On the uniqueness of the space-time energy in General Relativity: the illuminating case of the Schwarzschild metric

The case of asymptotic Minkowskian space-times is considered. A special class of asymptotic rectilinear coordinates at the spatial infinity, related to a specific system of free falling observers, is chosen. This choice is applied in particular to the Schwarzschild metric, obtaining a vanishing energy for this space-time. This result is compared with the result of some known theorems on the uniqueness of the energy of any asymptotic Minkowskian space, showing that there is no contradiction between both results, the differences becoming from the use of coordinates with different operational meanings. The suitability of Gauss coordinates when defining an intrinsic energy is considered and it is finally concluded that a Schwarzschild metric is a particular case of space-times with vanishing intrinsic 4-momenta.     

Exact Solutions of Dirac Equation and Particle Creation in (1+3)-Dimensional Robertson-Walker Spacetime

The exact solutions of the Dirac equation are discussed for a Robertson-Walker spacetime with asymptotically Minkowskian in and out regions. We obtain the mode solutions which reduce to positive and negative Minkowskian spinors in asymptotically regions. Using the obtained solutions we compute the density of created particles.     

Derivation of Einstein's velocity addition theorem through use of the invariant double ratio

The connection between the Minkowskian geometry of the plane and its projective geometry is exemplified by the Einstein velocity addition theorem.     

Bianchi type II,III and V diagonal Einstein metrics re-visited

We present, for both Minkowskian and Euclidean signatures, short derivations of the diagonal Einstein metrics for Bianchi type II, III and V. For the first two cases we show the integrability of the geodesic flow while for the third case a somewhat unusual bifurcation phenomenon takes place: for Minkowskian signature elliptic functions are essential in the metric while for Euclidean signature only elementary functions appear.     

Are the invariance principles really truly Lorentz-covariant?

It is shown that some sections of the invariance (or symmetry) principles, such as the space reversal symmetry (or parityP) and time reversal symmetryT (of elementary particle and condensed matter physics, etc.), are not really truly Lorentz covariant and hence are dependent on the chosen inertial frame; while the world parity or the proper parityW (i.e., the spacetime reversal symmetryPT) is a truly Lorentz covariant concept, the same for all inertial observers. The basic reason for this is that in theMinkowskian space-time continuum frames of special relativity (in contrast to the space and time frames) one cannot change either space or time keeping the other one fixed and also maintain the causality requirements that all world space mappings should be timelike. Indeed, I find that the Dirac-Wigner and Lee-Yang, etc. sense of Lorentz invarianceis not in full compliance with the Einstein-Minkowskirequirements of the Lorentz covariance (in conjunction with the causality requirements) of all physical laws (i.e., the worldspaceMach principle).     

Flat limit of the de Sitter QFT in the rest frame vacuum

The problem of the flat limits of the scalar and spinor fields on the de Sitter expanding universe is considered in the traditional adiabatic vacuum and in the new rest frame vacuum we proposed recently,in which the frequencies are separated in the rest frames as in special relativity.It is shown that only in the rest frame vacuum can the Minkowskian flat limit be reached naturally fbr any momentum,whereas in the adiabatic vacuum,this limit remains undefined in rest frames in which the momentum vanishes.An important role is played by the phases of the fundamental solutions in the rest frame vacuum,which must be regularized to obtain the desired Minkowskian flat limits.This procedure fixes the phases of the scalar mode functions and Dirac spinors,resulting in their definitive expressions derived here.The physical consequenee is that,in the rest frame vacuum,the flat limits of the oneparticle operators are simply the corresponding operators of special relativity.     

Possible Minkowskian language in two-level systems

One hundred years ago, in 1908, Hermann Minkowski completed his proof that Maxwell’s equations are covariant under Lorentz transformations. During this process, he introduced a four-dimensional space called the Minkowskian space. In 1949, P.A.M. Dirac showed the Minkowskian space can be handled with the light-cone coordinate system with squeeze transformations. While the squeeze is one of the fundamental mathematical operations in optical sciences, it could serve useful purposes in two-level systems. Some possibilities are considered in this report. It is shown possible to cross the light-cone boundary in optical and two-level systems while it is not possible in Einstein’s theory of relativity.     

On the geometrical interpretation of the theory of gravitation in flat space

In the framework of the flat space-time approach to gravitational theory the equations of motion of point particles are derived from a suitable Lagrangian. Attention is paid to the distinction of the different worldline parameters in Minkowskian und Riemannian space-time. It is shown that the world-lines of point particles are geodesics in a Riemannian space-time and permit a consistent geometrical interpretation of the theory.     

Self-duality in Euclidean supergravity

The compatibility of Euclidean supergravity with curvature satisfying (a) self-duality and (b) a double duality Ansatz are investigated. The Minkowskian version of (b) is also considered.     

199 Causal classes of space-time frames

It is shown that from the causal point of view Minkowskian space-time admits 199, and only 199, different classes of frames.     

The geodesics of the Kaluza-Klein wormhole soliton

The Kaluza-Klein wormhole soliton metric is a regular localized solution with Minkowskian signature, to the sourceless five-dimensional Einstein equations. We apply five-to-three dimensional reduction to convert the problem of geodesic motion of neutral or charged test particles in this metric to a non-relativistic potential problem, which we discuss in detail, studying bound and scattering states. We show that there is no observable difference between scattering of a spinless test particle by a point charge and by a wormhole soliton.     

Fermions in a Kerr-Newman space-time

The aim of this paper is to put the U(1) -gauge theory of fermions in the spacetime described by a Kerr-Newman metric. The field equations have rather complicated expressions essentially different from the Minkowskian spacetime.     

The Lewis metric and flat space-time

It is shown that the stationary solution of the Einstein equationsin vacuo, with the cylindrical symmetry obtained by Lewis, does not contain a space-time that is globally Minkowskian. It is shown that the inclusion of a certain constant of integration excludes this flat space-time metric.     

Nonminimal gravitational coupling: The spectrum of cosmic solutions

We present a complete analysis of the set of homogeneous and isotropic cosmological solutions generated by a vector field coupled nonminimally to gravity. As a consequence of this analysis we can interpret our universe as (classical) fluctuations in the infinite past of unstable Minkowskian space-time.     

From unstable Minkowski space to inflation

We present a perturbative approach to the equations describing the behavior of a quantum scalar field in a self-consistently generated Robertson-Walker universe. This approach throws new light on the significance of the Minkowskian instability and on the subtraction procedure which shows that a inflation cosmology is a possible future of the Minkowski space.     

Convolution of Ultradistributions,Field Theory,Lorentz Invariance and Resonances

In this work, a general definition of convolution between two arbitrary Ultradistributions of Exponential type (UET) is given. The product of two arbitrary UET is defined via the convolution of its corresponding Fourier Transforms. Some examples of convolution of two UET are given. Expressions for the Fourier Transform of spherically symmetric (in Euclidean space) and Lorentz invariant (in Minkowskian space) UET in term of modified Bessel distributions are obtained (Generalization of Bochner’s theorem). The generalization to UET of dimensional regularization in configuration space is obtained in both, Euclidean and Minkowskian spaces As an application of our formalism, we give a solution to the question of normalization of resonances in Quantum Mechanics. General formulae for convolution of even, spherically symmetric and Lorentz invariant UET are obtained and several examples of application are given. This work was partially supported by Consejo Nacional de Investigaciones Científicas and Comisión de Investigaciones Científicas de la Pcia. de Buenos Aires; Argentina.     

Real-time gauge theory simulations from stochastic quantization with optimized updating

Stochastic quantisation is applied to the problem of calculating real-time evolution on a Minkowskian space-time lattice. We employ optimized updatig using reweighting, or gauge fixing, respectively. These procedures do not affect the underlying theory, but strongly improve the stability properties of the stochastic dynamics.     

Hyperbolic complex numbers and nonlinear sigma models

We show that the hyperbolic complex numbers or double numbers can be used to generate solutions of two-dimensional Minkowskian sigma models with values on noncompact manifolds.     

Non-gravitating waves

It is pointed out that scalar-tensor theories of gravity admit solutions in which the metric is Minkowskian although the scalar and matter fields do not vanish. Explicit pp-wave solutions of the Brans-Dicke-Maxwell theory are presented. These include solutions with metrics that are flat or Ricci flat even though the Maxwell and scalar fields are non-zero.