Spacetime approach to force-free magnetospheres

Samuel E. Gralla, Ted Jacobson

Research output: Contribution to journalArticlepeer-review

100 Scopus citations


Force-free electrodynamics (FFE) describes magnetically dominated relativistic plasma via non-linear equations for the electromagnetic field alone. Such plasma is thought to play a key role in the physics of pulsars and active black holes. Despite its simple covariant formulation, FFE has primarily been studied in 3+1 frameworks, where spacetime is split into space and time. In this paper, we systematically develop the theory of force-free magnetospheres taking a spacetime perspective. Using a suite of spacetime tools and techniques (notably exterior calculus), we cover (1) the basics of the theory, (2) exact solutions that demonstrate the extraction and transport of the rotational energy of a compact object (in the case of a black hole, the Blandford-Znajek mechanism), (3) the behaviour of current sheets, (4) the general theory of stationary, axisymmetric magnetospheres, and (5) general properties of pulsar and black hole magnetospheres. We thereby synthesize, clarify, and generalize known aspects of the physics of force-free magnetospheres, while also introducing several new results.

Original languageEnglish (US)
Pages (from-to)2500-2534
Number of pages35
JournalMonthly Notices of the Royal Astronomical Society
Issue number3
StatePublished - Sep 5 2014
Externally publishedYes


  • Black hole physics
  • MHD
  • Methods: analytical
  • Plasmas
  • Pulsars: general

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science


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