scholarly journals Kaluza-Klein Multidimensional Models with Ricci-Flat Internal Spaces: The Absence of the KK Particles

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Alexey Chopovsky ◽  
Maxim Eingorn ◽  
Alexander Zhuk
Keyword(s):  
Statistical Physics ◽  
Internal Space ◽  
Nonzero Temperature ◽  
Ricci Flat ◽  
Radar Echoes ◽  
Astrophysical Objects ◽  
Correction Terms ◽  
Multidimensional Models ◽  
Metric Fluctuations ◽  
Kaluza Klein

We consider a multidimensional Kaluza-Klein (KK) model with a Ricci-flat internal space, for example, a Calabi-Yau manifold. We perturb this background metrics by a system of gravitating masses, for example, astrophysical objects such as our Sun. We suppose that these masses are pressureless in the external space but they have relativistic pressure in the internal space. We show that metric perturbations do not depend on coordinates of the internal space and gravitating masses should be uniformly smeared over the internal space. This means, first, that KK modes corresponding to the metric fluctuations are absent and, second, particles should be only in the ground quantum state with respect to the internal space. In our opinion, these results look very unnatural. According to statistical physics, any nonzero temperature should result in fluctuations, that is, in KK modes. We also get formulae for the metric correction terms which enable us to calculate the gravitational tests: the deflection of light, the time-delay of the radar echoes, and the perihelion advance.

MULTIDIMENSIONAL COSMOLOGY AND FUNDAMENTAL CONSTANTS

2009 ◽  
Vol 24 (08n09) ◽  
pp. 1473-1480 ◽  
Author(s):  
V. N. MELNIKOV
Keyword(s):  
Black Holes ◽  
Fundamental Constants ◽  
Fundamental Physical Constants ◽  
Cosmological Singularity ◽  
Brane Worlds ◽  
Multidimensional Cosmology ◽  
Multidimensional Models ◽  
Different Sources ◽  
Fundamental Physical ◽  
Kaluza Klein

Studies of multidimensional models with different sources (models with S -branes, thin and thick brane worlds, Kaluza-Klein type models in curvature-nonlinear multidimensional gravity etc.) and their application to the cosmological constant, cosmological singularity, hierarchy and coincidence problems are presented. Their observational predictions: variations of fundamental physical constants, new types of black holes and wormholes are discussed.

scholarly journals KALUZA–KLEIN DIMENSIONAL REDUCTION AND GAUSS–CODAZZI–RICCI EQUATIONS

2009 ◽  
Vol 24 (06) ◽  
pp. 1207-1220
Author(s):  
PEI WANG
Keyword(s):  
General Relativity ◽  
Dimensional Reduction ◽  
Traditional Method ◽  
Isometry Group ◽  
Extrinsic Curvature ◽  
Internal Space ◽  
Geometric Meaning ◽  
Reduced Dimensions ◽  
Lower Dimensional ◽  
Kaluza Klein

In this paper we imitate the traditional method which is used customarily in the general relativity and some mathematical literatures to derive the Gauss–Codazzi–Ricci equations for dimensional reduction. It would be more distinct concerning geometric meaning than the vielbein method. Especially, if the lower-dimensional metric is independent of reduced dimensions the counterpart of the symmetric extrinsic curvature is proportional to the antisymmetric Kaluza–Klein gauge field strength. For isometry group of internal space, the SO (n) symmetry and SU (n) symmetry are discussed. And the Kaluza–Klein instanton is also enquired.

INFLATION IN KALUZA-KLEIN COSMOLOGY II: FRIEDMANN MODELS

1990 ◽  
Vol 05 (24) ◽  
pp. 4671-4676 ◽  
Author(s):  
ULRICH BLEYER ◽  
HANS-JÜRGEN SCHMIDT
Keyword(s):  
Power Law ◽  
Fourth Order ◽  
Conformal Transformation ◽  
Preceding Paper ◽  
Internal Space ◽  
De Sitter ◽  
Scale Invariant ◽  
Attractor Solution ◽  
Friedmann Cosmological Models ◽  
Kaluza Klein

The conformal relation between scale-invariant fourth-order gravity and Kaluza-Klein models as derived in the preceding paper (I) is applied to Friedmann cosmological models. Especially, the result that power-law inflation is an attractor solution can be carried over, but the conformal transformation brings power-law inflation to de Sitter-like exponential inflation, or power-law inflation a ≈ t. The results depend essentially on the dimension of the internal space.

scholarly journals “Twisted” black holes are unphysical

2017 ◽  
Vol 32 (18) ◽  
pp. 1771001 ◽  
Author(s):  
Finnian Gray ◽  
Jessica Santiago ◽  
Sebastian Schuster ◽  
Matt Visser
Keyword(s):  
Black Holes ◽  
Event Horizon ◽  
Rotation Axis ◽  
Einstein Equations ◽  
Entire Region ◽  
Asymptotically Flat ◽  
Ricci Flat ◽  
Vacuum Einstein Equations ◽  
Astrophysical Objects

So-called “twisted” black holes were recently proposed by [H. Zhang, arXiv:1609.09721 ], and were further considered by [S. Chen and J. Jing, arXiv:1610.00886 ]. More recently, they were severely criticized by [Y. C. Ong, J. Cosmol. Astropart. Phys. 1701, 001 (2017)]. While these spacetimes are certainly Ricci-flat, and so mathematically satisfy the vacuum Einstein equations, they are also merely minor variants on Taub–NUT spacetimes. Consequently, they exhibit several unphysical features that make them quite unreasonable as realistic astrophysical objects. Specifically, these “twisted” black holes are not (globally) asymptotically flat. Furthermore, they contain closed time-like curves that are not hidden behind any event horizon — the most obvious of these closed time-like curves are small azimuthal circles around the rotation axis, but the effect is more general. The entire region outside the horizon is infested with closed time-like curves.

MASSLESS SCALAR FIELDS IN NON-ABELIAN KALUZA-KLEIN THEORY

1994 ◽  
Vol 09 (04) ◽  
pp. 507-515 ◽  
Author(s):  
M. ARIK ◽  
V. GABAY
Keyword(s):  
Cosmological Constant ◽  
Direct Product ◽  
Scalar Fields ◽  
Gauge Fields ◽  
Internal Space ◽  
Massless Scalar ◽  
Klein Theory ◽  
Euler Form ◽  
Odd Dimensions ◽  
Kaluza Klein

We investigate the presence of massless scalar fields in a Kaluza—Klein theory based on a dimensionally continued Euler-form action. We show that massless scalar fields exist provided that the internal space is a direct product of two irreducible manifolds. The condition of a vanishing effective four-dimensional cosmological constant and the presence of a graviton, gauge fields and massless scalar fields can be satisfied if both irreducible manifolds have odd dimensions and the sum of these dimensions is equal to the dimension of the Euler form.

SPONTANEOUS CONTRACTION

1988 ◽  
Vol 03 (15) ◽  
pp. 1473-1477 ◽  
Author(s):  
Y.M. CHO ◽  
P.Y. PAC
Keyword(s):  
Spontaneous Contraction ◽  
Internal Space ◽  
Higher Dimensional ◽  
Kaluza Klein

The phenomenon of a spontaneous contraction in higher-dimensional geometric theories of Kaluza-Klein type is discussed which could lead to a spontaneous decompactification of the internal space. In a spontaneous contraction, an isometry G is contracted to G′ by the vacuum which often breaks G′ further down to H spontaneously.

KALUZA-KLEIN THEORY

1986 ◽  
Vol 01 (01) ◽  
pp. 1-37 ◽  
Author(s):  
J. STRATHDEE
Keyword(s):  
Internal Space ◽  
Coset Space ◽  
Spontaneous Compactification ◽  
Zero Modes ◽  
Coset Spaces ◽  
Klein Theory ◽  
Recent Developments ◽  
Ground State Geometry ◽  
Energy Physics ◽  
Kaluza Klein

Recent developments in Kaluza-Klein theory are reviewed. Starting with the concept of spontaneous compactification, the problem of determining the ground state geometry and its symmetry is discussed. While it is generally believed that only the zero modes can be relevant for low energy physics, it is possible in some cases to deduce the entire excitation spectrum. This is true when the internal space is a coset space. A technique is described for setting up harmonic expansions on coset spaces. Consistency in chiral Kaluza-Klein theories demands freedom from both gauge and gravitational anomalies. General features of the chiral anomalies are reviewed.

scholarly journals A DISCRETIZED VERSION OF KALUZA–KLEIN THEORY WITH TORSION AND MASSIVE FIELDS

1996 ◽  
Vol 11 (13) ◽  
pp. 2403-2418 ◽  
Author(s):  
NGUYEN AI VIET ◽  
KAMESHWAR C. WALI
Keyword(s):  
Noncommutative Geometry ◽  
Vector Fields ◽  
Complex Structure ◽  
Scalar Fields ◽  
Type Model ◽  
Internal Space ◽  
Tensor Fields ◽  
Fifth Dimension ◽  
Klein Theory ◽  
Kaluza Klein

We consider an internal space of two discrete points in the fifth dimension of the Kaluza–Klein theory by using the formalism of noncommutative geometry — developed in a previous paper1 — of a spacetime supplemented by two discrete points. With the non-vanishing internal torsion two-form there are no constraints implied on the vielbeins. The theory contains a pair of tensor fields, a pair of vector fields and a pair of scalar fields. Using the generalized Cartan structure equation we are able to uniquely determine not only the Hermitian and metric-compatible connection one-forms, but also the nonvanishing internal torsion two-form in terms of vielbeins. The resulting action has a rich and complex structure, a particular feature being the existence of massive modes. Thus the nonvanishing internal torsion generates a Kaluza–Klein type model with zero and massive modes.

scholarly journals A correspondence between Ricci-flat Kerr and Kaluza-Klein AdS black hole

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Liang Ma ◽  
H. Lü
Keyword(s):  
Domain Walls ◽  
Einstein Gravity ◽  
Gravitational Instantons ◽  
Four Dimensions ◽  
Ricci Flat ◽  
Angular Momenta ◽  
Ads Black Holes ◽  
M Theory ◽  
Odd Dimensions ◽  
Kaluza Klein

Abstract We establish an explicit correspondence of Einstein gravity on the squashed spheres that are the U(1) bundles over ℂℙm to the Kaluza-Klein AdS gravity on the tori. This allows us to map the Ricci-flat Kerr metrics in odd dimensions with all equal angular momenta to charged Kaluza-Klein AdS black holes that can be lifted to become singly rotating M-branes and D3-branes. Furthermore, we find maps between Ricci-flat gravitational instantons to the AdS domain walls. In particular the supersymmetric bolt instantons correspond to domain walls that can be interpreted as distributed M-branes and D3-branes, whilst the non-supersymmetric Taub-NUT solutions yield new domain walls that can be lifted to become solutions in M-theory or type IIB supergravity. The correspondence also inspires us to obtain a new superpotential in the Kaluza-Klein AdS gravity in four dimensions.

TOPOLOGICAL ORIGIN OF THE COUPLING CONSTANTS HIERARCHY IN KALUZA–KLEIN APPROACH

2010 ◽  
Vol 25 (13) ◽  
pp. 2699-2733 ◽  
Author(s):  
VLADIMIR N. EFREMOV ◽  
ALFONSO M. HERNÁNDEZ MAGDALENO ◽  
CLAUDIA MORENO
Keyword(s):  
Energy Coupling ◽  
Coupling Constants ◽  
Internal Space ◽  
Partition Functions ◽  
Running Coupling ◽  
Dirac Quantization ◽  
Topology Changes ◽  
Ale Space ◽  
Kaluza Klein

We consider an Abelian BF-model in the frame of ten-dimensional Kaluza–Klein approach on the space T2×X×M, where X belongs to the class of four-dimension decorated plumbed cobordisms (dp-cobordisms) and M is an An-1-singularity resolution manifold homeomorphic to a compactified ALE space. These four-dimensional manifolds with boundaries possess nontrivial cohomology properties that lead to a specific generalization of the Dirac quantization conditions and enables us to express classical partition functions in terms of 4-form fluxes through the direct product of nontrivial 2-cycles associated with the manifolds X and M. The intersection matrices of these manifolds play the role of coupling constants for the fluxes. We build several examples of dp-cobordisms containing in their intersection matrices the hierarchy of dimensionless low-energy coupling constants of interactions which are available in the real universe. We also consider the phenomenon of "running coupling constants," in particular the cosmological constant evolution induced by the topology changes of internal space X.

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