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Relative Locality in Curved Space-time
High Energy Physics - Theory · Submitted 28 Mar 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim As a first example of this construction we describe the particle with kappa-Poincar\'e momentum space on a circular orbit in Schwarzschild spacetime, where the contributes of momentum space curvature turn out to be negligible.
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The abstract, sentence by sentence
In this paper we construct the action describing dynamics of the particle moving in curved spacetime, with a non-trivial momentum space geometry. Curved momentum space is the core feature of theories where relative locality effects are presents. So far aspects of nonlinearities in momentum space have been studied only for flat or constantly expanding (De Sitter) spacetimes, relying on the their maximally symmetric nature. The extension of curved momentum space frameworks to arbitrary spacetime geometries could be relevant for the opportunities to test Planck-scale curvature/deformation of particles momentum space. As a first example of this construction we describe the particle with kappa-Poincar\'e momentum space on a circular orbit in Schwarzschild spacetime, where the contributes of momentum space curvature turn out to be negligible. The analysis of this problem relies crucially on the solution of the soccer ball problem.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In this paper we construct the action describing dynamics of the particle moving in curved spacetime, with a non-trivial momentum space geometry. | contribution 1.00 | 0.94 | 0.08 | asserted 1.00 |
| s1 | Curved momentum space is the core feature of theories where relative locality effects are presents. | background 1.00 | 0.07 | 0.06 | asserted 1.00 |
| s2 | So far aspects of nonlinearities in momentum space have been studied only for flat or constantly expanding (De Sitter) spacetimes, relying on the their maximally symmetric nature. | gap 0.86 | 0.05 | 0.03 | asserted 1.00 |
| s3 | The extension of curved momentum space frameworks to arbitrary spacetime geometries could be relevant for the opportunities to test Planck-scale curvature/deformation of particles momentum space. | interpretation 0.32 | 0.08 | 0.09 | hedged possibility 1.00 |
| s4 | As a first example of this construction we describe the particle with kappa-Poincar\'e momentum space on a circular orbit in Schwarzschild spacetime, where the contributes of momentum space curvature turn out to be negligible. | contribution 0.77 | 0.92 | 0.13 | asserted 1.00 |
| s5 | The analysis of this problem relies crucially on the solution of the soccer ball problem. | method 0.97 | 0.45 | 0.05 | asserted 1.00 |
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The paper
Original abstract
In this paper we construct the action describing dynamics of the particle moving in curved spacetime, with a non-trivial momentum space geometry. Curved momentum space is the core feature of theories where relative locality effects are presents. So far aspects of nonlinearities in momentum space have been studied only for flat or constantly expanding (De Sitter) spacetimes, relying on the their maximally symmetric nature. The extension of curved momentum space frameworks to arbitrary spacetime geometries could be relevant for the opportunities to test Planck-scale curvature/deformation of particles momentum space. As a first example of this construction we describe the particle with kappa-Poincar\'e momentum space on a circular orbit in Schwarzschild spacetime, where the contributes of momentum space curvature turn out to be negligible. The analysis of this problem relies crucially on the solution of the soccer ball problem.
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How the literature uses it
5 arXiv papers cite this in 11 sentences
Papers citing it · 7 sentences without a confident label
Compares with it 1 paper
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However, the equations of motion are the same in both cases, so we may conclude that the actions are equivalent, the only difference being that the Lagrangian ([ref]) is invariant under local Lorentz symmetry, while in the action ([ref]) only the global Lorentz symmetry remains[Notice also that, with the same caveat, the action ([ref]) differs, up to a boundary term, from the action presented in [ref] (written for Fermi tetrads) by the term $( ∫ẋ^μe̅_μ^a - x^μe̅_μ^a) Ė^α_a p_α$.].
Generally covariant formulation of Relative Locality in curved spacetime · The action and equations of motion · 0.85
Cites it as background 2 papers
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So far many aspects of this theory have been examined: from the implications for interaction vertices conservation laws [ref] , to some attempts to generalise Relative Locality to curve space-time scenarios [ref] .
Exploring Special Relative Locality with deSitter momentum-space · Introduction · 0.98
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There are other recent works on this principle applied to the geometry in momentum space and gravity [ref] on which we will comment more in the Conclusion.
A Cosmology of a Trans-Planckian Theory and Dark Energy · Introduction · 0.94
What it cites · 19 sentences without a confident label
Cites as background 18 papers
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The relative locality perspective is then that the physical observations corresponds to the ones made by observers local to the event of measurement [ref] .
Taming nonlocality in theories with Planck-scale-deformed Lorentz symmetry · Introduction · 0.83
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As it is well known from previous studies on relative locality [ref] , the nontriviality (momentum dependence) in the (deformed-)relativistic transformations of spacetime coordinates imply that events distant from the origin of a given observer's frame are characterized by “misleading inferences” regarding their position in spacetime.
Speed of particles and a relativity of locality in $\kappa$-Minkowski quantum spacetime · Introduction · 0.85
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As it is well known from previous studies on relative locality [ref] , the nontriviality (momentum dependence) in the (deformed-)relativistic transformations of spacetime coordinates imply that events distant from the origin of a given observer's frame are characterized by “misleading inferences” regarding their position in spacetime.
Deformed Lorentz symmetry and relative locality in a curved/expanding spacetime · Introduction · 0.85
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