The Organ Works of Bach

Bach,; Allen, Alfred H.

doi:10.2307/909415

Cited by 1 publication

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“…Specifically, we will use "seed" geometries g ab with vanishing Bach tensor to generate solutionsg ab to quadratic gravity using the conformal transformation (8), implyingB ab = 0 due to (9). 4 It remains to satisfyR = 4Λ ,…”

Section: Conformally Kundt Solutions To Quadratic Gravitymentioning

confidence: 99%

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Exact solutions to quadratic gravity

et al. 2017

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Since all Einstein spacetimes are vacuum solutions to quadratic gravity in four dimensions, in this paper we study various aspects of non-Einstein vacuum solutions to this theory. Most such known solutions are of traceless Ricci and Petrov type N with a constant Ricci scalar. Thus we assume the Ricci scalar to be constant which leads to a substantial simplification of the field equations. We prove that a vacuum solution to quadratic gravity with traceless Ricci tensor of type N and aligned Weyl tensor of any Petrov type is necessarily a Kundt spacetime. This will considerably simplify the search for new non-Einstein solutions. Similarly, a vacuum solution to quadratic gravity with traceless Ricci type III and aligned Weyl tensor of Petrov type II or more special is again necessarily a Kundt spacetime.Then we study the general role of conformal transformations in constructing vacuum solutions to quadratic gravity. We find that such solutions can be obtained by solving one non-linear partial differential equation for a conformal factor on any Einstein spacetime or, more generally, on any background with vanishing Bach tensor. In particular, we show that all geometries conformal to Kundt are either Kundt or Robinson-Trautman, and we provide some explicit Kundt and Robinson-Trautman solutions to quadratic gravity by solving the above mentioned equation on certain Kundt backgrounds.

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Section: Conformally Kundt Solutions To Quadratic Gravitymentioning

confidence: 99%

“…Various four and higher-dimensional theories with such quadratic terms in the action and their exact solutions were studied in the literature (see e.g. [1][2][3][4][5][6]), with first particular theories proposed already shortly after the introduction of Einstein's general relativity [7,8].…”

Section: Introductionmentioning

confidence: 99%