Geometry of black hole spacetimes

  title={Geometry of black hole spacetimes},
  author={Lars-Erik Andersson and Thomas Backdahl and Pieter Blue},
  journal={arXiv: General Relativity and Quantum Cosmology},
These notes, based on lectures given at the summer school on Asymptotic Analysis in General Relativity, collect material on the Einstein equations, the geometry of black hole spacetimes, and the analysis of fields on black hole backgrounds. The Kerr model of a rotating black hole in vacuum is expected to be unique and stable. The problem of proving these fundamental facts provides the background for the material presented in these notes. Among the many topics which are relevant for the… 

Geometric background for the Teukolsky equation revisited

We present in detail the geometric framework necessary to understand the Teukolsky equation and we develop in particular the case of Kerr spacetime.

Second order symmetry operators for the massive Dirac equation

Employing the covariant language of two-spinors, we find what conditions a curved four-dimensional Lorentzian spacetime must satisfy for existence of a second order symmetry operator for the massive



Spin geometry and conservation laws in the Kerr spacetime

In this paper we will review some facts, both classical and recent, concerning the geometry and analysis of the Kerr and related black hole spacetimes. This includes the analysis of test fields on


In this paper, we will explore the geometry of the Kerr spacetime, a solution to the Einstein Equation in general relativity. We will first give physical and mathematical motivations, and sketch the

Black Hole Superradiance in Dynamical Spacetime

We study the superradiant scattering of gravitational waves by a nearly extremal black hole (dimensionless spin $a=0.99$) by numerically solving the full Einstein field equations, thus including

Weak null singularities in general relativity

We construct a class of spacetimes (without symmetry assumptions) satisfying the vacuum Einstein equations with singular boundaries on two null hypersurfaces intersecting in the future on a 2-sphere.

Introduction to Black Hole Physics

1. Black Holes: Big Picture 2. Physics in a Uniformly Accelerated Frame 3. Riemannian Geometry 4. Particles Motion in Curved Spacetime 5. Einstein Equations 6. Spherically Symmetric Black Holes 7.

The Formation of Black Holes in General Relativity

The subject of this work is the formation of black holes in pure general relativity, by the focusing of incoming gravitational waves. The theorems established in this monograph constitute the first

Einstein spaces as attractors for the Einstein flow

In this paper we prove a global existence theorem, in the direction of cosmological expansion, for sufficiently small perturbations of a family of n + 1-dimensional, spatially compact spacetimes,

Perturbations of a rotating black hole. I. Fundamental equations for gravitational, electromagnetic, and neutrino-field perturbations

Decoupled, separable equations describing perturbations of a Kerr black hole are derived. These equations can be used to study black-hole processes involving scalar, electromagnetic, neutrino or

Hyperbolic reductions for Einstein's equations

We consider the problem of reducing initial value problems for Einstein's field equations to initial value problems for hyperbolic systems, a problem of importance for numerical as well as analytical

Reconstruction of black hole metric perturbations from Weyl curvature: II. The Regge–Wheeler gauge

Perturbation theory of rotating black holes is described in terms of the Weyl scalars ψ4 and ψ0, each satisfying Teukolsky's complex master wave equation with spin s = ∓2, and respectively