Types III andsolutions to quadratic gravity
- 29 July 2011
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review D
- Vol. 84 (2)
Abstract
We study exact vacuum solutions to quadratic gravity (QG) of the Weyl types N and III. We show that in an arbitrary dimension all Einstein spacetimes of the Weyl type N with an appropriately chosen effective cosmological constant $\Lambda${} are exact solutions to QG and we refer to explicitly known metrics within this class. For type~III Einstein spacetimes, an additional constraint follows from the field equations of QG and examples of spacetimes obeying such constraint are given. However, type~III pp~waves do not satisfy this constraint and thus do not solve QG. For type~N, we also study a wider class of spacetimes admitting a pure radiation term in the Ricci tensor. In contrast to the Einstein case, the field equations of generic QG determine optical properties of the geometry and restrict such exact solutions to the Kundt class. We provide examples of these metrics.Keywords
All Related Versions
This publication has 30 references indexed in Scilit:
- Critical Gravity in Four DimensionsPhysical Review Letters, 2011
- AdS waves as exact solutions to quadratic gravityPhysical Review D, 2011
- Generalization of the Geroch–Held–Penrose formalism to higher dimensionsClassical and Quantum Gravity, 2010
- Massive higher derivative gravity in-dimensional anti–de Sitter spacetimesPhysical Review D, 2009
- The Newman–Penrose formalism in higher dimensions: vacuum spacetimes with a non-twisting geodetic multiple Weyl aligned null directionClassical and Quantum Gravity, 2008
- Classification of the Weyl tensor in higher dimensionsClassical and Quantum Gravity, 2004
- Energy in generic higher curvature gravity theoriesPhysical Review D, 2003
- The plane gravitational wave in quadratic gravityClassical and Quantum Gravity, 1990
- Dimensionally dependent identitiesMathematical Proceedings of the Cambridge Philosophical Society, 1970
- Einstein spaces which are mapped conformally on each otherMathematische Annalen, 1925