Siklos waves in Poincaré gauge theory

A class of Siklos waves, representing exact vacuum solutions of general relativity with a cosmological constant, is extended to a new class of Siklos waves with torsion, defined in the framework of the Poincaré gauge theory. Three particular exact vacuum solutions of this type, the generalized Kaigorodov, the homogeneous solution and the exponential solution, are explicitly constructed.

Figure 1

The plots of the torsion function $f_y$ in (6.6a), $8{\mu }^2{\ell }^2/\rho =-1$, $f_y[1]=1,f_y^{\prime }[1]=0$ (left), and in (6.6b), $f_y[1]=1$, $f_y^{\prime }[1]=0$ (right).

Figure 2

The plots of the torsion functions (7.7) for $D_1=D_2=1$, $8{\mu }^2{\ell }^2/\rho =-1$.