The Exterior Calculus of Quadratic Gravity

Abstract

The metric tensor field equations for the general quadratic curvature gravity in four spacetime dimensions are derived by making use of the algebra of the exterior forms defined on pseudo-Riemannian manifolds and the identities satisfied by the Riemann curvature tensor. The linearized metric field equations are formulated in terms of perturbation 1-form fields.

27 pages

References in corpus (40)

• f(R) Theories Of Gravity
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• Modified gravity with negative and positive powers of the curvature: unification of the inflation and of the cosmic acceleration
• Resummation of Massive Gravity
• Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance
• Generalization of the Fierz-Pauli Action
• Theoretical Aspects of Massive Gravity
• Chern-Simons Modification of General Relativity
• The Cosmology of Generalized Modified Gravity Models
• Energy in Generic Higher Curvature Gravity Theories
• Gravitational Energy in Quadratic Curvature Gravities
• Interacting Spin-2 Fields
• Black Holes in Higher-Derivative Gravity
• Critical Gravity in Four Dimensions
• Quadratic Gravity
• The Cotton tensor in Riemannian spacetimes
• Consistent Spin-Two Coupling and Quadratic Gravitation
• Gauge Symmetry and Gravito-Electromagnetism
• AdS Waves as Exact Solutions to Quadratic Gravity
• Explicit black hole solutions in higher-derivative gravity
• Nonlinear Properties of Vielbein Massive Gravity
• New Exact Solutions of Quadratic Curvature Gravity
• Energy and Angular Momentum in Generic F(Riemann) Theories
• Exact solutions to quadratic gravity
• AdS-plane wave and pp-wave solutions of generic gravity theories
• Conserved Charges in Extended Theories of Gravity
• Type III and N solutions to quadratic gravity
• Particle Content of Quadratic and $f(R_{\mu \nu \sigma \rho })$ Theories in $(A)dS$
• New vacuum solutions of conformal Weyl gravity
• A Stueckelberg Approach to Quadratic Curvature Gravity and its Decoupling Limits
• A Wald-like Formula for Energy
• Energy definition for quadratic curvature gravities
• Variational derivatives of gravitational actions
• The Newman-Penrose formalism in quadratic gravity
• Gravitational wave solutions of quadratic curvature gravity using a null coframe formulation
• Linearized gravity in terms of differential forms
• Weyl Covariant Quadratic Curvature Gravity in 3-Dimensional Riemann-Cartan-Weyl Space-Times
• Conservation laws in gauge gravity theory
• Abbott-Deser energy in connection with Thirring's superpotentials