We give a complete proof of the result stated in [1], that the general Einstein metric with a symmetry, an anti-self-dual Weyl tensor and nonzero scalar curvature is determined by a solution of the SU(∞)Toda field equation. We consider the two canonical forms found for solutions to the same problem by Przanowski [2] and show that his Class A will reduce to the Toda equation with respect to a se...

We start from the pure Einstein-Hilbert action S = λ 2 R ⋆ 1 in Metric-Affine-Gravity, with the orthonormal metric g ab = η ab. We get an effective Levi-Civita Dilaton gravity theory in which the Dilaton field is related to the scaling of the gravitational coupling. When the Weyl symmetry is broken the resulting Einstein-Hilbert term is equivalent to the Levi-Civita one, using the projective in...

The usual form of the C-metric has the structure function G(ξ) = 1 − ξ 2 − 2mAξ 3 , whose cubic nature can make calculations cumbersome, especially when explicit expressions for its roots are required. In this paper, we propose a new form of the C-metric, with the explicitly factorisable structure function G(ξ) = (1 − ξ 2)(1 + 2mAξ). Although this form is related to the usual one by a coordinat...

Perturbation theory of rotating black holes is usually described in terms of Weyl scalars c4 and c0, which each satisfy Teukolsky’s complex master wave equation and respectively represent outgoing and ingoing radiation. On the other hand metric perturbations of a Kerr hole can be described in terms of ~Hertz-like! potentials C in outgoing or ingoing radiation gauges. In this paper we relate the...

in this study, 2n -dimensional (n > 2) generalized conformally recurrent kaehlerian weyl spaces andgeneralized conharmonicaly recurrent kaehlerian weyl spaces are defined. it is proved that a kaehlerian weylspace is generalized conformally recurrent if and only if it is generalized recurrent.also, it is shown that akaehlerian weyl space will be generalized recurrent if and only if it is general...

In this work we study the stability of four vector irreducible pieces torsion and nonmetricity tensors in general quadratic metric-affine Lagrangian 4 dimensions. The goal will be to elucidate under which conditions spin-1 modes associated such vectors can propagate a safe way, together with graviton. This highly constrains theory reducing parameter space curvature part from 16 5 parameters. We...

We show how Einstein-Cartan gravity can accommodate both global scale and local (Weyl) invariance. To this end, we construct a wide class of models with nonpropagating torsion nonminimally coupled scalar field. In phenomenological applications the field is associated Higgs boson. For invariance, an additional field---dilaton---is needed to make theory phenomenologically viable. case Weyl symmet...

A bstract Irrelevant operators in a CFT modify the usual Weyl transformation of metric. metric beta-function turns on, which modifies anomalies as well. In this paper, we study relation between bulk diffeomorphisms and at boundary when massive scalar field, sources irrelevant boundary, is coupled to Considering effect backreaction generated by provide holographic description anomalies. Our resu...

A bstract We introduce a new gauge and solution space for three-dimensional gravity. As its name Bondi-Weyl suggests, it leads to non-trivial Weyl charges, uses Bondi-like coordinates allow an arbitrary cosmological constant therefore spacetimes which are asymptotically locally (A)dS or flat. explain how integrability requires choice of integrable slicing also the introduction corner term. Afte...