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Register a new userTheory of non-local point transformations - Part 3: Theory of NLPT-acceleration and the physical origin of acceleration effects in curved space-times
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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.
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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.
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.
In this paper the Feynman Green function for Maxwells theory in curved space-time is studied by using the Fock-Schwinger-DeWitt asymptotic expansion; the point-splitting method is then applied, since it is a valuable tool for regularizing divergent observables. Among these, the stress-energy tensor is expressed in terms of second covariant derivatives of the Hadamard Green function, which is also closely linked to the effective action; therefore one obtains a series expansion for the stress-energy tensor. Its divergent part can be isolated, and a concise formula is here obtained: by dimensional analysis and combinatorics, there are two kinds of terms: quadratic in curvature tensors (Riemann, Ricci tensors and scalar curvature) and linear in their second covariant derivatives. This formula holds for every space-time metric; it is made even more explicit in the physically relevant particular cases of Ricci-flat and maximally symmetric spaces, and fully evaluated for some examples of physical interest: Kerr and Schwarzschild metrics and de Sitter space-time.
Theories of scalars and gravity, with non-minimal interactions, $sim (M_P^2 +F(phi) )R +L(phi)$, have graviton exchange induced contact terms. These terms arise in single particle reducible diagrams with vertices $propto q^2$ that cancel the Feynman propagator denominator $1/q^2$ and are familiar in various other physical contexts. In gravity these lead to additional terms in the action such as $sim F(phi) T_mu^mu(phi)/M_P^2$ and $F(phi)partial^2 F(phi)/M_P^2$. The contact terms are equivalent to induced operators obtained by a Weyl transformation that removes the non-minimal interactions, leaving a minimal Einstein-Hilbert gravitational action. This demonstrates explicitly the equivalence of different representations of the action under Weyl transformations, both classically and quantum mechanically. To avoid such hidden contact terms one is compelled to go to the minimal Einstein-Hilbert representation.
We consider an extended scalar-tensor theory of gravity where the action has two interacting scalar fields, a Brans-Dicke field which makes the effective Newtonian constant a function of coordinates and a Higgs field which has derivative and non-derivative interaction with the lagrangian. There is a non-trivial interaction between the two scalar fields which dictates the dominance of different scalar fields in different era. We investigate if this setup can describe a late-time cosmic acceleration preceded by a smooth transition from deceleration in recent past. From a cosmological reconstruction technique we find the scalar profiles as a function of redshift. We find the constraints on the model parameters from a Markov Chain Monte Carlo analysis using observational data. Evolution of an effective equation of state, matter density contrast and thermodynamic equilibrium of the universe are studied and their significance in comparison with a LCDM cosmology is discussed.
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