Abstract We study a metric-affine gravitational theory given by the Einstein–Hilbert (EH) action plus parity violating contribution (which we will refer to as Hojman term, also known Holst term) in vacuum. find out that for certain value of Barbero–Immirzi (BI) parameter total possesses remarkable invariance under particular transformations affine connection. prove all cases, with appropriate g...

We show how the recently developed string-inspired, projectively invariant gravitational model Thomas-Whitehead gravity (TW gravity) naturally gives rise to a field acting as inflaton. In formulation of TW gravity, ${\mathcal{D}}_{ab}$ is introduced into projective connection components and related rank-two tensor ${\mathcal{P}}_{ab}$. Through dynamical action in terms curvature, ${\mathcal{P}}...

The complex Monge–Ampère (CMA) equation in a two-component form is treated as bi-Hamiltonian system. I present explicitly the first nonlocal symmetry flow each of two hierarchies this An invariant solution CMA with respect to these symmetries constructed, which, being noninvariant usual sense, does not undergo reduction number independent variables. also construct corresponding four-dimensional...

The low density van Stockum dust solution is extended by including an angular deficit factor. The resulting model describes a rotating Gott–Hiscock string surrounded by an annular dust atmosphere. The interior spacetime can be joined to a vacuum Levi-Civita solution with angular deficit. PACS numbers: 04.20.Jb, 04.40.−b, 98.80.Hw

Static cylindrical shells made of various types of matter are studied as sources of the vacuum Levi-Civita metrics. Their internal physical properties are related to the two essential parameters of the metrics outside. The total mass per unit length of the cylinders is always less than 1 4. The results are illustrated by a number of figures.

We consider the metric-affine formulation of bumblebee gravity, derive field equations, and show that connection can be written as Levi-Civita a disformally related metric in which determines disformal part. As consequence, gets coupled to all other matter fields present theory, potentially leading nontrivial phenomenological effects. To explore this issue we compute weak-field limit study resu...

It is well known that the disconnectedness of a non-Archimedean totally ordered field in the order topology makes integration more difficult than in the real case. In this paper, we present a remedy to that difficulty and study measure theory and integration on the Levi-Civita field. After reviewing basic elements of calculus on the field, we introduce a measure that proves to be a natural gene...