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The spacetime of the metric-affine gauge theory of gravity (MAG) encompasses nonmetricity Q αβ and torsion T α as post-Riemannian structures. The sources of MAG are the conserved currents of energy-momentum and dilation ⊕ shear ⊕ spin. We present an exact static spherically symmetric vacuum solution of the theory describing the exterior of a lump of matter carrying mass and dilation ⊕ shear ⊕ spin charges.

We present an exact stationary axially symmetric vacuum solution of metric-affine gravity (MAG) which generalises the recently reported spherically symmetric solution. Besides the metric, it carries nonmetricity and torsion as post-Riemannian geometrical structures. The parameters of the solution are interpreted as mass and angular momentum and as dilation, shear and spin charges.1 The geometry of MAG ('metric-affine gravity') is described by the curvature two-form R α β , the nonmetricity one-form Q αβ , and the torsion two-form T α which are the gravitational field strengths for linear connection, metric and coframe, respectively. The corresponding physical sources are the canonical energy-momentum and hypermomentum three-forms. The

The Proca wave equation describes a classical massive spin 1 particle. We analyze the gravitational interaction of this vector field. In particular, the spherically symmetric solutions of the Einstein-Proca coupled system are obtained numerically. Although at infinity the metric field approaches the usual Schwarzschild (Reissner-Nordstro È m) limit, we demonstrate the absence of black hole type configurations.

Anholonomic frames are employed to derive an electrovac solution with nonnull electromagnetic field in Moffat's nonsymmetric gravitational theory. It is shown that, in the limit g/sub / mu v// to 0, this solution reduces to the Einstein-Maxwell solution discussed by McIntosh. The author's solution, like its Einstein-Maxwell limit, has the property that the electromagnetic field does not admit the Killing vector field, xi , admitted by the symmetric part of the fundamental tensor. On the other hand, the antisymmetric part of the fundamental tensor does admit xi .