scholarly journals Proper time and conformal problem in Kaluza–Klein theory

2015 ◽  
Vol 12 (05) ◽  
pp. 1550063
Author(s):  
E. Minguzzi
Keyword(s):  
Scalar Field ◽  
Gordon Equation ◽  
Proper Time ◽  
Inertial Mass ◽  
Scalar Fields ◽  
Conformal Factor ◽  
Klein Theory ◽  
Klein Gordon ◽  
Klein Gordon Equation ◽  
Kaluza Klein

In the traditional Kaluza–Klein theory, the cylinder condition and the constancy of the extra-dimensional radius (scalar field) imply that time-like geodesics on the five-dimensional bundle project to solutions of the Lorentz force equation on spacetime. This property is lost for nonconstant scalar fields, in fact there appears new terms that have been interpreted mainly as new forces or as due to a variable inertial mass and/or charge. Here we prove that the additional terms can be removed if we assume that charged particles are coupled with the same spacetime conformal structure of neutral particles but through a different conformal factor. As a consequence, in Kaluza–Klein theory the proper time of the charged particle might depend on the charge-to-mass ratio and the scalar field. Then we show that the compatibility between the equation of the projected geodesic and the classical limit of the Klein–Gordon equation fixes unambiguously the conformal factor of the coupling metric solving the conformal ambiguity problem of Kaluza–Klein theories. We confirm this result by explicitly constructing the projection of the Klein–Gordon equation and by showing that each Fourier mode, even for a variable scalar field, satisfies the Klein–Gordon equation on the base.

scholarly journals Vaidya geometries and scalar fields with null gradients

2021 ◽  
Vol 81 (3) ◽  
Author(s):  
Valerio Faraoni ◽  
Andrea Giusti ◽  
Bardia H. Fahim
Keyword(s):  
Scalar Field ◽  
Gordon Equation ◽  
Plane Waves ◽  
Null Geodesic ◽  
Scalar Fields ◽  
Einstein Gravity ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Klein Gordon ◽  
Klein Gordon Equation

AbstractSince, in Einstein gravity, a massless scalar field with lightlike gradient behaves as a null dust, one could expect that it can act as the matter source of Vaidya geometries. We show that this is impossible because the Klein–Gordon equation forces the null geodesic congruence tangent to the scalar field gradient to have zero expansion, contradicting a basic property of Vaidya solutions. By contrast, exact plane waves travelling at light speed and sourced by a scalar field acting as a null dust are possible.

PARTICLE MASSES IN KALUZA–KLEIN–GORDON THEORY AND THE REALITY OF EXTRA DIMENSIONS

1998 ◽  
Vol 13 (33) ◽  
pp. 2689-2694 ◽  
Author(s):  
HONGYA LIU ◽  
PAUL S. WESSON
Keyword(s):  
Wave Function ◽  
Exact Solutions ◽  
Extra Dimension ◽  
Extra Dimensions ◽  
Gordon Equation ◽  
Superstring Theory ◽  
Klein Theory ◽  
Klein Gordon ◽  
Klein Gordon Equation ◽  
Kaluza Klein

To see how the effective 4-D mass of a particle is affected by the geometry of an ND space, we take the Klein–Gordon equation in 5-D and evaluate it in 4-D using two exact solutions of 5-D Kaluza–Klein theory. The mass (squared) turns out to be complex if the theory is independent of the extra coordinate, but can be made real if the wave function depends on an extra dimension which is physical. These results have significant implications for 10-D superstring theory.

Mechanics of a charged particle on the Kaluza–Klein background

1995 ◽  
Vol 73 (9-10) ◽  
pp. 602-607 ◽  
Author(s):  
S. R. Vatsya
Keyword(s):  
Electromagnetic Field ◽  
Charged Particle ◽  
Integral Method ◽  
Gordon Equation ◽  
Type Equation ◽  
Fifth Dimension ◽  
Klein Gordon ◽  
Path Integral Method ◽  
Klein Gordon Equation ◽  
Kaluza Klein

The path-integral method is used to derive a generalized Schrödinger-type equation from the Kaluza–Klein Lagrangian for a charged particle in an electromagnetic field. The compactness of the fifth dimension and the properties of the physical paths are used to decompose this equation into its infinite components, one of them being similar to the Klein–Gordon equation.

scholarly journals A Central Potential with a Massive Scalar Field in a Lorentz Symmetry Violation Environment

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
R. L. L. Vitória ◽  
H. Belich
Keyword(s):  
Scalar Field ◽  
Gordon Equation ◽  
Mass Term ◽  
Lorentz Symmetry ◽  
Massive Scalar ◽  
Symmetry Violation ◽  
Massive Scalar Field ◽  
Klein Gordon ◽  
Coulomb Type ◽  
Klein Gordon Equation

We investigate the behaviour of a massive scalar field under the influence of a Coulomb-type and central linear central potentials inserted in the Klein-Gordon equation by modifying the mass term in the spacetime with Lorentz symmetry violation. We consider the presence of a background constant vector field which characterizes the breaking of the Lorentz symmetry and show that analytical solutions to the Klein-Gordon equation can be achieved.

scholarly journals Does Inflationary Particle Production Suggest a Low-Density Flat Universe?

1999 ◽  
Vol 183 ◽  
pp. 314-314
Author(s):  
Varun Sahni ◽  
Salman Habib
Keyword(s):  
Scalar Field ◽  
Particle Production ◽  
Gordon Equation ◽  
Low Density ◽  
Frw Universe ◽  
Flat Universe ◽  
Klein Gordon ◽  
Klein Gordon Equation

In a FRW Universe a massless nonminimally coupled scalar field satisfies the Klein-Gordon equation.

scholarly journals THE QUANTUM THEORY OF SCALAR FIELDS ON THE DE SITTER EXPANDING UNIVERSE

2008 ◽  
Vol 23 (16n17) ◽  
pp. 2563-2577 ◽  
Author(s):  
ION I. COTĂESCU ◽  
COSMIN CRUCEAN ◽  
ADRIAN POP
Keyword(s):  
Scalar Field ◽  
Gordon Equation ◽  
Scalar Fields ◽  
Wave Functions ◽  
De Sitter ◽  
Scalar Quantum ◽  
Long Time ◽  
Klein Gordon ◽  
Free Scalar ◽  
Special Time

New quantum modes of the free scalar field are derived in a special time-evolution picture that may be introduced in moving charts of de Sitter backgrounds. The wave functions of these new modes are solutions of the Klein–Gordon equation and energy eigenfunctions, defining the energy basis. This completes the scalar quantum mechanics where the momentum basis is well known for long time. In this enlarged framework the quantization of the scalar field can be done in canonical way obtaining the principal conserved one-particle operators and the Green functions.

scholarly journals A NOTE ON KLEIN–GORDON EQUATION IN A GENERALIZED KALUZA–KLEIN MONOPOLE BACKGROUND

2007 ◽  
Vol 22 (22) ◽  
pp. 1621-1634 ◽  
Author(s):  
EUGEN RADU ◽  
MIHAI VISINESCU
Keyword(s):  
Black Holes ◽  
Gordon Equation ◽  
Asymptotic Structure ◽  
Klein Gordon ◽  
Monopole Solution ◽  
Klein Gordon Equation ◽  
Kaluza Klein

We investigate solutions to the Klein–Gordon equation in a class of five-dimensional geometries presenting the same symmetries and asymptotic structure as the Gross–Perry–Sorkin monopole solution. Apart from globally regular metrics, we consider also squashed Kaluza–Klein black holes backgrounds.

scholarly journals The spacetime between Einstein and Kaluza–Klein

2020 ◽  
Vol 35 (36) ◽  
pp. 2030020
Author(s):  
Chris Vuille
Keyword(s):  
General Relativity ◽  
Scalar Field ◽  
Differential Operators ◽  
Mathematical Structure ◽  
Field Equations ◽  
Five Dimensions ◽  
Four Dimensions ◽  
Klein Theory ◽  
Klein Gordon ◽  
Kaluza Klein

In this paper I introduce tensor multinomials, an algebra that is dense in the space of nonlinear smooth differential operators, and use a subalgebra to create an extension of Einstein’s theory of general relativity. In a mathematical sense this extension falls between Einstein’s original theory of general relativity in four dimensions and the Kaluza–Klein theory in five dimensions. The theory has elements in common with both the original Kaluza–Klein and Brans–Dicke, but emphasizes a new and different underlying mathematical structure. Despite there being only four physical dimensions, the use of tensor multinomials naturally leads to expanded operators that can incorporate other fields. The equivalent Ricci tensor of this geometry is robust and yields vacuum general relativity and electromagnetism, as well as a Klein–Gordon-like quantum scalar field. The formalism permits a time-dependent cosmological function, which is the source for the scalar field. I develop and discuss several candidate Lagrangians. Trial solutions of the most natural field equations include a singularity-free dark energy dust cosmology.

scholarly journals On f(R) gravity in scalar–tensor theories

2017 ◽  
Vol 14 (07) ◽  
pp. 1750107 ◽  
Author(s):  
Joseph Ntahompagaze ◽  
Amare Abebe ◽  
Manasse Mbonye
Keyword(s):  
Scalar Field ◽  
Gordon Equation ◽  
Gravity Models ◽  
Index Formula ◽  
Coupling Constant ◽  
The Third ◽  
Slow Roll ◽  
Klein Gordon ◽  
Early Universe Cosmology ◽  
Klein Gordon Equation

We study [Formula: see text] gravity models in the language of scalar–tensor (ST) theories. The correspondence between [Formula: see text] gravity and ST theories is revisited since [Formula: see text] gravity is a subclass of Brans–Dicke models, with a vanishing coupling constant ([Formula: see text]). In this treatment, four [Formula: see text] toy models are used to analyze the early-universe cosmology, when the scalar field [Formula: see text] dominates over standard matter. We have obtained solutions to the Klein–Gordon equation for those models. It is found that for the first model [Formula: see text], as time increases the scalar field decreases and decays asymptotically. For the second model [Formula: see text], it was found that the function [Formula: see text] crosses the [Formula: see text]-axis at different values for different values of [Formula: see text]. For the third model [Formula: see text], when the value of [Formula: see text] is small, the potential [Formula: see text] behaves like the standard inflationary potential. For the fourth model [Formula: see text], we show that there is a transition between [Formula: see text]. The behavior of the potentials with [Formula: see text] is totally different from those with [Formula: see text]. The slow-roll approximation is applied to each of the four [Formula: see text] models and we obtain the respective expressions for the spectral index [Formula: see text] and the tensor-to-scalar ratio [Formula: see text].

scholarly journals Scalar-field theory of dark matter

2014 ◽  
Vol 29 (13) ◽  
pp. 1450074 ◽  
Author(s):  
Kerson Huang ◽  
Chi Xiong ◽  
Xiaofei Zhao
Keyword(s):  
Dark Matter ◽  
Scalar Field ◽  
Gordon Equation ◽  
Galactic Halo ◽  
Galactic Rotation ◽  
Klein Gordon ◽  
External Sources ◽  
Galaxy Collisions ◽  
The Universe ◽  
Klein Gordon Equation

We develop a theory of dark matter based on a previously proposed picture, in which a complex vacuum scalar field makes the universe a superfluid, with the energy density of the superfluid giving rise to dark energy, and variations from vacuum density giving rise to dark matter. We formulate a nonlinear Klein–Gordon equation to describe the superfluid, treating galaxies as external sources. We study the response of the superfluid to the galaxies, in particular, the emergence of the dark-matter galactic halo, contortions during galaxy collisions and the creation of vortices due to galactic rotation.

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