The evolution of the Weyl and Maxwell fields in curved and space-times

被引:5
作者
deVries, A
机构
[1] Institut für Mathematik, Ruhr-Universität
关键词
general relativity; functional analysis; evolution equation; spinor functions;
D O I
10.1002/mana.19961790103
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The covariant Weyl (spin s = 1/2) and Maxwell (s = 1) equations in certain local charts (U, <(phi)over tilde>) of a space-time (M, g) are considered. It is shown that the condition g(oo)(x) > O for all x is an element of U is necessary and sufficient to rewrite them in a unified manner as evolution equations partial derivative(t) phi = L((s))phi. Here L((s)) is a linear first order differential operator on the pre-Hilbert space (C-o(infinity) (U-t, C-2s+1), [., .]), where U-t subset of R(3) is the image of the coordinate map of the spacelike hypersurface t = const, and [phi, psi] = integral U-t phi(star)Q psi d((3))x with a suitable Hermitian n x n-matrix Q = Q(t, x). The total energy of the spinor field phi with respect to U-t is then simply given by E = [phi, phi]. In this way inequalities for the energy change rate with respect to time, partial derivative(t) parallel to phi parallel to(2) = 2 Re [phi, L((s))phi], are obtained. As an application, the Kerr-Newman black hole is studied, yielding quantitative estimates for the energy change rate. These estimates especially confirm the energy conservation of the Weyl field and the well-known superradiance of electromagnetic waves.
引用
收藏
页码:27 / 45
页数:19
相关论文
共 21 条
[1]  
[Anonymous], EXACT SOLUTIONS EINS
[2]  
CARMELI M, 1977, GROUP THEORY GENERAL
[3]  
Chandrasekhar S., 1983, The mathematical theory of black holes
[4]  
CHERNOFF P., 1973, J FUNCT ANAL, V12, P401, DOI 10.1016/0022-1236(73)90003-7
[5]  
CHOQUET B, 1982, ANAL MANIFOLDS PHYSI
[6]   BOUNDS FOR MASS AND ROTATION OF BLACK-HOLES IN THE OBSERVABLE UNIVERSE [J].
DEVRIES, A ;
BOHME, R ;
SCHMIDTKALER, T .
ASTROPHYSICS AND SPACE SCIENCE, 1995, 225 (02) :221-226
[7]  
DEVRIES A, 1994, BESCHRANKTHEIT ENERG
[8]   WAVE MECHANICS OF ELECTRONS IN KERR GEOMETRY [J].
GUVEN, R .
PHYSICAL REVIEW D, 1977, 16 (06) :1706-1711
[9]  
Hawking S. W., 2011, LARGE SCALE STRUCTUR
[10]   SYMMETRY OPERATORS AND SEPARATION OF VARIABLES FOR SPIN-WAVE EQUATIONS IN OBLATE SPHEROIDAL COORDINATES [J].
KALNINS, EG ;
WILLIAMS, GC .
JOURNAL OF MATHEMATICAL PHYSICS, 1990, 31 (07) :1739-1744