相关论文: Superluminal solutions to the Klein-Gordon equatio…

Recent results demonstrating superluminal group velocities and tachyonic dispersion relations reopen the question of superluminal signals and causal loop paradoxes. The sense in which superluminal signals are permitted is explained in terms…

The problem of a Klein-Gordon particle moving in equal vector and scalar Rosen-Morse-type potentials is solved in the framework of Feynman's path integral approach. Explicit path integration leads to a closed form for the radial Green's…

The apparent Lorentz invariance of the laws of physics does not imply that space-time is indeed minkowskian. We consider a scenario where Lorentz invariance is only an approximate property of equations of matter above a certain distance…

In this paper we are interested in the coupled wave and Klein-Gordon equations in $\mathbb{R}^+\times\mathbb{R}^2$. We want to establish the global well-posedness of such system by showing the uniform boundedness of the energy for the…

We consider the spectral problem associated with the Klein-Gordon equation for unbounded electric potentials. If the spectrum of this problem is contained in two disjoint real intervals and the two inner boundary points are eigenvalues, we…

The existence of a faster-than-light particle is in direct opposition to Einstein's relativity and the principle of causality. However, we show that the theory of classical relativistic fields is not inherently inconsistent with the…

Solitons in space-time capable of transporting time-like observers at superluminal speeds have long been tied to violations of the weak, strong, and dominant energy conditions of general relativity. This trend was recently broken by a new…

We show the existence of physical superluminal modes and acausality in the Brans-Dicke type of extension of teleparallel gravity that includes F(T) gravity and teleparallel dark energy as special cases. We derive the characteristic…

The wave equation obeyed by the extraordinary component of the electric field in a hyperbolic metamaterial was shown to be a massless Klein-Gordon field living in a flat spacetime with two timelike and two spacelike dimensions. Such a wave…

We obtain the most general solution of the Einstein electro - vacuum equation for the stationary axially symmetric spacetime in which the Hamilton-Jacobi and Klein - Gordon equations are separable. The most remarkable feature of the…

The Cauchy problem for semi-linear Klein-Gordon equations is considered in Friedmann-Lema\^itre-Robertson-Walker spacetimes. The local and global well-posedness of the Cauchy problem is considered in Sobolev spaces. The non-existence of…

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 prove that small smooth solutions of semi-linear Klein-Gordon equations with quadratic potential exist over a longer interval than the one given by local existence theory, for almost every value of mass. We use normal form for the…

The problem of a spinless particle subject to a general mixing of vector and scalar screened Coulomb potentials in a two-dimensional world is analyzed and its bounded solutions are found. Some unusual results, including the existence of a…

By using geometric methods and superenergy tensors, we find new simple criteria for the causal propagation of physical fields in spacetimes of any dimension. The method can be applied easily to many different theories and to arbitrary…

We consider general semilinear, multispeed Klein-Gordon systems in space dimension two with some non-degeneracy conditions. We prove that with small initial data such solutions are always global and scatter to a linear solution. This result…

We consider waves, which obey the semilinear Klein-Gordon equation, propagating in the Friedmann-Lemaitre-Robertson-Walker spacetimes. The equations in the de Sitter and Einstein-de Sitter spacetimes are the important particular cases. We…

We consider Maxwell-Lorentz dynamics: that is to say, Newton's law under the action of a Lorentz's force which obeys the Maxwell equations. A natural class of solutions are those given by the Lagrangian submanifolds of the phase space when…

The eigenvalue problem for the square integrable solutions is studied usually for elliptic equations. In this note we consider such a problem for the hyperbolic Klein-Gordon equation on Lorentzian manifolds. The investigation could help to…

In this article one will develop a new type of energy method based on a foliation of spacetime into hyperboloidal hypersurfaces . As we will see, with this method, some classical results such as global existence and almost global existence…