57 citations · 350 across the 18 of their papers we have counts for
18 papers
Second order symmetry operators for the massive Dirac equation
Simon Jacobsson, Thomas Bäckdahl
Employing the covariant language of two-spinors, we find what conditions a curved Lorentzian spacetime must satisfy for existence of a second order symmetry operator for the massiv…
A space-time calculus based on symmetric 2-spinors
Steffen Aksteiner, Thomas Bäckdahl
In this paper we present a space-time calculus for symmetric spinors, including a product with a number of index contractions followed by symmetrization. As all operations stay wit…
Nonlinear radiation gauge for near Kerr spacetimes
Lars Andersson, Thomas Bäckdahl, Pieter Blue +1
In this paper, we introduce and explore the properties of a new gauge choice for the vacuum Einstein equation inspired by the ingoing and outgoing radiation gauges (IRG, ORG) for t…
Compatibility complex for black hole spacetimes
Steffen Aksteiner, Lars Andersson, Thomas Bäckdahl +2
The set of local gauge invariant quantities for linearized gravity on the Kerr spacetime presented by two of the authors (S.A, T.B.) in (arXiv:1803.05341) is shown to be complete.…
Stability for linearized gravity on the Kerr spacetime
Lars Andersson, Thomas Bäckdahl, Pieter Blue +1
In this paper we prove integrated energy and pointwise decay estimates for solutions of the vacuum linearized Einstein equation on the domain of outer communication of the Kerr bla…
Gauge-invariant perturbations of Schwarzschild spacetime
Abhay G. Shah, Bernard F. Whiting, Steffen Aksteiner +2
We study perturbations of Schwarzschild spacetime in a coordinate-free, covariant form. The GHP formulation, having the advantage of not only being covariant but also tetrad-rotati…
Gauge Invariant Perturbations of the Schwarzschild Spacetime
Jonathan E. Thompson, Hector Chen, Bernard F. Whiting
Beginning with the pioneering work of Regge and Wheeler (Phys. Rev. 108, 1957), there have been many studies of perturbations away from the Schwarzschild spacetime background. In p…
Geometry of black hole spacetimes
Lars Andersson, Thomas Bäckdahl, Pieter Blue
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 space…
Symmetries of linearized gravity from adjoint operators
Steffen Aksteiner, Thomas Bäckdahl
Based on operator identities and their formal adjoints, we derive two symmetry operators for the linearized Einstein operator on vacuum backgrounds of Petrov type D and in particul…
New identities for linearized gravity on the Kerr spacetime
Steffen Aksteiner, Lars Andersson, Thomas Bäckdahl
In this paper we derive a differential identity for linearized gravity on the Kerr spacetime and more generally on vacuum spacetimes of Petrov type D. We show that a linear combina…
A formalism for the calculus of variations with spinors
Thomas Bäckdahl, Juan A. Valiente Kroon
We develop a frame and dyad gauge-independent formalism for the calculus of variations of functionals involving spinorial objects. As part of this formalism we define a modified va…
Spin geometry and conservation laws in the Kerr spacetime
Lars Andersson, Thomas Bäckdahl, Pieter Blue
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 o…
Decay of solutions to the Maxwell equation on the Schwarzschild background
Lars Andersson, Thomas Bäckdahl, Pieter Blue
A new Morawetz or integrated local energy decay estimate for Maxwell test fields on the exterior of a Schwarzschild black hole spacetime is proved. The proof makes use of a new sup…
A new tensorial conservation law for Maxwell fields on the Kerr background
Lars Andersson, Thomas Bäckdahl, Pieter Blue
A new, conserved, symmetric tensor field for a source-free Maxwell test field on a four-dimensional spacetime with a conformal Killing-Yano tensor, satisfying a certain compatibili…
Second order symmetry operators
Lars Andersson, Thomas Bäckdahl, Pieter Blue
Using systematic calculations in spinor language, we obtain simple descriptions of the second order symmetry operators for the conformal wave equation, the Dirac-Weyl equation and…
Hertz potentials and asymptotic properties of massless fields
Lars Andersson, Thomas Bäckdahl, Jérémie Joudioux
In this paper we analyze Hertz potentials for free massless spin-s fields on the Minkowski spacetime, with data in weighted Sobolev spaces. We prove existence and pointwise estimat…
On the construction of a geometric invariant measuring the deviation from Kerr data
Thomas Bäckdahl, Juan A. Valiente Kroon
This article contains a detailed and rigorous proof of the construction of a geometric invariant for initial data sets for the Einstein vacuum field equations. This geometric invar…
Geometric Invariant Measuring the Deviation from Kerr Data
Thomas Bäckdahl, Juan A. Valiente Kroon
A geometrical invariant for regular asymptotically Euclidean data for the vacuum Einstein field equations is constructed. This invariant vanishes if and only if the data correspond…