Visualizing Spacetime Curvature via Gradient Flows I: Introduction

Abstract

Traditional approaches to the study of the dynamics of spacetime curvature in a very real sense hide the intricacies of the nonlinear regime. Whether it be huge formulae, or mountains of numerical data, standard methods of presentation make little use of our remarkable skill, as humans, at pattern recognition. Here we introduce a new approach to the visualization of spacetime curvature. We examine the flows associated with the gradient fields of invariants derived from the spacetime. These flows reveal a remarkably rich structure, and offer fresh insights even for well known analytical solutions to Einstein's equations. This paper serves as an overview and as an introduction to this approach.

10 pages twocolumn revtex 4-1 two figures. Final form to appear in Phys Rev D

References in corpus (4)

• Mimicking Dark Energy with Lemaitre-Tolman-Bondi Models: Weak Central Singularities and Critical Points
• Understanding the "anti-kick" in the merger of binary black holes
• On the Newtonian Limit of the Weyl Tensor
• Nonvanishing Local Scalar Invariants even in VSI Spacetimes with all Polynomial Curvature Scalar Invariants Vanishing

Cited by in corpus (5)

• 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
• On geometry of deformed black holes: I. Majumdar-Papapetrou binary
• Visualizing Spacetime Curvature via Gradient Flows II: An Example of the Construction of a Newtonian analogue
• Visualizing Spacetime Curvature via Gradient Flows III: The Kerr Metric and the Transitional Values of the Spin Parameter