Some classical aspects of Metric–Affine Gravity are reviewed in the context [Formula: see text] type models (polynomials degree Riemann tensor) and topologically massive gravity. At nonperturbative level, we explore consistency field equations when reduced to a Riemann–Christoffel (RCh) space–time, either via Riemann–Cartan (RC) space or an Einstein–Weyl (EW) space. It is well known for case th...

A class of stationary rigidly rotating perfect fluid coupled with nonlinear electromagnetic fields was investigated. An exact solution of the Einstein equations with sources for the Carter B(+) branch was found, for the equation of state 3p + = constant. We use a structural function for the Born-Infeld non-linear electrodynamics which is invariant under duality rotations and a metric possessing...

In this paper we introduce a reference along a null curve in an n-dimensional Lorentzian space with the minimun number of curvatures. That reference generalizes the reference of Bonnor for null curves in Minkowski space-time and it is called the Cartan frame of the curve. The associated curvature functions are called the Cartan curvatures of the curve. We characterize the null helices (that is,...

In this paper we relate the Fefferman–Graham ambient metric construction for conformal manifolds to the approach to conformal geometry via the canonical Cartan connection. We show that from any ambient metric that satisfies a weakening of the usual normalisation condition, one can construct the conformal standard tractor bundle and the normal standard tractor connection, which are equivalent to...

Two classes of avalanche-finite matrices and their critical groups (integer cokernels) are studied from the viewpoint of chip-firing/sandpile dynamics, namely, the Cartan matrices of finite root systems and the McKay-Cartan matrices for finite subgroups G of general linear groups. In the root system case, the recurrent and superstable configurations are identified explicitly and are related to ...

We present an explicit numerical method to obtain the Cartan-KhanejaGlaser decomposition of a general element G ∈ SU(2 ) in terms of its ‘Cartan’ and ‘non-Cartan’ components. This effectively factors G in terms of group elements that belong in SU(2) with n < N , a procedure that an be iterated down to n = 2. We show that every step reduces to solving the zeros of a matrix polynomial, obtained b...