An axially symmetric solution of metric-affine gravity

We present an exact stationary {\it 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.Comment: 5 pages, RevTe

Black Hole Entropy in Induced Gravity: Reduction to 2D Quantum Field Theory on the Horizon

It is argued that degrees of freedom responsible for the Bekenstein-Hawking entropy of a black hole in induced gravity are described by two dimensional quantum field theory defined on the bifurcation surface of the horizon. This result is proved for a class of induced gravity models with scalar, spinor and vector heavy constituents.Comment: 19 pages, latex, no figure

Higher-order Abel equations: Lagrangian formalism, first integrals and Darboux polynomials

A geometric approach is used to study a family of higher-order nonlinear Abel equations. The inverse problem of the Lagrangian dynamics is studied in the particular case of the second-order Abel equation and the existence of two alternative Lagrangian formulations is proved, both Lagrangians being of a non-natural class (neither potential nor kinetic term). These higher-order Abel equations are studied by means of their Darboux polynomials and Jacobi multipliers. In all the cases a family of constants of the motion is explicitly obtained. The general n-dimensional case is also studied

A Lagrangian Description of the Higher-Order Painlev\'e Equations

We derive the Lagrangians of the higher-order Painlev\'e equations using Jacobi's last multiplier technique. Some of these higher-order differential equations display certain remarkable properties like passing the Painlev\'e test and satisfy the conditions stated by Jur\'a$\check{s}$, (Acta Appl. Math. 66 (2001) 25--39), thus allowing for a Lagrangian description.Comment: 16 pages, to be published in Applied Mathematics and Computatio