Related papers: Maximal acceleration in a Lorentz invariant non-co…
This is an introduction to an algebraic construction of a gravity theory on noncommutative spaces which is based on a deformed algebra of (infinitesimal) diffeomorphisms. We start with some fundamental ideas and concepts of noncommutative…
We extend de la Fuente and Romero's defining equation for uniform acceleration in a general curved spacetime from linear acceleration to the full Lorentz covariant uniform acceleration. In a flat spacetime background, we have explicit…
In particular cases of stationary and stationary axially symmetric space-time passage to non-relativistic limit of Einstein equation is completed. For this end the notions of absolute space and absolute time are introduced due to…
We present a framework which unifies a large class of non-commutative spacetimes that can be described in terms of a deformed Heisenberg algebra. The commutation relations between spacetime coordinates are up to linear order in the…
We consider three possible approaches to formulating coordinate transformations on position space associated with non-linear Lorentz transformations on momentum space. The first approach uses the definition of velocity and gives the…
The relativistic acceleration of an electron in a uniform gravitational field is calculated numerically using the generalization of the Dirac equation to curved spacetime. Equivalent results are also obtained analytically using an iterative…
In this paper, we derive corrections to the geodesic equation due to the $k$-deformation of curved space-time, up to the first order in the deformation parameter a. This is done by generalizing the method from our previous paper [31], to…
We discuss the Newtonian limit of boost-rotation symmetric spacetimes by means of the Ehler's frame theory. Conditions for the existence of such a limit are given and, in particular, we show that asymptotic flatness is an essential…
We improve the previous study of the Klein-Gordon equation in a non-commutative space-time as applied to the Hydrogen atom to extract the energy levels, by considering the second-order corrections in the non-commutativity parameter.…
In this paper we study the large-time behavior of perturbative classical solutions to the hard and soft potential Boltzmann equation without the angular cut-off assumption in the whole space $\threed_x$ with $\DgE$. We use the existence…
We propose a new Doubly Special Relativity theory based on the generalization of the $\kappa$-deformation of the Poincar\'e algebra acting along one of the null directions. We recall the quantum Hopf structure of such deformed Poincar\'e…
Quantum speed limits of relativistic charged spin-0 and spin-1 bosons in the background of a homogeneous magnetic field are studied on both commutative and oncommutative planes. We show that, on the commutative plane, the average speeds of…
In a flat spacetime with one spatial dimension compactified, inertial reference frames are not all equivalent, but there are the preferred ones. This paper investigates the nonequivalence of inertial frames and also that of uniformly…
Beginning with a relativistic action principle for the irrotational flow of collisionless matter, we compute higher order corrections to the Zel'dovich approximation by deriving a nonlinear Hamilton-Jacobi equation for the velocity…
The standard approaches of phenomenology of Quantum Gravity have usually explicitly violated Lorentz invariance, either in the dispersion relation or in the addition rule for momenta. We investigate whether it is possible in 3+1 dimensions…
Based on unified theory of electromagnetic interactions and gravitational interactions, the non-relativistic limit of the equation of motion of a charged Dirac particle in gravitational field is studied. From the Schrodinger equation…
We construct and analyze a model of the neutron star in the k deformed space-time. This is done by first deriving the k deformed generalization of the Einstein tensor, starting from the non-commutative generalization of the metric tensor.…
We study a non-commutative deformation of general relativity based on spectral invariants of a partial differential operator acting on sections of a vector bundle over a smooth manifold. We compute the first non-commutative corrections to…
In an attempt to clarify what is the velocity of a particle in doubly special relativity, we solve Maxwell's equations invariant under the position-space nonlinear Lorentz transformation proposed by Kimberly, Magueijo, and Medeiros. We show…
Doubly Special Relativity (DSR) theory is a recently proposed theory with two observer-independent scales (of velocity and mass), which is to describe a kinematic structure underlining the theory of Quantum Gravity. We observe that there is…