A new vector field is introduced into 2-form Einstein gravity in four dimensions to restore a large symmetry of its topological version. Two different expressions for the BRST charge are given in the system: one of them associated with a set of irreducible symmetries and the other with a set of on-shell reducible symmetries. ⋆ e-mail address: [email protected] † e-mail address: tatsuya@ph...

We construct a dark energy model where a scalar field non-minimally coupled to gravity plays the role of the dark component. We compare cosmological consequences of this non-minimal coupling of the scalar field and gravity in the spirit of the dark energy paradigm in Jordan and Einstein frames. Some important issues such as phantom divide line crossing, existence of the bouncing solutions and t...

In this paper, we study the stability and multiple solutions to Einstein-scalar field Lichnerowicz equation on compact Riemannian manifolds. In particular, in dimension no more than 5, we can find a different way (comparing with the previous result of Hebey-PacardPollack) by showing that there are at least two positive solutions or a unique positive solution according to the coercivity property...

Non-invariant solutions of the Boyer-Finley equation determine exact solutions of the Einstein field equations with only one rotational Killing vector. For the case of Euclidean signature such a metric was constructed by Calderbank and Tod. Recently Martina, Sheftel and Winternitz applied the method of group foliation to the Boyer-Finley equation and reproduced the Calderbank-Tod solution toget...

We show that the Einstein covariance principle provides an opportunity to generate infinitely many solutions of given covariant equation from a known one. With use of this statement we derive exact expressions for charge and current densities in a medium in an arbitrary external field. We obtain that in a homogeneous nondisipersive medium the field of a point particle differs at short-distances...

With applying of new proposed electromagnetic gravity Lagrangian together with Einstein-Hilbert equation not zero space curvature was derived. The curvature gives “a priory” postulate of equivalence of mass and electro-magnetic field gravity properties. The non-zero trace of energy-stress tensor of electrical field changes space curvature of gravity mass, which yields to prediction of dependenc...

Recently, it has been shown that the wave equation for a scalar field on the exterior part of the Schwarzschild manifold satisfies local decay estimates useful for scattering theory and global existence [2]. The extension for the linearized Einstein equation is considered here. In 1957, Regge and Wheeler investigated spin 2 tensor fields on the Schwarzschild manifold [4]. They classified such f...

We display a logarithmic divergence in the density matrix of a scalar field in the presence of an Einstein-Yang-Mills black hole in four dimensions. This divergence is related to a previously-found logarithmic divergence in the entropy of the scalar field, which cannot be absorbed into a renormalization of the Hawking-Bekenstein entropy of the black hole. As the latter decays, the logarithmic d...

The cubic complex Ginzburg-Landau equation is one of the most-studied nonlinear equations in the physics community. It describes a vast variety of phenomena from nonlinear waves to secondorder phase transitions, from superconductivity, superfluidity and Bose-Einstein condensation to liquid crystals and strings in field theory. Our goal is to give an overview of various phenomena described the c...

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...