Haji Ahmedov

The general type N solution of new massive gravity

Abstract We find the most general algebraic type N solution with non-vanishing scalar curvature, which comprises all type N solutions of new massive gravity in three dimensions. We also give the special forms of this solution, which correspond to certain critical values of the topological mass. Finally, we show that at the special limit, the null Killing isometry of the spacetime is restored and the solution describes AdS pp-waves.

Type D solutions of 3D new massive gravity

In a recent reformulation of three-dimensional new massive gravity, the field equations of the theory consist of a massive (tensorial) Klein-Gordon type equation with a curvature-squared source term and a constraint equation. Using this framework, we present all algebraic type D solutions of new massive gravity with constant and nonconstant scalar curvatures. For constant scalar curvature, they include homogeneous anisotropic solutions which encompass both solutions originating from topologically massive gravity, Bianchi types II, VIII, IX, and those of non-topologically massive gravity origin, Bianchi types VI{sub 0} and VII{sub 0}. For a special relation between the cosmological and mass parameters, {lambda}=m{sup 2}, they also include conformally flat solutions, and, in particular, those being locally isometric to the previously-known Kaluza-Klein type AdS{sub 2}xS{sup 1} or dS{sub 2}xS{sup 1} solutions. For nonconstant scalar curvature, all the solutions are conformally flat and exist only for {lambda}=m{sup 2}. We find two general metrics which possess at least one Killing vector and comprise all such solutions. We also discuss some properties of these solutions, delineating among them black hole type solutions.

Uniqueness of Rotating Charged Black Holes in Five-Dimensional Minimal Gauged Supergravity

Abstract We study a five-dimensional spacetime admitting, in the presence of torsion, a non-degenerate conformal Killing–Yano 2-form which is closed with respect to both the usual exterior differentiation and the exterior differentiation with torsion. Furthermore, assuming that the torsion is closed and co-closed with respect to the exterior differentiation with torsion, we prove that such a spacetime is the only spacetime given by the Chong–Cvetic–Lu–Pope solution for stationary, rotating charged black holes with two independent angular momenta in five-dimensional minimal gauged supergravity.

SUSY in the Spacetime of Higher-Dimensional Rotating Black Holes

General higher-dimensional rotating black hole spacetimes of any dimensions admit the Killing and Killing-Yano tensors, which generate the hidden symmetries just as in four-dimensional Kerr spacetime. We study these properties of the black holes using the formalism of supersymmetric mechanics of pseudoclassical spinning point particles. We present two nontrivial supercharges, corresponding to the Killing-Yano and conformal Killing-Yano tensors of the second rank. We demonstrate that an unusual extended Poisson-Dirac algebra of these supercharges results in two independent Killing tensors in spacetime dimensions D{>=}6, giving explicit examples for the Myers-Perry black holes in D=6 dimensions.

Type N spacetimes as solutions of extended new massive gravity

Abstract We study algebraic type N spacetimes in the extended new massive gravity (NMG), considering both the Born-Infeld model (BI-NMG) and the model of NMG with any finite order curvature corrections. We show that for these spacetimes, the field equations of BI-NMG take the form of the massive (tensorial) Klein–Gordon type equation, just as it happens for ordinary NMG. This fact enables us to obtain the type N solution to BI-NMG, utilizing the general type N solution of NMG, earlier found in our work. We also obtain type N solutions to NMG with all finite order curvature corrections and show that, in contrast to BI-NMG, this model admits the critical point solutions, which are counterparts of “logarithmic” AdS pp-waves solutions of NMG.

Casimir energy for a wedge with three surfaces and for a pyramidal cavity

Casimir energy calculations for the conformally coupled massless scalar field for a wedge defined by three intersecting planes and for a pyramid with four triangular surfaces are presented. The group generated by reflections are employed in the formulation of the required Green functions and the wave functions.

NON-ABELIAN FRACTIONAL SUPERSYMMETRY IN TWO DIMENSIONS

Non-Abelian fractional supersymmetry algebra in two dimensions is introduced utilizing Uq(sl(2,ℝ)) at roots of unity. Its representations and the matrix elements are obtained. The dual of it is constructed and the corepresentations are studied. Moreover, a differential realization of the non-Abelian fractional supersymmetry generators is given in the generalized superspace defined by two commuting and two generalized Grassmann variables. An invariant action under the fractional supersymmetry transformations is given.

Black string and Gödel-type solutions of Chern-Simons modified gravity

We show that Chern-Simons (CS) modified gravity with a prescribed CS scalar field admits rotating black hole/string/> solutions with cylindrical topology of the horizon, and we present two intriguing physical examples of such configurations. First, we show that the Banados-Teitelboim-Zanelli stationary black string, which is obtained by adding a spacelike flat dimension to the Banados-Teitelboim-Zanelli black hole metric of three-dimensional gravity, solves the field equations of CS modified gravity with a specific source term irrespective of the choice of CS scalar field. Next, we consider the Lemos solution for a rotating, straight black string in general relativity and show that, for the CS scalar field being a function of the radial coordinate alone, this solution persists in CS modified gravity. We also present a new nontrivial (non-general relativity) Goedel-type solution to the vacuum field equations of CS modified gravity.

Stationary spinning strings and symmetries of classical spacetimes

Abstract We explore the symmetries of classical stationary spacetimes in terms of the dynamics of a spinning string described by a worldsheet supersymmetric action. We show that for stationary configurations of the string, the action reduces to that for a pseudo-classical spinning point particle in an effective space, which is a conformally scaled quotient space of the original spacetime. As an example, we consider the stationary spinning string in the Kerr–Newman spacetime, whose motion is equivalent to that of the spinning point particle in the three-dimensional effective space. We present the Killing tensor as well as the spin-valued Killing vector of this space. However, the nongeneric supersymmetry corresponding to the Killing–Yano tensor of the Kerr–Newman spacetime is lost in the effective space.

Green function on the q-symmetric space

Invariant distance on the non-commutative -algebra is constructed and the generalized functions on the q-symmetric space are introduced. The Green function and the kernel on M are derived. A path integration is formulated. The Green function for the free massive scalar field on the non-commutative Einstein space is presented.