole and pp-wave and demonstrate that their geodesic flows are completely integrable by giving all independent conserved charges in involution. We then find that all form bilinears of pp-wave and KK-monopole solutions generate (hidden) symmetries for spinning particle probes propagating on these backgrounds. Moreover, there are Killing spinors such that some of the 1-, 2-and 3-form bilinears of the M2-brane solution also generate symmetries for spinning particle probes. We also explore the question on whether the form bilinears are sufficient to prove the integrability of particle probe dynamics on 11-dimensional supersymmetric backgrounds.

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Killing tensors in pp-wave spacetimes

Cited by 13 publications

References 29 publications

Variational contact symmetries of constrained Lagrangians

Variational contact symmetries of constrained Lagrangians

Caustics and wave propagation in curved spacetimes

TCFHs, hidden symmetries and M-theory backgrounds

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