Scalar Curvature Invariants in Classical and Quantum Gravity

Abstract

A short review of scalar curvature invariants in gravity theories is presented. We introduce how these invariants are constructed and discuss the minimal number of invariants required for a given spacetime. We then discuss applications of these invariants and focus on three topics that are of particular interest in modern gravity theories.

arXiv commentEssay written for the Gravity Research Foundation 2021 Awards for Essays on Gravitation

References in corpus (21)

• Asymptotic safety of quantum gravity beyond Ricci scalars
• Spacetimes characterized by their scalar curvature invariants
• The Invar tensor package: Differential invariants of Riemann
• Curvature invariants, geodesics and the strength of singularities in Bianchi-I loop quantum cosmology
• From a locality-principle for new physics to image features of regular spinning black holes with disks
• Invariant characterization of the Kerr spacetime: Locating the horizon and measuring the mass and spin of rotating black holes using curvature invariants
• Local Invariants Vanishing on Stationary Horizons: A Diagnostic for Locating Black Holes
• The Weyl curvature conjecture and black hole entropy
• Scalar Polynomial Curvature Invariant Vanishing on the Event Horizon of Any Black Hole Metric Conformal to a Static Spherical Metric
• All local gauge invariants for perturbations of the Kerr spacetime
• Geometric surfaces: An invariant characterization of spherically symmetric black hole horizons and wormhole throats
• Curvature Invariants for the Alcubierre and Natário Warp Drives
• Curvature Invariants for Lorentzian Traversable Wormholes
• An Exploration of the Black Hole Entropy via the Weyl Tensor
• Event Horizon Detecting Invariants
• Cartan Invariants and Event Horizon Detection, Extended Version
• The structure of the singular ring in Kerr-like metrics
• Singularities in Quantum Corrected Space-times
• On the Curvature Invariants of the Massive Banados-Teitelboim-Zanelli Black Holes and Their Holographic Pictures
• IR-improved DGLAP parton shower effects in W + jets in pp collisions at $\sqrt{s}=7$ TeV
• Curvature Invariants for Wormholes and Warped Spacetimes

Cited by in corpus (1)

• A non-local way around the no-global-symmetries conjecture in quantum gravity?