– in this paper we consider some (α ,β ) -metrics such as generalized kropina, matsumoto and f (α β )2α = + metrics, and obtain necessary and sufficient conditions for them to be einstein metrics when βis a constant killing form. then we prove with this assumption that the mentioned einstein metrics must beriemannian or ricci flat.

The canonical quantization of dynamical systems with curved phase space introduced by I.A. Batalin, E.S. Fradkin and T.E. Fradkina is applied to the four– dimensional Einstein–Maxwell Dilaton–Axion theory. The spherically symmetric case with radial fields is considered. The Lagrangian density of the theory in the Einstein frame is written as an expression with first order in time derivatives of...

We consider asymptotically-flat, static and stationary solutions of the Einstein equations representing Einstein-Maxwell space-times in which the Maxwell field is not constant along the Killing vector defining stationarity, so that the symmetry of the space-time is not inherited by the electromagnetic field. We find that static degenerate black hole solutions are not possible and, subject to st...

We study the near-flat space limit for strings on AdS5 × M5, where the internal manifold M5 is equipped with a generic metric with U(1)3 isometry. In the bosonic sector, the limiting sigma model is similar to the one found for AdS5 × S5, as the global symmetries are reduced in the most general case. When M5 is a SasakiEinstein space like T 1,1, Y p,q and Lp,q,r, whose dual CFT’s have N = 1 supe...

This paper argues that the Einstein-Minkowski space-time of special relativity provides an adequate model for classical tense logic, including rigorous definitions of tensed becoming and of the logical priority of proper time. In addition, the extension of classical tense logic with an operator for predicate-term negation provides us with a framework for interpreting and defending the significa...

Let (M, g) be a compact Kähler-Einstein manifold with c1 > 0. Denote by K → M the canonical line-bundle, with total space X, and X0 the singular space obtained by blowing down X along its zero section. We employ a construction by Page and Pope and discuss an interesting multi-parameter family of Poincaré–Einstein metrics on X. One 1-parameter subfamily {gt}t>0 has the property that as t ց 0, gt...

A contribution linear in r to the gravitational potential can be created by a suitable conformal duality transformation: the conformal factor is 1/(1 + r) and r will be replaced by r/(1 + r), where r is the Schwarzschild radial coordinate. Thus, every spherically symmetric solution of conformal Weyl gravity is conformally related to an Einstein space. This result finally resolves a long controv...

We produce some explicit examples of conformally compact Einstein manifolds, whose conformal compactifications are foliated by Riemannian products of a closed Einstein manifold with the total space of a principal circle bundle over products of Kähler-Einstein manifolds. We compute the associated conformal invariants, i.e., the renormalized volume in even dimensions and the conformal anomaly in ...

We clarify the relation between 2-form Einstein gravity and its topological version. The physical space of the topological version is contained in that of the Einstein gravity. Moreover a new vector field is introduced into 2-form Einstein gravity to restore the large symmetry of its topological version. The wave function of the universe is obtained for each model. † Talk given at the Workshop ...

The role of space-time torsion in general relativity is reviewed in accordance with some recent results on the subject. It is shown that, according to the connection compatibility condition, the usual Riemannian volume element is not appropriate in the presence of torsion. A new volume element is proposed and used in the Lagrangian formulation for Einstein-Cartan theory of gravity. The dynamica...