Related papers: Localized Propagating Tachyons in Extended Relativ…
In this article, the general solution of the tachyonic Klein-Gordon equation is obtained as a Fourier integral performed on a suitable path in the complex \omega-plane. In particular, it is proved that under given boundary conditions this…
We study the Cauchy problem on the real line for the nonlocal Fisher-KPP equation in one spatial dimension, \[ u_t = D u_{xx} + u(1-\phi*u), \] where $\phi*u$ is a spatial convolution with the top hat kernel, $\phi(y) \equiv…
We discuss phenomenology of extra time dimensions in a scenario where the standard model particles are localized in ``our'' time, whereas gravity can propagate in all time dimensions. For an odd number of extra times, at small distances,…
We consider a 5-dimensional scalar-tensor theory which is a direct generalization of the original 4-dimensional Brans-Dicke theory to 5-dimensions. By assuming that there is a hypersurface-orthogonal spacelike Killing vector field in the…
Although the traditional form of the Einstein field equations is intrinsically four-dimensional, the field of numerical general relativity focuses on the reformulation of these equations as a 3 + 1-dimensional Cauchy problem, in which…
We study time-dependent solutions of Einstein-Maxwell gravity in four dimensions coupled to tachyon matter--the Dirac-Born-Infeld Lagrangian that provides an effective description of a decaying tachyon on an unstable D-brane in string…
A consistent theory of faster-than-light particles (tachyons) can be built replacing the standard Lorentz-invariant approach to the quantum field theory of tachyons by the Lorentz-covariant one, invoking a concept of the preferred reference…
Within Yang-Mills gravity with translation group $T(4)$ in flat space-time, the invariant action involving quadratic translation gauge-curvature leads to quadrupole radiations which are shown to be consistent with experiments. The radiation…
We formulate the locally supersymmetric E$_{7(7)}$ exceptional field theory in a $(4+56|32)$ dimensional superspace, corresponding to a 4D $N\!=\!8$ "external" superspace augmented with an "internal" 56-dimensional space. This entails the…
We analyze the Cauchy problem for the Klein-Gordon equation on the type IIB supergravity backgrounds $AdS^5 \times Y^{p,q}$, where $Y^{p,q}$ is any of the Sasaki-Einstein 5-manifolds recently discovered by Gaunlett, Martelli, Sparks and…
We construct a class of solutions to the Cauchy problem of the Klein-Gordon equation on any standard static spacetime. Specifically, we have constructed solutions to the Cauchy problem based on any self-adjoint extension (satisfying a…
The paper examines stochastic diffusion within an expanding space-time framework. It starts with providing a rationale for the considered model and its motivation from cosmology where the expansion of space-time is used in modelling various…
The notion of maximal extension of a globally hyperbolic space-time arises from the notion of maximal solutions of the Cauchy problem associated to the Einstein's equations of general relativity. In 1969 Choquet-Bruhat and Geroch proved…
The Cauchy problem for the Schr\"odinger equations is studied with time-dependent potentials growing polynomially in the spatial direction. First the existence and the uniqueness of solutions are shown in the weighted Sobolev spaces. In…
Superluminal electromagnetic fields of dyons are described in T^{4}- space and Quaternion formulation of various quantum equations is derived. It is shown that on passing from subluminal to superluminal realm via quaternion the theory of…
We show that the scalar-vacuum Brans-Dicke equations in 5D are equivalent to Brans-Dicke theory in 4D with a self interacting potential and an effective matter field. The cosmological implication, in the context of FRW models, is that the…
We investigate the differential geometry and topology of four-dimensional Lorentzian manifolds $(M,g)$ equipped with a real Killing spinor $\varepsilon$, where $\varepsilon$ is defined as a section of a bundle of irreducible real Clifford…
We consider two examples of solutions of the equations of motion of scalar field theories with higher derivatives. These are the cosmology of the rolling tachyon and static spherically symmetric solutions of the scalar field in flat space.…
We study the massless scalar, Dirac and electro-magnetic fields propagating on a 4D-brane, which is embedded in higher dimensional Gauss-Bonnet space-time. We calculate, in time-domain, the fundamental quasi-normal modes of a spherically…
We review some recent results on the theory of scattering and more precisely on the local Cauchy problem at infinity in time for some long range nonlinear systems including some form of the Schr"odinger equation. We consider in particular…