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