A new class of exact solutions of the vacuum quadratic Poincar� gauge field theory

pp-waves with torsion and metric-affine gravity

“…The new vacuum solutions of quadratic metric-affine gravity presented in Theorem 1 are similar to those of Singh and Griffiths [17]. The main differences are as follows.…”

“…• The solutions in [17] satisfy the condition {Ric} = 0 whereas our solutions satisfy the weaker condition {∇}{Ric} = 0 (see also last paragraph of Section 6).…”

“…• The solutions in [17] were obtained for the Yang-Mills case (4) whereas we deal with a general O(1, 3)-invariant quadratic form q with 16 coupling constants.…”

Plane waves in metric-affine gravity

“…The relevant investigation of the gravitational waves in general relativity has a long and rich history, see, e.g., [2][3][4][5][6][7]. The discussion of the possible generalizations of such solutions revealed the exact wave solutions in Poincaré gauge gravity [8][9][10][11][12][13], in teleparallel gravity [14], in generalized Einstein theories [15,16], in supergravity [17][18][19][20][21], as well as, more recently, in superstring theories [22][23][24][25][26][27][28]. Some attention has also been paid to the higher-dimensional generalizations of the gravitational wave solutions [29][30][31][32].…”

Quadratic non-Riemannian Gravity

“…For the Yang-Mills case (5.9) the "torsion wave" solution described above was first obtained by Singh and Griffiths: see last paragraph of Section 5 in [5] and put k = 0, N = e −il·x . Our contribution is the observation that this torsion wave remains a solution for a general quadratic action (1.1) and that this fact can be established without having to write down explicitly the field equations.…”