Symmetries of the Robinson-Trautman equation

Natorf, W; Tafel, J.

doi:10.1063/1.2359139

Cited by 1 publication

(2 citation statements)

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“…recent work [30] on type II metrics which provides some explicit solutions that are not asymptotically flat. The main interest in type II solutions stems from the fact that both gravitational radiation and black hole formation can be studied simultaneously in exact terms in the vacuum.…”

Section: Jhep10(2005)038mentioning

confidence: 99%

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The algebraic structure of geometric flows in two dimensions

Bakas

2005

J. High Energy Phys.

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There is a common description of different intrinsic geometric flows in two dimensions using Toda field equations associated to continual Lie algebras that incorporate the deformation variable t into their system. The Ricci flow admits zero curvature formulation in terms of an infinite dimensional algebra with Cartan operator ∂/∂t. Likewise, the Calabi flow arises as Toda field equation associated to a supercontinual algebra with odd Cartan operator ∂/∂θ − θ∂/∂t. Thus, taking the square root of the Cartan operator allows to connect the two distinct classes of geometric deformations of second and fourth order, respectively. The algebra is also used to construct formal solutions of the Calabi flow in terms of free fields by Bäcklund transformations, as for the Ricci flow. Some applications of the present framework to the general class of Robinson-Trautman metrics that describe spherical gravitational radiation in vacuum in four space-time dimensions are also discussed. Further iteration of the algorithm allows to construct an infinite hierarchy of higher order geometric flows, which are integrable in two dimensions and they admit immediate generalization to Kähler manifolds in all dimensions. These flows provide examples of more general deformations introduced by Calabi that preserve the Kähler class and minimize the quadratic curvature functional for extremal metrics.

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Section: Jhep10(2005)038mentioning

confidence: 99%

“…Next, specializing to two dimensions and using a system of conformally flat (Kähler) coordinates, ds 30) we find that the only non-vanishing component of the Ricci curvature tensor is R zz = −∂∂Φ. Then, the two different geometric deformations take the following neat form for…”

Section: Landing In Two Dimensionsmentioning

confidence: 99%

The algebraic structure of geometric flows in two dimensions

Bakas

2005

J. High Energy Phys.

View full text Add to dashboard Cite

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Symmetries of the Robinson-Trautman equation

Cited by 1 publication

References 24 publications

The algebraic structure of geometric flows in two dimensions

The algebraic structure of geometric flows in two dimensions

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