Geometrically Degenerate Solutions of the Kilmister-Yang Equations

Abstract

where R 0 is the constant scalar curvature. Both (8) and (10) are second order in A and $'; hence the general solution of (8) and (10) has four arbitrary parameters. (Because of nonlinearity there might be a discrete number of such sets of four parameters.) The additive constant in <£> can be removed by a change of time scale. Therefore the general static spherical-symmetric solution has four arbitrary parameters. This demonstrates that the solution of (1) is much richer than that of (2) (two parameters) or (3) (one parameter). As a matter of fact ds 2 = -dt 2 + (l+c 1 /r + c 2 r 2 )' 1 dr 2 + r 2 (d9 2 +sin 2 0d(p 2 ) >is a solution of (1) but not of (2) or (3); (11) possesses no gravitational red shifts. 7 The problems of boundary conditions and sources for (1) deserve extensive studies to clear up this richness of solutions. In view of the present success of the renormalization of gauge theories, these studies could contribute to the solution of the long-standing problems of quantum gravity. I am grateful to K.

PP-waves with torsion: a metric-affine model for the massless neutrino

“…Yang [74] and E.W. Mielke [46] who showed, respectively, that Einstein spaces satisfy equations (3) and (2).There is a substantial bibliography devoted to the study of the system (2), (3) in the special case (4) and one can get an idea of the historical development of the Yang-Mielke theory of gravity from [13,19,20,50,55,64,66,67,73].…”

Gravitational Gauge Theory Developed Based on the Stephenson-Kilmister-Yang Equation

“…In 1974 Yang considered an integral formalism of gauge fields and suggested such a new gravitational field equation [16], where the Christoffel symbol (Levi-Civita connection) serves as a non-Abelian gauge field [16]. Pavelle immediately pointed out that this gravitational field equation is identical with that proposed by Kilmister in 1959 [17], and then in the references published later, some authors referred to it as the Kilmister-Yang equation [18]. But actually, it might be Stephenson who was the first one to propose such a kind of theory (even one year earlier than Kilmister did) [19].…”

“…Later, the SKY vacuum field equation received increasingly more attentions from researchers. For example, the SKY equation for the geometrically degenerate cases of conformally flatness and decomposability of spacetime was studied [18,21], and the possible unphysical metrics [20] that belong to these degenerate classes [18,21] were considered. Some specific physical properties such as the monopole gravitational radiation and the Birkhoff theorem relevant to the SKY equation were discovered [22].…”

Gauge Invariance

“…The advantage of this Utiyama procedure is that it may be generalized to include general relativity (see Utiyama [6], Kibble [8], and more recent works [9][10][11][12]). The advantage of this Utiyama procedure is that it may be generalized to include general relativity (see Utiyama [6], Kibble [8], and more recent works [9][10][11][12]).…”