A proposal for Heisenberg uncertainty principle and STUR for curved backgrounds: an application to white dwarf, neutron stars and black holes

Abstract

After a critical overview of the Generalized Uncertainty Principle (GUP) applied to compact objects, we propose a texture of Heisenberg uncertainty principle in curved spacetimes (CHUP). CHUP allows to write down physically motivated STUR (spacetime uncertainty relations) in a generic background for a non commutative spacetime in terms of tetrad variables. In order to study possible quantum effects for compact astrophysical objects as white dwarf, neutron stars and black holes, an expression for quantum fluctuations is outlined. As a result, contrary to GUP-based claims, we found no evidence for quantum effects concerning equilibrium equation and critical mass $M_c$ for white dwarf and neutron stars. Conversely, our expression for CHUP confirms that general relativistic effects strongly reduce the Oppenheimer-Volkoff Newtonian limit for very compact astrophysical objects as neutron stars. In particular, we found that for a degenerate relativistic Fermi gas, the maximum mass decreases for increasing compactness of the star with a minimum critical mass $M_c\simeq 0.59M_{\odot }$ at the Buchdahl limit. Finally, we study possible non commutative effects near the event horizon of a black hole.

arXiv commentAccepted for publication in Class. Quant. Grav

References in corpus (25)

• The quantum structure of spacetime at the Planck scale and quantum fields
• A Generalized Uncertainty Principle in Quantum Gravity
• Generalized Uncertainty Principle in Quantum Gravity from Micro-Black Hole Gedanken Experiment
• Uncertainty Relation in Quantum Mechanics with Quantum Group Symmetry
• GUP parameter from quantum corrections to the Newtonian potential
• Generalized Uncertainty Principle and Corpuscular Gravity
• Generalized Uncertainty Principle, Black Holes, and White Dwarfs: A Tale of Two Infinities
• Lorentz violation and generalized uncertainty principle
• GUP parameter from Maximal Acceleration
• Can we measure structures to a precision better than the Planck length?
• Generalized Uncertainty Principle and White Dwarfs Redux: How Cosmological Constant Protects Chandrasekhar Limit
• Physically motivated uncertainty relations at the Planck length for an emergent non commutative spacetime
• Generalized Uncertainty Principle Removes The Chandrasekhar Limit
• Quantum Geometry on Quantum Spacetime: Distance, Area and Volume Operators
• Building non commutative spacetimes at the Planck length for Friedmann flat cosmologies
• Atomistic S-matrix method for numerical simulation of phonon reflection, transmission and boundary scattering
• General Relativistic Calculations for White Dwarf Stars
• Quantum Spacetime: a Disambiguation
• On a physical description and origin of the cosmological constant
• Comment on "Can we measure structures to a precision better than the Planck length?"[arXiv:1205.3636], by Sabine Hossenfelder
• A New Approach to Generalised Uncertainty Relations
• A Remark on Polar Noncommutativity
• The cosmological constant from Planckian fluctuations and the averaging procedure
• Non-commutativity in polar coordinates
• The physical origin of the cosmological constant: continuum limit and the analogy with the Casimir effect

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