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- Kälin, Gregor, et al.
(author)
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From boundary data to bound states
- 2020
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In: Journal of High Energy Physics (JHEP). - : SPRINGER. - 1126-6708 .- 1029-8479.
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Journal article (peer-reviewed)abstract
- We introduce a - somewhat holographic - dictionary between gravitational observables for scattering processes (measured at the boundary) and adiabatic invariants for bound orbits (in the bulk), to all orders in the Post-Minkowskian (PM) expansion. Our map relies on remarkable connections between the relative momentum of the two-body problem, the classical limit of the scattering amplitude and the deflection angle in hyperbolic motion. These relationships allow us to compute observables for generic orbits (such as the periastron advance increment phi) through analytic continuation, via a radial action depending only on boundary data. A simplified (more geometrical) map can be obtained for circular orbits, enabling us to extract the orbital frequency as a function of the (conserved) binding energy, omega(E), directly from scattering information. As an example, using the results in Bernet al. [36, 37], we readily derive omega(E) and increment phi(J, E) to two-loop orders. We also provide closed-form expressions for the orbital frequency and periastron advance at tree-level and one-loop order, respectively, which capture a series of exact terms in the Post-Newtonian expansion. We then perform a partial PM resummation, using a no-recoil approximation for the amplitude. This limit is behind the map between the scattering angle for a test-particle and the two-body dynamics to 2PM. We show that it also captures a subset of higher order terms beyond the test-particle limit. While a (rather lengthy) Hamiltonian may be derived as an intermediate step, our map applies directly between gauge invariant quantities. Our findings provide a starting point for an alternative approach to the binary problem. We conclude with future directions and some speculations on the classical double copy.
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- Kälin, Gregor, et al.
(author)
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From boundary data to bound states. Part II. Scattering angle to dynamical invariants (with twist)
- 2020
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In: Journal of High Energy Physics (JHEP). - : SPRINGER. - 1126-6708 .- 1029-8479. ; :2
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Journal article (peer-reviewed)abstract
- We recently introduced in [9] a boundary-to-bound dictionary between gravitational scattering data and observables for bound states of non-spinning bodies. In this paper, we elaborate further on this holographic map. We start by deriving the following - remarkably simple - formula relating the periastron advance to the scattering angle: Delta phi via analytic continuation in angular momentum and binding energy. Using explicit expressions from [9], we confirm its validity to all orders in the Post-Minkowskian (PM) expansion. Furthermore, we reconstruct the radial action for the bound state directly from the knowledge of the scattering angle. The radial action enables us to write compact expressions for dynamical invariants in terms of the deflection angle to all PM orders, which can also be written as a function of the PM-expanded amplitude. As an example, we reproduce our result in [9] for the periastron advance, and compute the radial and azimuthal frequencies and redshift variable to two-loops. Agreement is found in the overlap between PM and Post-Newtonian (PN) schemes. Last but not least, we initiate the study of our dictionary including spin. We demonstrate that the same relation between deflection angle and periastron advance applies for aligned-spin contributions, with J the (canonical) total angular momentum. Explicit checks are performed to display perfect agreement using state-of-the-art PN results in the literature. Using the map between test- and two-body dynamics, we also compute the periastron advance up to quadratic order in spin, to one-loop and to all orders in velocity. We conclude with a discussion on the generalized 'impetus formula' for spinning bodies and black holes as 'elementary particles'. Our findings here and in [9] imply that the deflection angle already encodes vast amount of physical information for bound orbits, encouraging independent derivations using numerical and/or self-force methodologies.
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- Pinotti, Rafael, et al.
(author)
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A link between the semimajor axis of extrasolar gas giant planets and stellar metallicity
- 2005
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In: Monthly Notices of the Royal Astronomical Society. ; :364, s. 29-
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Journal article (peer-reviewed)abstract
- The fact that most extrasolar planets found to date are orbiting metal-rich stars lends credence to the core accretion mechanism of gas giant planet formation over its competitor, the disc instability mechanism. However, the core accretion mechanism is not refined to the point of explaining orbital parameters such as the unexpected semimajor axes and eccentricities. We propose a model that correlates the metallicity of the host star with the original semimajor axis of its most massive planet, prior to migration, assuming that the core accretion scenario governs giant gas planet formation. The model predicts that the optimum regions for planetary formation shift inwards as stellar metallicity decreases, providing an explanation for the observed absence of long-period planets in metal-poor stars. We compare our predictions with the available data on extrasolar planets for stars with masses similar to the mass of the Sun. A fitting procedure produces an estimate of what we define as the zero-age planetary orbit (ZAPO) curve as a function of the metallicity of the star. The model hints that the lack of planets circling metal-poor stars may be partly caused by an enhanced destruction probability during the migration process, because the planets lie initially closer to their central star.
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