pp-waves with torsion and metric-affine gravity

Abstract

Abstract. A classical pp-wave is a 4-dimensional Lorentzian spacetime which admits a nonvanishing parallel spinor field; here the connection is assumed to be Levi-Civita. We generalise this definition to metric compatible spacetimes with torsion and describe basic properties of such spacetimes. We use our generalised pp-waves for constructing new explicit vacuum solutions of quadratic metric-affine gravity.

Plane waves in metric-affine gravity

“…This extends the previous study of the waves in the Yang-Mills type models of the Poincaré gauge gravity [8][9][10][11][12][13]. As compared to the other exact wave solutions available in the literature [33][34][35][36][37][38] The results obtained have a number of interesting mathematical and physical applications. To begin with, the curvature quadratic Lagrangian is potentially important for a quantized theory of gravity.…”

“…Let us consider the general Yang-Mills type (curvature quadratic) Lagrangian for the MAG model which was studied recently in the literature (see, for example, [33][34][35][36][37][38]):…”

Linear connections with a propagating spin-3 field in gravity

“…Actually, we can put the plane-wave solutions (49) in exactly the same form as that found by Obukhov [41] for metric-affine gravity, see also Pasic and Vassiliev [46]. One must identify…”

Rotating Black Holes in Metric-Affine Gravity

“…The group of Dereli, Tucker, and Wang 17,58,59 applied such theories to the dark matter problem, inter alia, Minkevich et al 33,37,34,35,36 , Puetzfeld et al 48,49,50,51 , and Babourova & Frolov 3,2,4 mainly to cosmological solutions. New exact solutions were found, amongst others, by Vassiliev & King 31,60,61,43 . The determination of the energy and of the other conserved quantities of exact solutions of MAG has been developed in particular by Nester and his group 14,63,39,64,65 , see also Baekler et al 9 .…”