scholarly journals Cosmological solutions in Einstein–Gauss–Bonnet gravity with static curved extra dimensions

2021 ◽  
Vol 81 (2) ◽  
Author(s):  
Dmitry Chirkov ◽  
Alex Giacomini ◽  
Sergey A. Pavluchenko ◽  
Alexey Toporensky
Keyword(s):  
Extra Dimensions ◽  
Negative Curvature ◽  
Narrow Range ◽  
Positive Curvature ◽  
Three Dimensional ◽  
Dimensional Subspace ◽  
Systematic Investigation ◽  
Spatial Curvature ◽  
Geometric Frustration ◽  
Cosmological Solutions

AbstractIn this paper we perform systematic investigation of all possible solutions with static compact extra dimensions and expanding three-dimensional subspace (“our Universe”). Unlike previous papers, we consider extra-dimensional subspace to be constant-curvature manifold with both signs of spatial curvature. We provide a scheme how to build solutions in all possible number of extra dimensions and perform stability analysis for the solutions found. Our study suggests that the solutions with negative spatial curvature of extra dimensions are always stable while those with positive curvature are stable for a narrow range of the parameters and the width of this range shrinks with growth of the number of extra dimensions. This explains why in the previous papers we detected compactification in the case of negative curvature but the case of positive curvature remained undiscovered. Another interesting feature which distinguish cases with positive and negative curvatures is that the latter do not coexist with maximally-symmetric solutions (leading to “geometric frustration” of a sort) while the former could – this difference is noted and discussed.

scholarly journals AN INFINITE NUMBER OF CLOSED FLRW UNIVERSES FOR ANY VALUE OF THE SPATIAL CURVATURE

2012 ◽  
Vol 18 ◽  
pp. 77-80
Author(s):  
HELIO V. FAGUNDES
Keyword(s):  
Finite Volume ◽  
Infinite Number ◽  
Negative Curvature ◽  
Large Scale ◽  
Positive Curvature ◽  
Cosmological Models ◽  
Infinite Volume ◽  
Spatial Curvature ◽  
Multiply Connected ◽  
Simply Connected

The Friedman-Lemaître-Robertson-Walker cosmological models are based on the assumptions of large-scale homogeneity and isotropy of the distribution of matter and energy. They are usually taken to have spatial sections that are simply connected; they have finite volume in the positive curvature case, and infinite volume in the null and negative curvature ones. I want to call the attention to the existence of an infinite number of models, which are based on these same metrics, but have compact, finite volume, multiply connected spatial sections. Some observational implications are briefly mentioned.

scholarly journals GRAVITY-WAVE DETECTORS AS PROBES OF EXTRA DIMENSIONS

2005 ◽  
Vol 14 (12) ◽  
pp. 2347-2353 ◽  
Author(s):  
CHRIS CLARKSON ◽  
ROY MAARTENS
Keyword(s):  
Black Holes ◽  
String Theory ◽  
Gravity Wave ◽  
Gravity Waves ◽  
Extra Dimensions ◽  
State Of The Art ◽  
Three Dimensional ◽  
Observable Universe ◽  
Dimensional Spacetime ◽  
Higher Dimensional

If string theory is correct, then our observable universe may be a three-dimensional "brane" embedded in a higher-dimensional spacetime. This theoretical scenario should be tested via the state-of-the-art in gravitational experiments — the current and upcoming gravity-wave detectors. Indeed, the existence of extra dimensions leads to oscillations that leave a spectroscopic signature in the gravity-wave signal from black holes. The detectors that have been designed to confirm Einstein's prediction of gravity waves, can in principle also provide tests and constraints on string theory.

Negative Gaussian curvature induces significant suppression of thermal conduction in carbon crystals

Nanoscale ◽  
2017 ◽  
Vol 9 (37) ◽  
pp. 14208-14214 ◽  
Author(s):  
Zhongwei Zhang ◽  
Jie Chen ◽  
Baowen Li
Keyword(s):  
Gaussian Curvature ◽  
Thermal Conduction ◽  
Negative Curvature ◽  
Positive Curvature ◽  
Significant Suppression ◽  
Carbon Allotropes ◽  
Zero Curvature ◽  
Negative Gaussian Curvature

From the mathematic category of surface Gaussian curvature, carbon allotropes can be classified into three types: zero curvature, positive curvature, and negative curvature.

TRANSPORT IN MgB2 IN HIGH MAGNETIC FIELDS

2002 ◽  
Vol 16 (20n22) ◽  
pp. 3222-3222
Author(s):  
P. SZABO ◽  
P. SAMUELY ◽  
A. G. M. JANSEN ◽  
T. KLEIN ◽  
J. MARCUS ◽  
...  
Keyword(s):  
Temperature Dependence ◽  
Negative Curvature ◽  
Andreev Reflection ◽  
Positive Curvature ◽  
Upper Critical Field ◽  
Critical Magnetic Field ◽  
High Magnetic Fields ◽  
Reflection Spectroscopy ◽  
Upper Critical Magnetic Field ◽  
Energy Gaps

Magnetotransport measurements are presented on polycrystalline MgB 2 samples. The 'resistive' upper critical magnetic field reveals a temperature dependence with positive curvature from Tc = 39.3 K down to about 20 K, then changes to slightly negative curvature reaching 26 T at 1.5 K. The 26-Tesla upper critical field is much higher than what is known so far on polycrystals of MgB 2 but it is in agreement with the recent data obtained on epitaxial MgB 2 films.1 The deviation of Hc2(T) from standard BCS might be due to the proposed two-gap superconductivity in this compound.2 Recently we have found evidence for the existence of two superconducting energy gaps in this system using Andreev reflection spectroscopy.3 The temperature dependence of the resistivity and the normal state magnetoresistance are analyzed.

scholarly journals A Kähler Einstein structure on the tangent bundle of a space form

2001 ◽  
Vol 25 (3) ◽  
pp. 183-195 ◽  
Author(s):  
Vasile Oproiu
Keyword(s):  
Riemannian Manifold ◽  
Riemannian Manifolds ◽  
Tangent Bundle ◽  
Negative Curvature ◽  
Space Form ◽  
Positive Curvature ◽  
Holomorphic Sectional Curvature ◽  
Zero Section ◽  
Constant Negative Curvature ◽  
Constant Positive Curvature

We obtain a Kähler Einstein structure on the tangent bundle of a Riemannian manifold of constant negative curvature. Moreover, the holomorphic sectional curvature of this Kähler Einstein structure is constant. Similar results are obtained for a tube around zero section in the tangent bundle, in the case of the Riemannian manifolds of constant positive curvature.

scholarly journals Quaternionic Bézier curves, surfaces and volume

2013 ◽  
Vol 54 ◽  
Author(s):  
Severinas Zube
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Dimensional Subspace ◽  
Bezier Curves ◽  
Bézier Curves ◽  
The Real

We extended the rational Bézier construction for linear, bi-linear and threelinear map, by allowing quaternion weights. These objects are Möbius invariant and have halved degree with respect to the real parametrization. In general, these parametrizations are in four dimensional space. We analyse when a special the three-linear parametrized volume is in usual three dimensional subspace and gives three orthogonal family of Dupine cyclides.

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