Asymptotic generalized extended uncertainty principle

@article{Dabrowski2020AsymptoticGE,
  title={Asymptotic generalized extended uncertainty principle},
  author={Mariusz P. Da̧browski and Fabian Wagner},
  journal={arXiv: General Relativity and Quantum Cosmology},
  year={2020}
}
We present a formalism which allows for the perturbative derivation of the Extended Uncertainty Principle (EUP) for arbitrary spatial curvature models and observers. Entering the realm of small position uncertainties, we derive a general asymptotic EUP. The leading 2nd order curvature induced correction is proportional to the Ricci scalar, while the 4th order correction features the 0th order Cartan invariant Psi^2 (a scalar quadratic in curvature tensors) and the curved space Laplacian of the… 

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References

SHOWING 1-10 OF 55 REFERENCES
On scalar curvature invariants in three dimensional spacetimes
We wish to construct a minimal set of algebraically independent scalar curvature invariants formed by the contraction of the Riemann (Ricci) tensor and its covariant derivatives up to some order of
Uncertainty Principle on 3-Dimensional Manifolds of Constant Curvature
We consider the Heisenberg uncertainty principle of position and momentum in 3-dimensional spaces of constant curvature K. The uncertainty of position is defined coordinate independent by the
On the uncertainty principle in Rindler and Friedmann spacetimes
We revise the extended uncertainty relations for the Rindler and Friedmann spacetimes recently discussed by Dabrowski and Wagner in [ 9 ]. We reveal these results to be coordinate dependent
Generalized uncertainty principle and white dwarfs redux: How the cosmological constant protects the Chandrasekhar limit
It was previously argued that generalized uncertainty principle (GUP) with a positive parameter removes the Chandrasekhar limit. One way to restore the limit is by taking the GUP parameter to be
On Gravity and the Uncertainty Principle
Heisenberg showed in the early days of quantum theory that the uncertainty principle follows as a direct consequence of the quantization of electromagnetic radiation in the form of photons. As we
Extended uncertainty principle for rindler and cosmological horizons
We find exact formulas for the Extended Uncertainty Principle (EUP) for the Rindler and Friedmann horizons and show that they can be expanded to obtain asymptotic forms known from the previous
...
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2
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4
5
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