The Newman-Penrose formalism in quadratic gravity

Abstract

The quadratic gravity constraints are reformulated in terms of the Newman-Penrose-like quantities. In such a frame language, the field equations represent a linear algebraic system for the Ricci tensor components. In principle, a procedure for the combination of the Ricci components with standard geometric identities can be applied in a similar way as in the case of general relativity. These results could serve in various subsequent analyses and physical interpretations of admitted solutions to quadratic gravity. Here, we demonstrate the utility of such an approach by explicitly proving general propositions restricting the spacetime geometry under assumptions on a specific algebraic type of curvature tensors.

arXiv comment25 pages, to be submitted

References in corpus (25)

• f(R) Theories Of Gravity
• Modified Gravity and Cosmology
• f(R) theories
• Extended Theories of Gravity
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• Black Holes in Higher-Derivative Gravity
• Classification of the Weyl Tensor in Higher Dimensions
• Spherically Symmetric Solutions in Higher-Derivative Gravity
• Quadratic Gravity
• Alignment and algebraically special tensors in Lorentzian geometry
• Algebraic classification of higher dimensional spacetimes based on null alignment
• Generalization of the Geroch-Held-Penrose formalism to higher dimensions
• Ricci identities in higher dimensions
• Perturbations of near-horizon geometries and instabilities of Myers-Perry black holes
• Explicit black hole solutions in higher-derivative gravity
• Black holes and other exact spherical solutions in Quadratic Gravity
• Exact black holes in quadratic gravity with any cosmological constant
• Exact solutions to quadratic gravity
• Peeling of the Weyl tensor and gravitational radiation in higher dimensions
• Type III and N solutions to quadratic gravity
• Gravitational perturbations of a Kerr black hole in $f(R)$ gravity
• Supersymmetric field theory with benign ghosts
• A higher-dimensional generalization of the geodesic part of the Goldberg-Sachs theorem
• Black holes and other spherical solutions in quadratic gravity with a cosmological constant
• Classification of Robinson-Trautmann and Kundt Geometries with Large D Limit

Cited by in corpus (4)

• Newman-Penrose formalism and exact vacuum solutions to conformal Weyl gravity
• Testing gravity with gauge-invariant polarization states of gravitational waves: Theory and pulsar timing sensitivity
• Linear perturbations of Kerr black hole in quadratic gravity
• The Exterior Calculus of Quadratic Gravity