Linear perturbations in force-free black hole magnetospheres - I. General theory

Details Linear perturbations in force-free black hole magnetospheres - I. General theory Linear perturbations in force-free black hole magnetospheres - I. General theory

Apr 1997

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997mnras.286..931u&link_type=abstract

Monthly Notices of the Royal Astronomical Society, Volume 286, Issue 4, pp. 931-947.

Physics

3

Black Hole Physics, Mhd, Galaxies: Jets, Galaxies: Nuclei

Scientific paper

A Lagrangian perturbation theory for the treatment of small disturbances of force-free electromagnetic fields is developed in a covariant way. The geometrical nature of degenerate electromagnetic fields permits us to develop a Lagrangian treatment. A Lagrangian displacement similar to the one used in the perturbation theory of the ideal fluid is introduced. In the Lagrangian displacement, the basic equation is given as a set of two-component second-order partial differential equations. The action that yields our basic equation is also obtained. Using this action, conserved quantities and the energy-momentum tensor of disturbances are studied. Further, it is shown that there exists intrinsic arbitrariness in our theory. It corresponds to the so-called trivial displacement and arises from the gauge freedom of the electromagnetic fields. We apply the theory to the stationary and axisymmetric force-free black hole magnetosphere. The boundary condition at the event horizon is considered. It is shown that the boundary condition for pure-mode solutions takes the same form as that of the case of electromagnetic waves and gravitational waves scattered by the black hole in vacuum. Lastly, in a special limiting example, we discuss the consistency of our theory with the result from the black hole physics.

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