Full three-body problem in effective-field-theory models of gravity

Battista, Emmanuele; Esposito, Giampiero

doi:10.1103/physrevd.90.084010

Cited by 14 publications

(24 citation statements)

References 20 publications

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“…This topic is investigated in Sec. V, where we also show that, among all quantum coefficients κ 1 and κ 2 in the long-distance corrections to the Newtonian potential available in literature [5,[12][13][14][15], the most suitable ones to describe the gravitational interactions involving (at least) three bodies are those connected to the bound-states potential. Finally, conclusions and open problems are discussed in Sec.…”

Section: Introductionsupporting

confidence: 58%

Earth-moon Lagrangian points as a test bed for general relativity and effective field theories of gravity

et al. 2015

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We first analyse the restricted four-body problem consisting of the Earth, the Moon and the Sun as the primaries and a spacecraft as the planetoid. This scheme allows us to take into account the solar perturbation in the description of the motion of a spacecraft in the vicinity of the stable Earth-Moon libration points L 4 and L 5 both in the classical regime and in the context of effective field theories of gravity. A vehicle initially placed at L 4 or L 5 will not remain near the respective points. In particular, in the classical case the vehicle moves on a trajectory about the libration points for at least 700 days before escaping away. We show that this is true also if the modified long-distance Newtonian potential of effective gravity is employed. We also evaluate the impulse required to cancel out the perturbing force due to the Sun in order to force the spacecraft to stay precisely at L 4 or L 5 . It turns out that this value is slightly modified with respect to the corresponding Newtonian one. In the second part of the paper, we first evaluate the location of all Lagrangian points in the Earth-Moon system within the framework of general relativity. For the points L 4 and L 5 , the corrections of coordinates are of order a few millimeters and describe a tiny departure from the equilateral triangle. After that, we set up a scheme where the theory which is quantum corrected has as its classical counterpart the Einstein theory, instead of the Newtonian one. In other words, we deal with a theory involving quantum corrections to Einstein gravity, rather than to Newtonian gravity. By virtue of the effective-gravity correction to the longdistance form of the potential among two point masses, all terms involving the ratio between the gravitational radius of the primary and its separation from the planetoid get modified. Within this framework, for the Lagrangian points of stable equilibrium, we find quantum corrections of order two millimeters, whereas for Lagrangian points of unstable equilibrium we find quantum corrections below a millimeter. Finally, general relativity corrections to Newtonian position of collinear Lagrangian points turn out to be below the millimiter, whereas on stable equilibrium points they are of order of a few millimiters.

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Section: Introductionsupporting

confidence: 58%

Earth-moon Lagrangian points as a test bed for general relativity and effective field theories of gravity

et al. 2015

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“…The first who dealt with the cancellation of internal structure at the first post-Newtonian order in the external problem was Levi-Civita [13] (for a recent application of the Levi-Civita model, motivated by the work in Refs. [25][26][27][28], see also Ref. [29]).…”

Section: Relativistic Tidal and Multipole Expansionsmentioning

confidence: 90%

“…(2. 26) λ(x µ ) being an arbitrary differentiable function. The (approximate) gauge invariance (2.28) shows a manifest analogy with typical U (1) transformations underlying Maxwell theory and it is related to the above-mentioned time coordinate freedom, being expressible as a shift…”

Section: )mentioning

confidence: 99%

On the foundations of general relativistic celestial mechanics

Battista

Esposito

Dell’Agnello

2017

Int. J. Mod. Phys. A

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Towards the end of nineteenth century, Celestial Mechanics provided the most powerful tools to test Newtonian gravity in the solar system, and led also to the discovery of chaos in modern science. Nowadays, in light of general relativity, Celestial Mechanics leads to a new perspective on the motion of satellites and planets. The reader is here introduced to the modern formulation of the problem of motion, following what the leaders in the field have been teaching since the nineties. In particular, the use of a global chart for the overall dynamics of N bodies and N local charts describing the internal dynamics of each body. The next logical step studies in detail how to split the N-body problem into two sub-problems concerning the internal and external dynamics, how to achieve the effacement properties that would allow a decoupling of the two sub-problems, how to define external-potential-effacing coordinates and how to generalize the Newtonian multipole and tidal moments. The review paper ends with an assessment of the nonlocal equations of motion obtained within such a framework, a description of the modifications induced by general relativity of the theoretical analysis of the Newtonian three-body problem, and a mention of the potentialities of the analysis of solar-system metric data carried out with the Planetary Ephemeris Program.Comment: 26 pages, 1 figur

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“…However, as has been shown in Refs. [10,11,14,15], in the low-energy regime the quantum theory of gravitation gives some effects regarding the position of the Earth-Moon Lagrangian points which could have the opportunity to be measured in the next future.…”

Section: Quantum Corrected Time Delaymentioning

confidence: 99%

“…(3.12), (3.13), and Unfortunately this deviation from the underlying classical theory has no chance to be tested, unlike, for example, the effects some of us predicted in Refs. [10,11,14,15], where it is shown that Earth-Moon Lagrangian points are expected to undergo a displacement of the order of few millimetres from their classical position. Furthermore, we have proved that the result reported in Eq.…”

Section: Concluding Remarks and Open Problemsmentioning

confidence: 99%

Quantum time delay in the gravitational field of a rotating mass

Battista¹,

Tartaglia²,

Esposito³

et al. 2017

Class. Quantum Grav.

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We examine quantum corrections of time delay arising in the gravitational field of a spinning oblate source. Low-energy quantum effects occurring in Kerr geometry are derived within a framework where general relativity is fully seen as an effective field theory. By employing such a pattern, gravitational radiative modifications of Kerr metric are derived from the energy-momentum tensor of the source, which at lowest order in the fields is modelled as a point mass. Therefore, in order to describe a quantum corrected version of time delay in the case in which the source body has a finite extension, we introduce a hybrid scheme where quantum fluctuations affect only the monopole term occurring in the multipole expansion of the Newtonian potential. The predicted quantum deviation from the corresponding classical value turns out to be too small to be detected in the next future, showing that new models should be examined in order to test low-energy quantum gravity within the solar system.

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Full three-body problem in effective-field-theory models of gravity

Cited by 14 publications

References 20 publications

Earth-moon Lagrangian points as a test bed for general relativity and effective field theories of gravity

Earth-moon Lagrangian points as a test bed for general relativity and effective field theories of gravity

On the foundations of general relativistic celestial mechanics

Quantum time delay in the gravitational field of a rotating mass

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