Related papers: On Spacetimes with Given Kinematical Invariants: C…
One of basic difficulties of machine learning is handling unknown rotations of objects, for example in image recognition. A related problem is evaluation of similarity of shapes, for example of two chemical molecules, for which direct…
Many astrophysical simulations involve extreme dynamic range of timescales around 'special points' in the domain (e.g. black holes, stars, planets, disks, galaxies, shocks, mixing interfaces), where processes on small scales couple strongly…
We construct four-dimensional effective field theories of a generalized DBI galileon field, the dynamics of which naturally take place on a Friedmann-Robertson-Walker spacetime. The theories are invariant under non-linear symmetry…
The time dependent conformally-flat spherical Rindler spacetime is investigated. The geometry has an apparent horizon that coincides with the causal horizon. The scalar acceleration of a static observer is constant and equals to the…
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…
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…
We derive quantum kinetic equations for scalar fields undergoing coherent evolution either in time (coherent particle production) or in space (quantum reflection). Our central finding is that in systems with certain space-time symmetries,…
We consider cosmological models in scalar tensor theories of gravity that describe an accelerating universe, and we study a family of inverse power law potentials, for which exact solutions of the Einstein equations are known. We also…
A mathematical model of the Universe evolution, based on asymmetric doublet of classical and phantom dcalar Higgs fields with a kinetic connection between the components, has been constructed and studied. A detailed qualitative analysis was…
A dynamical resolution to the cosmological constant fine-tuning problem has been previously put forward, based on a scalar-tensor gravitational theory possessing de Sitter attractor solutions characterized by a small Hubble expansion rate,…
We examine some Weyl invariant cosmological models in the framework of generalized dilaton gravity, in which the action is made of a set of $N$ conformally coupled scalar fields. It will be shown that when the FRW ansatz for the spacetime…
A solution to the equivalence problem in three-dimensional gravity is given and a practically useful method to obtain a coordinate invariant description of local geometry is presented. The method is a nontrivial adaptation of Karlhede…
A model of the thin shell expanding into a uniform ambient medium is developed. Density perturbations are described using equations with linear and quadratic terms, and the linear and the nonlinear solutions are compared. We follow the time…
We construct the linear and quadratic polynomial dynamical invariants for the classical and quantum time-dependent harmonic oscillator driven by a time-dependent force. To obtain them, we use exclusively the associated equations of motion…
We provide a novel approach to model space-time random fields where the temporal argument is decomposed into two parts. The former captures the linear argument, which is related, for instance, to the annual evolution of the field. The…
In recent years there has been a lot of interest in discussing frame dependences/independences of the cosmological perturbations under the conformal transformations. This problem has previously been investigated in terms of the covariant…
The geodesic deviation equation (`GDE') provides an elegant tool to investigate the timelike, null and spacelike structure of spacetime geometries. Here we employ the GDE to review these structures within the…
In a number of astrophysical applications one tries to determine the two-dimensional or three-dimensional structure of an object from a time series of measurements. While most methods used for reconstruction assume that object is static,…
The model of a stationary universe and the notion of local times presented in [10] are reviewed with some alternative formulation of the consistent unification of the Riemannian and Euclidean geometries of general relativity and quantum…
We propose a step-by-step manual for the construction of alternative theories of gravity, perturbatively as well as nonperturbatively. The construction is guided by no more than two fundamental principles that we impose on the gravitational…