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Register a new userTheory of non-local point transformations - Part 2: General form and Gedanken experiment
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The problem is posed of further extending the axiomatic construction proposed in Part 1 for non-local point transformations mapping in each other different curved space times. The new transformations apply to curved space times when expressed in arbitrary coordinate systems. It is shown that the solution permits to achieve an ideal (Gedanken) experiment realizing a suitable kind of phase-space transformation on point-particle classical dynamical systems. Applications of the theory are discussed both for diagonal and non-diagonal metric tensors.
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In this paper the extension of the functional setting customarily adopted in General Relativity (GR) is considered. For this purpose, an explicit solution of the so-called Einsteins Teleparallel problem is sought. This is achieved by a suitable extension of the traditional concept of GR reference frame and is based on the notion of non-local point transformation (NLPT). In particular, it is shown that a solution to the said problem can be reached by introducing a suitable subset of transformations denoted here as textit{special} textit{NLPT}. These are found to realize a phase-space transformation connectingemph{}the flat Minkowski space-time with, in principle, an arbitrary curved space-time. The functional setting and basic properties of the new transformations are investigated.
This paper is motivated by the introduction of a new functional setting of General Relativity (GR) based on the adoption of suitable group non-local point transformations (NLPT). Unlike the customary local point transformatyion usually utilized in GR, these transformations map in each other intrinsically different curved space-times. In this paper the problem is posed of determining the tensor transformation laws holding for the $4-$% acceleration with respect to the group of general NLPT. Basic physical implications are considered. These concern in particular the identification of NLPT-acceleration effects, namely the relationship established via general NLPT between the $4-$accelerations existing in different curved-space times. As a further application the tensor character of the EM Faraday tensor.with respect to the NLPT-group is established.
The theoretical interpretation of measurements of wavefunctions and spectra in electromagnetic cavities excited by antennas is considered. Assuming that the characteristic wavelength of the field inside the cavity is much larger than the radius of the antenna, we describe antennas as point-like perturbations. This approach strongly simplifies the problem reducing the whole information on the antenna to four effective constants. In the framework of this approach we overcame the divergency of series of the phenomenological scattering theory and justify assumptions lying at the heart of wavefunction measurements. This selfconsistent approach allowed us to go beyond the one-pole approximation, in particular, to treat the experiments with degenerated states. The central idea of the approach is to introduce ``renormalized Green function, which contains the information on boundary reflections and has no singularity inside the cavity.
We obtain the complete theory of Newton-Cartan gravity in a curved spacetime by considering the large $c$ limit of the vielbein formulation of General Relativity. Milne boosts originate from local Lorentzian transformations, and the special cases of torsionless and twistless torsional geometries are explained in the context of the larger locally Lorentzian theory. We write the action for Newton-Cartan fields in the first order Palatini formalism, and the large $c$ limit of the Einstein equations. Finally, we obtain the generalised Eisenhart-Duval lift of the metric that plays an important role in non-relativistic holography.
We derive a formula describing the transformation of the Hawking-Hayward quasi-local energy under a conformal rescaling of the spacetime metric. A known formula for the transformation of the Misner-Sharp-Hernandez mass is recovered as a special case.
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