相关论文: A 4+1 Formalism for the Evolving Stueckelberg-Horw…
We present a canonical Hamiltonian formulation of GR in which $\tau$, the parameter of system evolution, is external to spacetime, playing a role similar to what we call time in nonrelativistic mechanics. This approach, known as…
In a series of recent papers we developed a formulation of general relativity in which spacetime and the dynamics of matter evolve with a Poincar\'e invariant parameter $\tau$. In this paper, we apply the formalism to derive the metric…
In this paper, we study fundamental aspects of electrostatics as a special case in Stueckelberg-Horwitz electromagnetic theory. In this theory, spacetime events $x^\mu(\tau)$ evolve in an unconstrained 8-dimensional phase space, interacting…
We first consider the Klein-Gordon equation in the 6-dimensional space $M_{2,4}$ with signature $+ - - - - +$ and show how it reduces to the Stueckelberg equation in the 4-dimensional spacetime $M_{1,3}$. A field that satisfies the…
It is well-known that the 5D gauge structure of Stueckelberg-Horwitz-Piron (SHP) electrodynamics permits the exchange of mass between particles and the fields induced by their motion, even at the classical level. This phenomenon presents…
We analyze properties of the Sp(2M) conformally invariant field equations in the recently proposed generalized $\half M(M+1)$-dimensional space-time $\M_M$ with matrix coordinates. It is shown that classical solutions of these field…
The standard theory of General Relativity (GR) currently provides the most reliable description of all gravitational events in Astrophysics and Cosmology. However, current Astronomy allows measurements that contradict the predictions of GR…
The current paper is dedicated to developing a (3+1) decomposition for the minimal gravitational Standard-Model Extension. Our setting is explicit diffeomorphism violation and we focus on the background fields known in the literature as $u$…
We review the classical and quantum mechanics of Stueckelberg, and introduce the compensation fields necessary for the gauge covariance of the Stueckelberg- Schr\"odinger equation. To achieve this, one must introduce a fifth, Lorentz…
We present a 3+1 formulation of the effective field theory framework called the Standard-Model Extension in the gravitational sector. The explicit local Lorentz and diffeomorphism symmetry breaking assumption is adopted and we perform a…
We present SphericalNR, a new framework for the publicly available Einstein Toolkit that numerically solves the Einstein field equations coupled to the equations of general relativistic magnetohydrodynamics (GRMHD) in a 3+1 split of…
In general relativity, the Einstein equations provide spherically symmetric static spacetimes with dynamics defined as an evolution along the radial coordinate $r$. The geometrical sector becomes a one-dimensional mechanical system, with…
We consider spacetime to be a 4-dimensional differentiable manifold that can be split locally into time and space. No metric, no linear connection are assumed. Matter is described by classical fields/fluids. We distinguish electrically…
We develop a gauge-invariant formalism to describe metric perturbations in five-dimensional brane-world theories. In particular, this formalism applies to models originating from heterotic M-theory. We introduce a generalized longitudinal…
A modification of General Relativity that is based on the gravitational Standard-Model Extension and incorporates nondynamical background fields has recently been studied via the ADM formalism. Our objective in this paper is to develop a…
We derive a formalism of numerical relativity for higher-dimensional spacetimes and develop numerical codes for simulating a wide variety of five-dimensional (5D) spacetimes for the first time. First, the Baumgarte-Shapiro-Shibata-Nakamura…
A relativistic 4D string is described in the framework of the covariant quantum theory first introduced by Stueckelberg (1941) [1], and further developed by Horwitz and Piron (1973) [2], and discussed at length in the book of Horwitz (2015)…
We propose a Kaluza-Klein approach to general relativity of 4-dimensional spacetimes. This approach is based on the (2,2)-splitting of a generic 4-dimensional spacetime, which is viewed as a local product of a (1+1)-dimensional base…
The numerical evolution of Einstein's field equations in a generic background has the potential to answer a variety of important questions in physics: from applications to the gauge-gravity duality, to modelling black hole production in TeV…
We propose a Robinson-Trautman evolution in $(2+1)$-dimensional spacetime that retains key structural features of the four-dimensional case. We consider a recently studied exact family of metrics to select a nonstationary geometry with a…