The current article offers a mathematical toolkit for the study of waves propagating on spacetimes with nonvanishing torsion. comprises generalized versions Lichnerowicz–de Rham and Beltrami wave operators, Weitzenböck identity relating them Riemann–Cartan geometries. construction applies to any field belonging matrix representation Lie (super) algebra containing an $$\mathfrak {so} \left( \eta...

The weakest known criterion for local rotational symmetry (LRS) in spacetimes of Petrov type D is due to Goode and Wainwright (1986). Here it shown, using methods related the Cartan-Karlhede procedure, be equivalent spatial rotation invariance Riemann tensor its first derivatives. Conformally flat are similarly studied shown that almost all cases same ensures LRS. Only conformally accelerated p...

We characterize the Einstein tensor as the only, up to a constant factor, 2covariant tensor naturally constructed from a semiriemannian metric which is divergence-free and invariant under constant rescalings of the metric. Since these two conditions are also satisfied by the energy-impulse tensor of a relativistic space-time, we discuss how this theorem and its variations can be used to derive ...

In the present work, two SIR patterns with demography will be considered: classical pattern and a modified linear coefficient of infection transmission. By reformulating each first-order differential systems as system second-order equations, we examine nonlinear dynamics from Jacobi stability perspective through Kosambi–Cartan–Chern (KCC) geometric theory. The intrinsic properties studied by de...

In this paper we investigate the gravitational-wave generation problem at first post-Newtonian order in context of Einstein-Cartan theory by exploiting Blanchet-Damour formalism. The quantum intrinsic spin carried slowly moving, weakly stressed, self-gravitating sources is described geometrically means torsion tensor. We obtain expression source multipole moments with required accuracy. analysi...

In this paper we consider the product of two complex Cartan manifolds, the outcome being a class of product complex Cartan spaces. Then, we study the relationships between the geometric objects of a product complex Cartan space and its components, (e.g. Chern-Cartan complex nonlinear connection, Cartan tensors). By means of these, we establish the necessary and sufficient conditions under which...

We find a one parameter family of Lagrangians, describing Einstein's general relativ-ity in terms of tetrads which are not c-numbers but obey exotic commutation relations. The noncommutativity completely drops out at the level of the metric theory, where the Christoffel symbols and the components of the Riemann tensor are ordinary numbers and have the usual form in terms of the space–time metri...

We study the representation theory of Kazama-Suzuki coset vertex operator superalgebra associated with pair a complex simple Lie algebra and its Cartan subalgebra. In case type $A_{1}$, B.L. Feigin, A.M. Semikhatov, I.Yu. Tipunin introduced another construction, which is "inverse" construction. this paper we generalize latter construction to arbitrary establish categorical equivalence between c...

We examine actions of finite-dimensional pointed Hopf algebras on central simple division in characteristic 0. (By a action we mean module algebra structure.) In all examples considered, show that the given does admit faithful algebra, and construct such algebra. This is contrast to earlier work Etingof Walton, which it was shown most do not fields. consider bosonizations Nichols finite Cartan ...