Related papers: Space-time deformations as extended conformal tran…

In this paper we develop a new framework for non-linear perturbations of the Kerr spacetime. This is based on a characterization of the Kerr spacetime in terms of a Killing spinor. On the perturbed spacetime, one can construct an…

The decomposition of the linear-order metric perturbation is discussed in the context of the higher-order gauge-invariant perturbation theory. We show that the linear order metric perturbation is decomposed into gauge-invariant and…

We discuss the quantization of mechanical systems for which the Hamiltonian vector fields of observables form the deformation of $n$-dimensional oscilator algebra. Because of this fact these systems can be considered as "deformations" of…

Some examples of three-dimensional metrics of constant curvature defined by solutions of nonlinear integrable differential equations and their generalizations are constructed. The properties of Riemann extensions of the metrics of constant…

We consider mappings satisfying an upper bound for the distortion of families of curves. We establish lower bounds for the distortion of distances under such mappings. As applications, we obtain theorems on the discreteness of the limit…

General covariant expressions for measurable angles, distances, velocities, and accelerations are provided in terms of fundamental parameters that can be applied in any setup. The relativistic aberration of light relationship is presented…

Deformation theory of complex manifolds is a classical subject with recent new advances in the noncompact case using both algebraic and analytic methods. In this note, we recall some concepts of the existing theory and introduce new notions…

We consider conformal deformations within a class of incomplete Riemannian metrics which generalize conic orbifold singularities by allowing both warping and any compact manifold (not just quotients of the sphere) to be the "link" of the…

We have estimated higher order quantum gravity corrections to de~Sitter spacetime. Our results suggest that, while the classical spacetime metric may be distorted by the graviton self-interactions, the corrections are relatively weaker than…

Geometric torsions are torsions of acyclic complexes of vector spaces which consist of differentials of geometric quantities assigned to the elements of a manifold triangulation. We use geometric torsions to construct invariants for a…

We study conformal field theories (CFTs) on curved spaces including both orientable and unorientable manifolds possibly with boundaries. We first review conformal transformations on curved manifolds. We then compute the identity components…

In this paper we have introduced a new symmetry property of spacetime which is named as semiconformal curvature collineation, and its relationship with other known symmetry properties has been established. This new symmetry property of the…

Space time is described as a continuum four-dimensional medium similar to ordinary elastic continua. Exploiting the analogy internal stress states are considered. The internal ''stress'' is originated by the presence of defects. The defects…

Starting from the classical r-matrix of the non-standard (or Jordanian) quantum deformation of the sl(2,R) algebra, new triangular quantum deformations for the real Lie algebras so(2,2), so(3,1) and iso(2,1) are simultaneously constructed…

We introduce a definition of symmetry generating vector fields on manifolds which are equipped with a first-order reductive Cartan geometry. We apply this definition to a number of physically motivated examples and show that our newly…

This article is a summary of a series of papers to be published where I examine a special kind of geometric objects that can be defined in space-time --- five-dimensional tangent vectors. Similar objects exist in any other differentiable…

Deformed special relativity is embedded in deformed general relativity using the methods of canonical relativity and loop quantum gravity. Phase-space dependent deformations of symmetry algebras then appear, which in some regimes can be…

We study the dynamics of extended test bodies in flat Friedmann-Robertson-Walker spacetimes. It is shown that such objects can usually alter their inertial mass, spin, and center-of-mass trajectory purely through the use of internal…

We show that, in the framework of Deformed Special Relativity (DSR), namely a (four-dimensional) generalization of the (local) space-time struc- ture based on an energy-dependent "deformation" of the usual Minkowski geometry, two kinds of…

We study N=2 superconformal theories on Euclidean and Lorentzian four-manifolds with a view toward applications to holography and localization. The conditions for supersymmetry are equivalent to a set of differential constraints including a…