scholarly journals New improved massive gravity and three-dimensional spacetimes of constant curvature and constant torsion

2016 ◽  
Vol 94 (6) ◽  
Author(s):  
Tekin Dereli ◽  
Cem Yetişmişoğlu
Keyword(s):  
Constant Curvature ◽  
Three Dimensional ◽  
Massive Gravity ◽  
Constant Torsion

Center of Mass Theorem and the Separation of Variables for Two-Body System on a Three-Dimensional Sphere

2020 ◽  
Vol 23 (3) ◽  
pp. 306-311
Author(s):  
Yu. Kurochkin ◽  
Dz. Shoukavy ◽  
I. Boyarina
Keyword(s):  
Constant Curvature ◽  
Jacobi Equation ◽  
Separation Of Variables ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Relative Distance ◽  
Dimensional Sphere ◽  
Body System ◽  
Spaces Of Constant Curvature ◽  
Hamilton Jacobi Equation

The immobility of the center of mass in spaces of constant curvature is postulated based on its definition obtained in [1]. The system of two particles which interact through a potential depending only on the distance between particles on a three-dimensional sphere is considered. The Hamilton-Jacobi equation is formulated and its solutions and trajectory equations are found. It was established that the reduced mass of the system depends on the relative distance.

scholarly journals Thurston Geometries in Three-Dimensional New Massive Gravity

2021 ◽  
Vol 127 (6) ◽  
Author(s):  
Daniel Flores-Alfonso ◽  
Cesar S. Lopez-Monsalvo ◽  
Marco Maceda
Keyword(s):  
Three Dimensional ◽  
Massive Gravity ◽  
Thurston Geometries

A three-dimensional magnetohydrodynamic equilibrium in an axial coordinate with a constant curvature

2019 ◽  
Vol 59 (8) ◽  
pp. 086004 ◽  
Author(s):  
M.S. Chu ◽  
Wenfeng Guo ◽  
Wandong Liu ◽  
Qilong Ren ◽  
K.C. Shaing ◽  
...  
Keyword(s):  
Constant Curvature ◽  
Three Dimensional ◽  
Axial Coordinate

Causality of 3D extended gravity theories

2019 ◽  
Vol 34 (16) ◽  
pp. 1950122
Author(s):  
Meguru Komada
Keyword(s):  
Shock Wave ◽  
Three Dimensional ◽  
Massive Gravity ◽  
Gravity Theory ◽  
Delay Effect ◽  
Fundamental Physics ◽  
Extended Gravity ◽  
3D Gravity ◽  
Gravity Theories ◽  
Time Delay Effect

Causality is one of the most important properties to understand gravity theories. It gives us not only a method to confirm that the gravity theories are really consistent, but also gives implications about the properties which unknown fundamental physics should obey. We investigate the causality of three-dimensional (3D) gravity theories, which are considered to be important, by using the Shapiro time delay effect in the Shock wave geometry. One of such gravity theories is the Zwei-Dreibein Gravity (ZDG) theory, which is a consistent 3D gravity theory. In ZDG theory, the serious problems can be removed that have appeared in another important gravity theory called New Massive Gravity (NMG). We study whether the ZDG theory could preserve the causality without losing the above good properties and how the causality structure is related to the structure of the NMG theory.

scholarly journals GENERALIZATION OF HASIMOTO'S TRANSFORMATION

2009 ◽  
Vol 06 (04) ◽  
pp. 625-630 ◽  
Author(s):  
MATHIEU MOLITOR
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Constant Curvature ◽  
Schrodinger Equation ◽  
Three Dimensional ◽  
Nonlinear Schrodinger Equation ◽  
Vortex Filament ◽  
Dimensional Manifold ◽  
Moving Frames ◽  
Natural Complex

In this paper, we generalize the famous Hasimoto's transformation by showing that the dynamics of a closed unidimensional vortex filament embedded in a three-dimensional manifold M of constant curvature, gives rise under Hasimoto's transformation to the nonlinear Schrödinger equation. We also give a natural interpretation of the function ψ introduced by Hasimoto in terms of moving frames associated to a natural complex bundle over the filament.

scholarly journals Discrete canonical analysis of three-dimensional gravity with cosmological constant

2015 ◽  
Vol 30 (15) ◽  
pp. 1550080
Author(s):  
J. Berra-Montiel ◽  
J. E. Rosales-Quintero
Keyword(s):  
Cosmological Constant ◽  
Constant Curvature ◽  
Three Dimensional ◽  
Canonical Analysis ◽  
Gauge Freedom ◽  
Dimensional Gravity ◽  
Local Symmetries ◽  
Lattice Approach ◽  
Hamiltonian Analysis ◽  
The Continuum

We discuss the interplay between standard canonical analysis and canonical discretization in three-dimensional gravity with cosmological constant. By using the Hamiltonian analysis, we find that the continuum local symmetries of the theory are given by the on-shell space–time diffeomorphisms, which at the action level, correspond to the Kalb–Ramond transformations. At the time of discretization, although this symmetry is explicitly broken, we prove that the theory still preserves certain gauge freedom generated by a constant curvature relation in terms of holonomies and the Gauss's law in the lattice approach.

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