scholarly journals Kepler problem in a constant-curvature space

2008 ◽  
Vol 155 (2) ◽  
pp. 780-788 ◽  
Author(s):  
G. P. Pronko
Keyword(s):  
Constant Curvature ◽  
Kepler Problem ◽  
Constant Curvature Space

Dynamics and Regularization of the Kepler Problem on Surfaces of Constant Curvature

2017 ◽  
Vol 69 (5) ◽  
pp. 961-991 ◽  
Author(s):  
Jaime Andrade ◽  
Nestor Dàvila ◽  
Ernesto Pérez-Chavela ◽  
Claudio Vidal
Keyword(s):  
Angular Momentum ◽  
Vector Field ◽  
Constant Curvature ◽  
Kepler Problem ◽  
Phase Portraits ◽  
Problem Of Time

AbstractWe classify and analyze the orbits of the Kepler problemon surfaces of constant curvature (both positive and negative, 𝕊2and ℍ2, respectively) as functions of the angular momentum and the energy. Hill's regions are characterized, and the problem of time-collision is studied. We also regularize the problem in Cartesian and intrinsic coordinates, depending on the constant angular momentum, and we describe the orbits of the regularized vector field. The phase portraits both for 𝕊2and ℍ2are pointed out.

scholarly journals A MINIMAL MODEL OF LORENTZ GAUGE GRAVITY WITH DYNAMICAL TORSION

2010 ◽  
Vol 25 (14) ◽  
pp. 2867-2882 ◽  
Author(s):  
Y. M. CHO ◽  
D. G. PAK ◽  
B. S. PARK
Keyword(s):  
Constant Curvature ◽  
Quantum Dynamics ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Space Time ◽  
Effective Theory ◽  
Metric Tensor ◽  
Lorentz Gauge ◽  
Constant Curvature Space ◽  
Gauge Gravity

A new Lorentz gauge gravity model with R2-type Lagrangian is proposed. In the absence of classical torsion, the model admits a topological phase with an arbitrary metric. We analyze the equations of motion in constant curvature space–time background using the Lagrange formalism and demonstrate that the model possesses a minimal set of dynamic degrees of freedom for the torsion. Surprisingly, the number of torsion dynamic degrees of freedom equals the number of physical degrees of freedom for the metric tensor. An interesting feature of the model is that the spin-2 mode of torsion becomes dynamical essentially due to the nonlinear structure of the theory. We perform covariant one-loop quantization of the model for a special case of constant curvature space–time background. We treat the contortion as a quantum field variable whereas the metric tensor is kept as a classical object. We discuss a possible mechanism of an emergent Einstein gravity as a part of the effective theory induced due to quantum dynamics of torsion.

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