Second Order Scalar Invariants of the Riemann Tensor: Applications to Black Hole Spacetimes

Abstract

We discuss the Kretschmann, Chern-Pontryagin and Euler invariants among the second order scalar invariants of the Riemann tensor in any spacetime in the Newman-Penrose formalism and in the framework of gravitoelectromagnetism, using the Kerr-Newman geometry as an example. An analogy with electromagnetic invariants leads to the definition of regions of gravitoelectric or gravitomagnetic dominance.

19 pages, uses ijmpd macros, 8 eps figures

Cited by in corpus (79)

• f(R) theories
• Chern-Simons Modified General Relativity
• Logarithmic Corrections to Schwarzschild and Other Non-extremal Black Hole Entropy in Different Dimensions
• Spin-induced scalarized black holes
• Logarithmic Corrections to Rotating Extremal Black Hole Entropy in Four and Five Dimensions
• How do Black Holes Spin in Chern-Simons Modified Gravity?
• Spontaneous scalarization
• The Invar Tensor Package
• Black hole solutions in F(R) gravity with conformal anomaly
• Avoiding singularities in Lorentzian-Euclidean black holes: the role of atemporality
• A gravito-electromagnetic analogy based on tidal tensors
• Vacuum structure for scalar cosmological perturbations in Modified Gravity Models
• Gravito-electromagnetic analogies
• Tidal invariants for compact binaries on quasi-circular orbits
• f(G) Noether cosmology
• Spin-induced dynamical scalarization, de-scalarization and stealthness in scalar-Gauss-Bonnet gravity during black hole coalescence
• Schwarzschild and Kerr Solutions of Einstein's Field Equation -- an introduction
• Characterizing repulsive gravity with curvature eigenvalues
• A simple theorem to generate exact black hole solutions
• Mass Quadrupole as a Source of Naked Singularities
• Electromagnetic duality anomaly in curved spacetimes
• Invariant characterization of the Kerr spacetime: Locating the horizon and measuring the mass and spin of rotating black holes using curvature invariants
• Spacetime dynamics of spinning particles - exact electromagnetic analogies
• Heat Kernel Expansion and Extremal Kerr-Newmann Black Hole Entropy in Einstein-Maxwell Theory
• On the propagation across the big bounce in an open quantum FLRW cosmology
• What does a measurement of mass and/or radius of a neutron star constrain: Equation of state or gravity?
• Holographic dark matter and dark energy with second order invariants
• Structure of Lanczos-Lovelock Lagrangians in Critical Dimensions
• New form of all black holes of type D with a cosmological constant
• Conformastatic disk-haloes in Einstein-Maxwell gravity
• Constraining spontaneous black hole scalarization in scalar-tensor-Gauss-Bonnet theories with current gravitational-wave data
• Weak field limit and gravitational waves in higher-order gravity
• An Algebraic Approach to Physical Fields
• Seeley-DeWitt Coefficients in $\mathcal{N}=2$ Einstein-Maxwell Supergravity Theory and Logarithmic Corrections to $\mathcal{N}=2$ Extremal Black Hole Entropy
• On geometry of deformed black holes: I. Majumdar-Papapetrou binary
• Integrability of geodesics of totally geodesic metrics
• Gravitationally induced electromagnetism at the Compton scale
• Curvature Invariants for accelerating Kerr-Newman black holes in (anti-)de Sitter spacetime
• Generalized Einstein-Maxwell theory: Seeley-DeWitt coefficients and logarithmic corrections to the entropy of extremal and non-extremal black holes
• Curvature Invariants for Lorentzian Traversable Wormholes
• Simple regular black hole with logarithmic entropy correction
• Logarithmic corrections to black hole entropy in matter coupled $\mathcal{N}\ge 1$ Einstein-Maxwell supergravity
• Plebański-Demiański solution of general relativity and its expressions quadratic and cubic in curvature: analogies to electromagnetism
• On geometry of deformed black holes: II. Schwarzschild hole surrounded by a Bach-Weyl ring
• Geometry of Vaidya spacetimes
• Logarithmic correction to the entropy of extremal black holes in $\mathcal{N}=1$ Einstein-Maxwell supergravity
• Gravitomagnetism and the significance of the curvature scalar invariants
• Energy Conditions in Gauss-Bonnet Gravity
• Logarithmic corrections to the entropy of non-extremal black holes in $\mathcal{N}=1$ Einstein-Maxwell supergravity
• An Eternal gravitational collapse in $f(R)$ theory of gravity and their astrophysical implications
• Black hole formation in gravitational collapse and their astrophysical implications
• Black holes with constant topological Euler density
• Invariants of the Kerr Vacuum
• Riemann curvature of a boosted spacetime geometry
• Lovelock-Brans-Dicke gravity
• Active gravitational mass and the invariant characterization of Reissner-Nordstrom spacetime
• Second order invariants and holography
• Chern-Weil theorem, Lovelock Lagrangians in critical dimensions and boundary terms in gravity actions
• Modified Gravity Models Admitting Second Order Equations of Motion
• The square of the Weyl tensor can be negative
• A connection between linearized Gauss-Bonnet gravity and classical electrodynamics II: Complete dual formulation
• On parity-odd sector in metric-affine theories
• Noncommutative Reissner-Nordstrøm Black hole
• Exact vacuum solution with Hopf structure in general relativity
• Eternal homogeneous gravitational collapse: A comprehensive analysis from $\Theta$ parametrization
• Astrophysical implications of an eternal homogeneous gravitational collapse model with a parametrization of expansion scalar
• Capturing the Page Curve and Entanglement Dynamics of Black Holes in Quantum Computers
• Numerical Evidence for Non-Axisymmetric Gravitational "Hair" for Extremal Kerr Black Hole Spacetimes with Hyperboloidal Foliations
• Bounding the Cosmological Constant using Galactic Rotation Curves from the SPARC Dataset
• Geometric Properties of Stationary and Axisymmetric Killing Horizons
• Visualization and analysis of the curvature invariants in the Alcubierre warp-drive spacetime
• Curvature and dynamical spacetimes: can we peer into the quantum regime?
• Schwarzschild binary supported by an Appell ring
• General gravitational properties of neutron stars: curvature invariants, binding energy, and trace anomaly
• A Closer Look at Natário's Zero-Expansion Warp Drive
• Impact of Anisotropy on Neutron Star Structure and Curvature
• The ghost of vector fields in compact stars
• Symplectic charges in the Yang-Mills theory of the normal conformal Cartan connection: applications to gravity
• Note on identifying four-dimensional vacuum solutions from Weyl invariants