Spinless Matter in Transposed-Equi-Affine Theory of Gravity

We derive and discuss the equations of motion for spinless matter: relativistic spinless scalar fields, particles and fluids in the model of gravity recently proposed by A. Saa with covariantly constant volume with respect to the transposed connection in Einstein-Cartan spaces. A new interpretation of this theory as a theory with variable Planck constant is suggested. We show that the consistency of the semiclassical limit of the wave equation and classical motion dictates a new definite universal interaction of torsion with massive fields.     

Killing Pairs in Flat Space

In this paper the integrability conditions for Killing pairs in flat spaces are investigated and it is shown that only trivial Killing pairs exist.     

Geodesic Motions in 2 + 1-Dimensional Charged Black Holes

We study the geodesic motions of a test particle around 2 + 1-dimensional charged black holes. We obtain a class of exact geodesic motions for the massless test particle when the ratio of its energy and angular momentum is given by the square root of the cosmological constant. The other geodesic motions for both massless and massive test particles are analyzed using the numerical method.