Snyder dynamics in a Schwarzschild spacetime

Abstract

We calculate the orbits of a particle in Schwarzschild spacetime, assuming that the dynamics is governed by a Snyder symplectic structure. With this assumption, the perihelion shift of the planets acquires an additional contribution with respect to the one predicted by general relativity. Moreover, the equivalence principle is violated. If one assumes that Snyder mechanics is valid also for macroscopic systems, these results impose strong constraints on the value of the coupling parameter of the Snyder model.

7 pages

References in corpus (7)

• Multi-Particle States in Deformed Special Relativity
• Scalar field theory in Snyder space-time: alternatives
• Yang's Model as Triply Special Relativity and the Snyder's Model--de Sitter Special Relativity Duality
• Doubly special relativity and translation invariance
• The Area Quantum and Snyder Space
• Symmetries of Snyder--de Sitter space and relativistic particle dynamics
• Snyder-de Sitter model from two-time physics

Cited by in corpus (10)

• Bumblebee gravity and particle motion in Snyder noncommutative spacetime structures
• Heisenberg doubles for Snyder type models
• $\kappa$-deformed phase spaces, Jordanian twists, Lorentz-Weyl algebra and dispersion relations
• Macroscopic body in Snyder space and minimal length estimation
• Deformed Quantum Phase Spaces, Realizations, Star Products and Twists
• Minimal length estimation on the basis of studies of the Sun-Earth-Moon system in deformed space
• Snyder and their representation with creation and annihilation operators
• Some features of a Schwarzchild Black Hole from a Snyder perspective
• Noncommutative Classical Dynamics on Velocity Phase Space and Souriau Formalism
• Realizations of the Extended Snyder Model