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Uncertainty relations and precession of perihelion
No full textWe compute the corrections to the Schwarzschild metric necessary to reproduce the Hawking temperature derived from a Generalized Uncertainty Principle (GUP), so that the GUP deformation parameter is directly linked to the deformation of the metric. Using this modified Schwarzschild metric, we compute corrections to the standard General Relativistic predictions for the perihelion precession for planets in the solar system, and for binary pulsars. This analysis allows us to set bounds for the GUP deformation parameter from well-known astronomical measurements
A metric for Planck Stars derived from Gravity in Asymptotic Safety
No full textThe Asymptotically Safe Gravity (ASG) framework suggests a "running"Newtonian coupling constant, which depends on two free parameters ω and γ. The new black hole metrics inferred from such a "running"gravitational constant naturally match with a Schwarzschild metric at large radial coordinate. By further imposing the matching with the Donoghue quantum corrections to the Schwarzschild field, we find a negative value of the ω∼ parameter, and this leads to a not yet explored black hole metric, which surprisingly turns out to describe the so-called Planck stars
GUP parameter from quantum corrections to the Newtonian potential
Full text linkWe propose a technique to compute the deformation parameter of the generalized uncertainty principle by using the leading quantum corrections to the Newtonian potential. We just assume General Relativity as theory of Gravitation, and the thermal nature of the GUP corrections to the Hawking spectrum. With these minimal assumptions our calculation gives, to first order, a specific numerical result. The physical meaning of this value is discussed, and compared with the previously obtained bounds on the generalized uncertainty principle deformation parameter
Lorentz violation and generalized uncertainty principle
Full text linkInvestigations on possible violation of Lorentz invariance have been widely pursued in the last decades,
both from theoretical and experimental sides. A comprehensive framework to formulate the problem is the
standard model extension (SME) proposed by A. Kostelecky, where violation of Lorentz invariance is
encoded into specific coefficients. Here we present a procedure to link the deformation parameter β of the
generalized uncertainty principle to the SME coefficients of the gravity sector. The idea is to compute the
Hawking temperature of a black hole in two different ways. The first way involves the deformation
parameter β, and therefore we get a deformed Hawking temperature containing the parameter β. The second
way involves a deformed Schwarzschild metric containing the Lorentz violating terms ̄sμν of the gravity
sector of the SME. The comparison between the two different techniques yields a relation between β and
̄sμν. In this way bounds on β transferred from ̄sμν are improved by many orders of magnitude when
compared with those derived in other gravitational frameworks. Also the opposite possibility of bounds
transferred from β to ̄sμν is briefly discussed
Planck Stars from a Scale-dependent Gravity theory
Full text linkScale dependence of fundamental physical parameters is a generic feature of
ordinary quantum field theory. When applied to gravity, this idea produces
effective actions generically containing a running Newtonian coupling constant,
from which new (spherically symmetric) black hole spacetimes can be inferred.
As a minimum useful requirement, of course, the new metrics should match with a
Schwarzschild field at large radial coordinate. By further imposing to the new
scale dependent metric the simple request of matching with the Donoghue quantum
corrected potential, we find a not yet explored black hole spacetime, which
naturally turns out to describe the so-called Planck stars.Comment: 15 pages, 3 figures. Final version, to appear in Physical Review
Generalized Uncertainty Principle, Classical Mechanics, and General Relativity
Full text linkThe Generalized Uncertainty Principle (GUP) has been directly applied to the motion of (macroscopic) test bodies on a given space-time in order to compute corrections to the classical orbits predicted in Newtonian Mechanics or General Relativity. These corrections generically violate the Equivalence Principle. The GUP has also been indirectly applied to the gravitational source by relating the GUP modified Hawking temperature to a deformation of the background metric. Such a deformed background metric determines new geodesic motions without violating the Equivalence Principle. We point out here that the two effects are mutually exclusive when compared with experimental bounds. Moreover, the former stems from modified Poisson brackets obtained from a wrong classical limit of the deformed canonical commutators
Minimum length (scale) in Quantum Field Theory, Generalized Uncertainty Principle and the non-renormalisability of gravity
Full text linkThe notions of minimum geometrical length and minimum length scale are
discussed with reference to correlation functions obtained from in-in and
in-out amplitudes in quantum field theory. Whereas the in-in propagator for
metric perturbations does not admit the former, the in-out Feynman propagator
shows the emergence of the latter. A connection between the Feynman propagator
of quantum field theories of gravity and the deformation parameter
of the generalised uncertainty principle (GUP) is then exhibited, which allows
to determine an exact expression for in terms of the residues of the
causal propagator. A correspondence between the non-renormalisability of (some)
theories (of gravity) and the existence of a minimum length scale is then
conjectured to support the idea that non-renormalisable theories are
self-complete and finite. The role played by the sign of the deformation
parameter is further discussed by considering an implementation of the GUP on
the lattice.Comment: LaTeX, 12 pages, no figures, final version to appear in PL
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