scholarly journals THE HIERARCHY PROBLEM, RADION MASS, LOCALIZATION OF GRAVITY AND 4D EFFECTIVE NEWTONIAN POTENTIAL IN STRING THEORY ON S1/Z2

2010 ◽  
Vol 25 (08) ◽  
pp. 1661-1698 ◽  
Author(s):  
ANZHONG WANG ◽  
N. O. SANTOS
Keyword(s):  
String Theory ◽  
Matter Field ◽  
Newtonian Potential ◽  
Field Equations ◽  
Hierarchy Problem ◽  
Large Extra Dimension ◽  
Gravitational Field Equations ◽  
Spatial Dimensions ◽  
Derivatives Of ◽  
Kaluza Klein

In this paper, we present a systematical study of braneworlds of string theory on S1/Z2. In particular, starting with the toroidal compactification of the Neveu–Schwarz/Neveu–Schwarz sector in D + d dimensions, we first obtain an effective D-dimensional action, and then compactify one of the D - 1 spatial dimensions by introducing two orbifold branes as its boundaries. We divide the whole set of the gravitational and matter field equations into two groups, one holds outside the two branes, and the other holds on them. By combining the Gauss–Codacci and Lanczos equations, we write down explicitly the general gravitational field equations on each of the two branes, while using distribution theory we express the matter field equations on the branes in terms of the discontinuities of the first derivatives of the matter fields. Afterwards, we address three important issues: (i) the hierarchy problem; (ii) the radion mass; and (iii) the localization of gravity, the four-dimensional Newtonian effective potential and the Yukawa corrections due to the gravitational high-order Kaluza–Klein (KK) modes. The mechanism of solving the hierarchy problem is essentially the combination of the large extra dimension and warped factor mechanisms together with the tension coupling scenario. With very conservative arguments, we find that the radion mass is of the order of 10-2 GeV. The gravity is localized on the visible brane, and the spectrum of the gravitational KK modes is discrete and can be of the order of TeV. The corrections to the four-dimensional Newtonian potential from the higher order of gravitational KK modes are exponentially suppressed and can be safely neglected in current experiments. In an appendix, we also present a systematical and pedagogical study of the Gauss–Codacci equations and Israel's junction conditions across a (D - 1)-dimensional hypersurface, which can be either spacelike or timelike.

GRAVITY IN CURVED PHASE-SPACES, FINSLER GEOMETRY AND TWO-TIMES PHYSICS

2012 ◽  
Vol 27 (12) ◽  
pp. 1250069 ◽  
Author(s):  
CARLOS CASTRO
Keyword(s):  
Phase Space ◽  
Tangent Bundle ◽  
Finsler Geometry ◽  
Space Time ◽  
Vacuum Field ◽  
Field Equations ◽  
Problem Of Time ◽  
Gravitational Field Equations ◽  
Cotangent Space ◽  
Kaluza Klein

The generalized (vacuum) field equations corresponding to gravity on curved 2d-dimensional (dim) tangent bundle/phase spaces and associated with the geometry of the (co)tangent bundle TMd-1, 1(T*Md-1, 1) of a d-dim space–time Md-1, 1 are investigated following the strict distinguished d-connection formalism of Lagrange–Finsler and Hamilton–Cartan geometry. It is found that there is no mathematical equivalence with Einstein's vacuum field equations in space–times of 2d dimensions, with two times, after a d+d Kaluza–Klein-like decomposition of the 2d-dim scalar curvature R is performed and involving the introduction of a nonlinear connection [Formula: see text]. The physical applications of the 4-dim phase space metric solutions found in this work, corresponding to the cotangent space of a 2-dim space–time, deserve further investigation. The physics of two times may be relevant in the solution to the problem of time in quantum gravity and in the explanation of dark matter. Finding nontrivial solutions of the generalized gravitational field equations corresponding to the 8-dim cotangent bundle (phase space) of the 4-dim space–time remains a challenging task.

BRANEWORLD BLACK HOLES IN COSMOLOGY AND ASTROPHYSICS

2005 ◽  
Vol 14 (07) ◽  
pp. 1095-1129 ◽  
Author(s):  
A. S. MAJUMDAR ◽  
N. MUKHERJEE
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Gravitational Lensing ◽  
Strong Field ◽  
Planck Scale ◽  
High Energy ◽  
Field Equations ◽  
Large Extra Dimension ◽  
Gravitational Field Equations ◽  
Fundamental Scale

The braneworld description of our universe entails a large extra dimension and a fundamental scale of gravity that might be lower by several orders of magnitude compared to the Planck scale. An interesting consequence of the braneworld scenario is in the nature of spherically symmetric vacuum solutions to the brane gravitational field equations which could represent black holes with properties quite distinct compared to ordinary black holes in 4-dimensions. We discuss certain key features of some braneworld black hole geometries. Such black holes are likely to have diverse cosmological and astrophysical ramifications. The cosmological evolution of primordial braneworld black holes is described highlighting their longevity due to modified evaporation and effective accretion of radiation during the early braneworld high energy era. Observational abundance of various evaporation products of the black holes at different eras impose constraints on their initial mass fraction. Surviving primordial black holes could be candidates of dark matter present in galactic haloes. We discuss gravitational lensing by braneworld black holes. Observables related to the relativistic images of strong field gravitational lensing could in principle be used to distinguish between different braneworld black hole metrics in future observations.

Matter field equations derived from fourth-order gravity by the Kaluza–Klein principle

2002 ◽  
Vol 14 (8) ◽  
pp. 1255-1261 ◽  
Author(s):  
R. Schimming ◽  
M. Abdel-Megied ◽  
F. Ibrahim
Keyword(s):  
Fourth Order ◽  
Matter Field ◽  
Field Equations ◽  
Kaluza Klein

SPIN FROM THE NONSYMMETRIC METRIC TENSOR

2013 ◽  
Vol 22 (12) ◽  
pp. 1342009 ◽  
Author(s):  
RICHARD T. HAMMOND
Keyword(s):  
Gravitational Field ◽  
String Theory ◽  
Field Equations ◽  
Metric Tensor ◽  
Spin Field ◽  
Intimate Connection ◽  
Gravitational Field Equations ◽  
Nonsymmetric Metric

A solution to the gravitational field equations based on a nonsymmetric metric tensor is examined. Unlike Einstein's interpretation of electromagnetism, or Moffat's generalized gravity, it is shown that the nonsymmetric part of the metric tensor is the potential of the spin field, and its intimate connection to string theory is established. This formulation solves the longstanding problem of electromagnetism and torsion, naturally showing how electromagnetism, through its intrinsic spin, can create torsion.

Topology knots and hierarchy problem

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Quantum Theory ◽  
String Theory ◽  
Quantum Gravity ◽  
Dimensional Space ◽  
Space Time ◽  
Elementary Particles ◽  
Hierarchy Problem ◽  
Topological Quantum ◽  
Dimensional Space Time ◽  
New Formula

Many approaches to quantum gravity consider the revision of the space-time geometry and the structure of elementary particles. One of the main candidates is string theory. It is possible that this theory will be able to describe the problem of hierarchy, provided that there is an appropriate Calabi-Yau geometry. In this paper we will proceed from the traditional view on the structure of elementary particles in the usual four-dimensional space-time. The only condition is that quarks and leptons should have a common emerging structure. When a new formula for the mass of the hierarchy is obtained, this structure arises from topological quantum theory and a suitable choice of dimensional units.

scholarly journals Hierarchical structure of physical Yukawa couplings from matter field Kähler metric

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Keiya Ishiguro ◽  
Tatsuo Kobayashi ◽  
Hajime Otsuka
Keyword(s):  
String Theory ◽  
Hierarchical Structure ◽  
Matter Field ◽  
Heterotic String ◽  
Heterotic String Theory ◽  
Kähler Metric ◽  
Yukawa Couplings ◽  
String Compactifications ◽  
Kahler Metric ◽  
Matter Fields

Abstract We study the impacts of matter field Kähler metric on physical Yukawa couplings in string compactifications. Since the Kähler metric is non-trivial in general, the kinetic mixing of matter fields opens a new avenue for realizing a hierarchical structure of physical Yukawa couplings, even when holomorphic Yukawa couplings have the trivial structure. The hierarchical Yukawa couplings are demonstrated by couplings of pure untwisted modes on toroidal orbifolds and their resolutions in the context of heterotic string theory with standard embedding. Also, we study the hierarchical couplings among untwisted and twisted modes on resolved orbifolds.

scholarly journals Sensitivity of the Second Order Homogenized Elasticity Tensor to Topological Microstructural Changes

2021 ◽  
Author(s):  
V. Calisti ◽  
A. Lebée ◽  
A. A. Novotny ◽  
J. Sokolowski
Keyword(s):  
Circular Inclusion ◽  
Elasticity Tensor ◽  
Second Order ◽  
Topological Derivative ◽  
Microstructural Changes ◽  
Topological Derivatives ◽  
Spatial Dimensions ◽  
Elasticity Tensors ◽  
Derivatives Of ◽  
Optimization Of Microstructures

AbstractThe multiscale elasticity model of solids with singular geometrical perturbations of microstructure is considered for the purposes, e.g., of optimum design. The homogenized linear elasticity tensors of first and second orders are considered in the framework of periodic Sobolev spaces. In particular, the sensitivity analysis of second order homogenized elasticity tensor to topological microstructural changes is performed. The derivation of the proposed sensitivities relies on the concept of topological derivative applied within a multiscale constitutive model. The microstructure is topologically perturbed by the nucleation of a small circular inclusion that allows for deriving the sensitivity in its closed form with the help of appropriate adjoint states. The resulting topological derivative is given by a sixth order tensor field over the microstructural domain, which measures how the second order homogenized elasticity tensor changes when a small circular inclusion is introduced at the microscopic level. As a result, the topological derivatives of functionals for multiscale models can be obtained and used in numerical methods of shape and topology optimization of microstructures, including synthesis and optimal design of metamaterials by taking into account the second order mechanical effects. The analysis is performed in two spatial dimensions however the results are valid in three spatial dimensions as well.

scholarly journals Physical Acceptability of the Renyi, Tsallis and Sharma-Mittal Holographic Dark Energy Models in the f(T,B) Gravity under Hubble’s Cutoff

Universe ◽  
2021 ◽  
Vol 7 (3) ◽  
pp. 67
Author(s):  
Salim Harun Shekh ◽  
Pedro H. R. S. Moraes ◽  
Pradyumn Kumar Sahoo
Keyword(s):  
Dark Energy ◽  
Holographic Dark Energy ◽  
Cosmological Parameters ◽  
Field Equations ◽  
Eos Parameter ◽  
Two Fluids ◽  
Gravitational Field Equations ◽  
Energy Models ◽  
Different Types ◽  
The Universe

In the present article, we investigate the physical acceptability of the spatially homogeneous and isotropic Friedmann–Lemâitre–Robertson–Walker line element filled with two fluids, with the first being pressureless matter and the second being different types of holographic dark energy. This geometric and material content is considered within the gravitational field equations of the f(T,B) (where T is the torsion scalar and the B is the boundary term) gravity in Hubble’s cut-off. The cosmological parameters, such as the Equation of State (EoS) parameter, during the cosmic evolution, are calculated. The models are stable throughout the universe expansion. The region in which the model is presented is dependent on the real parameter δ of holographic dark energies. For all δ≥4.5, the models vary from ΛCDM era to the quintessence era.

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