The rate of growth of the magnetic energy density during a gravitational collapse.
Abstract
It is shown that during an isotropic gravitational collapse of a fluid with infinite electrical conductivity, the magnetic energy density cannot grow faster thanθ 4/3 no matter the equation of state, whereϱ is the total proper energy density. If the equation of state isθ=αθc 2, where 0⩽α⩽1, then the rate of growth of the magnetic energy density in such a collapse is proportional toρ 4/3(1+α). If an isotropic collapse is also locally adiabatic, it is shown, independently of any equation of state, that the rate of increase of the magnetic energy density is proportional tor 4/3, wherer is the proper material density. If the collapse is nonisotropic, shear can modify these results. Numerical estimates of the magnetic field strength at various stages in the collapse of a magnetic star are given.
- Publication:
-
General Relativity and Gravitation
- Pub Date:
- March 1976
- DOI:
- 10.1007/BF00768529
- Bibcode:
- 1976GReGr...7..287M