The present paper contains a systematic study of the structure of metric Lie algebras, i.e., finite-dimensional real Lie algebras equipped with a non-degenerate invariant symmetric bilinear form. We show that any metric Lie algebra g without simple ideals has the structure of a so called balanced quadratic extension of an auxiliary Lie algebra l by an orthogonal l-module a in a canonical way. I...

We give an exact solution of the quadratic gravity in D dimensions. The solution is a plane-fronted wave metric with a cosmological constant. This metric solves not only the full quadratic gravity field equations but also the linearized ones which include the linearized equations of the recently found critical gravity. A subset of the solutions change the asymptotic structure of the anti-de Sit...

Abstract We consider the most general 11 parameter parity even quadratic Metric-Affine Theory whose action consists of usual Einstein–Hilbert plus terms in torsion, non-metricity as well their mixing. By following a certain procedure and using simple trick we are able to find unique solution affine connection an arbitrary hypermomentum. Given fairly non-degeneracy condition our result provides ...

In this paper, we have obtained and presented new relativistic stellar configurations considering an anisotropic fluid distribution with a charge distribution and a gravitational potential Z(x) that depends on an adjustable parameter. The quadratic equation of state based on Feroze and Siddiqui viewpoint is used for the matter distribution. The new solutions can be written in terms of elementar...

We show that both Teichmüller space (with the Teichmüller metric) and the mapping class group (with a word metric) have geodesic divergence that is intermediate between the linear rate of flat spaces and the exponential rate of hyperbolic spaces. For every two geodesic rays in Teichmüller space, we find that their divergence is at most quadratic. Furthermore, this estimate is shown to be sharp ...