Bootstrapped Newtonian quantum gravity

Casadio, Roberto; Kuntz, Iberê

doi:10.1140/epjc/s10052-020-8146-9

Cited by 12 publications

(5 citation statements)

References 15 publications

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“…It is interesting to notice that the lower bounds on the eigenvalue E n ≥ E N M and radius R n G N M could not be obtained in the Newtonian theory, since E = E in that approximation, and the entire spectrum n with n ≥ 1 would be physically acceptable therein. The bound (2.11) on the compactness therefore follows from the nonlinearity of General Relativity and agrees with previous results [20] obtained by adding a gravitational self-interaction term to the Newtonian theory [21][22][23][24]. It also agrees with those results following from the quantum description of the gravitational radius and black hole horizon [15][16][17][18].…”

Section: Concluding Remarks and Outlooksupporting

confidence: 90%

A quantum bound on the compactness

Casadio

2022

Eur. Phys. J. C

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We present a simple quantum description of the gravitational collapse of a ball of dust which excludes those states whose width is arbitrarily smaller than the gravitational radius of the matter source and supports the conclusion that black holes are macroscopic extended objects. We also comment briefly on the relevance of this result for the ultraviolet self-completion of gravity and the connection with the corpuscular picture of black holes.

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Section: Concluding Remarks and Outlooksupporting

confidence: 90%

A quantum bound on the compactness

Casadio

2022

Eur. Phys. J. C

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“…This work arrives at the conclusion that while there is no minimum geometrical length, there is a minimum length scale (identified as the Planck scale) beyond which scattering experiments become useless. Further reference [31] suggests, as does the present work, that quantum gravity effects can not be probed by looking for dispersion of photons propagating through spacetime.…”

Section: Discussionmentioning

confidence: 59%

“…Recent work [31] uses the Schwinger-Keldysh formalism to investigate the existence (or not) of a minimum geometrical length versus a minimum length scale. This work arrives at the conclusion that while there is no minimum geometrical length, there is a minimum length scale (identified as the Planck scale) beyond which scattering experiments become useless.…”

Section: Discussionmentioning

confidence: 99%

Modified Commutators vs Modified Operators in a Quantum Gravity minimal length scale

Contreras

Singleton

Bishop

et al. 2021

Proceedings of 1st Electronic Conference on Universe

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Generic theories of quantum gravity often postulate that at some high energy/momentum scale there will be a fixed, minimal length. Such a minimal length can be phenomenologically investigated by modifying the standard Heisenberg Uncertainty relationship. This is generally done in practice by modifying the commutator between position and momentum operators, which in turn means modifying these operators. However, modifications such that the uncertainty relation changes lead to conflicts with observational data (gamma ray bursts). This arises in the form of a predicted minimal length energy scale that is above the Planck energy rather than below it. As a result there seems to be an implication that there is no minimal length scale in these generic theories. Meanwhile, modifying the operators such that the standard uncertainty relation retains the same form, leads to no such conflict with observational data. We show that it is this modification of the position and momentum operators that is the key determining factor in the existence (or not) of a minimal length scale. By focusing primarily on the role of these operators we also show that one can avoid the constraints from the observations of short gamma ray bursts, which in certain cases seem to push the minimal length scale above the Planck scale.

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“…Another motivation for the present analysis is given by bootstrapped Newtonian gravity (see [19][20][21][22][23][24][25][26][27][28][29][30][31]) which is built by adding non-linear terms to the Poisson equation for the Newtonian potential in 1 + 3 dimensions. In [29], the exact bootstrapped Newtonian potential in the vacuum in 1 + 3 dimensions [19] was used to reconstruct a full space-time metric in harmonic coordinates, as this is the reference frame in which the Newtonian regime is recovered, and orbits were then studied in [30].…”

Section: Introductionmentioning

confidence: 99%

Newtonian approximation in (1 + 1) dimensions

Casadio¹,

Micu²,

Mureika³

2022

Phys. Scr.

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We study the possible existence of a Newtonian regime of gravity in 1 + 1 dimensions, considering metrics in both the Kerr-Schild and conformal forms. In the former case, the metric gives the exact solution of the Poisson equation in ﬂat space, but the weak-ﬁeld limit of the solutions and the non-relativistic regime of geodesic motion are not trivial. We show that using harmonic coordinates, the metric is conformally ﬂat and a weak-ﬁeld expansion is straightforward. An analysis of the non-relativistic regime of geodesic motion remains non-trivial and the weak-ﬁeld potential only satisﬁes the ﬂat space Poisson equation approximately.

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Bootstrapped Newtonian quantum gravity

Cited by 12 publications

References 15 publications

A quantum bound on the compactness

A quantum bound on the compactness

Modified Commutators vs Modified Operators in a Quantum Gravity minimal length scale

Newtonian approximation in (1 + 1) dimensions

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