Schwarzschild-Tangherlini metric from scattering amplitudes

Jakobsen, Gustav Uhre

doi:10.1103/physrevd.102.104065

Cited by 16 publications

(14 citation statements)

References 18 publications

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“…Notice that the coherent state is gauge invariant, while the quantum operator may not be (in quantum gravity, only asymptotic observables may be associated with gauge-invariant operators). This procedure would allow us to perturbatively construct the Schwarzschild metric, along the lines of [66,146,147] but in a manifestly on-shell formalism; see also [6] for an alternative approach based on an intermediate matching with an effective theory of sources coupled to gravitons. We leave this programme for future work.…”

Section: Jhep05(2021)268mentioning

confidence: 99%

Classical solutions and their double copy in split signature

Monteiro

O’Connell

Veiga

et al. 2021

J. High Energ. Phys.

130

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The three-point amplitude is the key building block in the on-shell approach to scattering amplitudes. We show that the classical objects computed by massive three-point amplitudes in gauge theory and gravity are Newman-Penrose scalars in a split-signature spacetime, where three-point amplitudes can be defined for real kinematics. In fact, the quantum state set up by the particle is a coherent state fully determined by the three-point amplitude due to an eikonal-type exponentiation. Having identified this simplest classical solution from the perspective of scattering amplitudes, we explore the double copy of the Newman-Penrose scalars induced by the traditional double copy of amplitudes, and find that it coincides with the Weyl version of the classical double copy. We also exploit the Kerr-Schild version of the classical double copy to determine the exact spacetime metric in the gravitational case. Finally, we discuss the direct implication of these results for Lorentzian signature via analytic continuation.

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Section: Jhep05(2021)268mentioning

confidence: 99%

Classical solutions and their double copy in split signature

Monteiro

O’Connell

Veiga

et al. 2021

J. High Energ. Phys.

130

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“…the generation of gravitational waves. The associated amplitudes may have more matter sources but only one outgoing graviton [6,47,51,105,106], making them suitable for the techniques presented (see [34] for a recent discussion of retarded vs Feynman propagators in this context). They are controlled to some extent by soft factorization [46]: Indeed the amplitude M 3 treated here is the simplest instance of such, where the Coulomb poles of the soft factor 1 u•k±i are equivalent to the delta function δ(u • k).…”

Section: Open Questionsmentioning

confidence: 99%

“…Recently, a novel body of research has shown that dynamical observables for compact bodies in GR, such as black holes, can be derived from massive QFT particles interacting with gravitons, see e.g. [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. This entails that such spacetimes can be treated as perturbations of flat space sourced by these particles: Perturbative precission is attained by evaluating the classical limit of scattering amplitudes to the desired order in G. Pushing the state-of-the-art accuracy in GR, the correspondence has mainly emerged through the evaluation of observables such as radiated momentum, waveforms, or on-shell effective actions .…”

Section: Introductionmentioning

confidence: 99%

Reconstructing Classical Spacetimes from the S-Matrix in Twistor Space

Guevara¹

2021

Preprint

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We present a holographic construction of solutions to the gravitational wave equation starting from QFT scattering amplitudes. The construction amounts to a change of basis from momentum to (2, 2) twistor space, together with a recently introduced analytic continuation between (2, 2) and (1, 3) spacetimes. We test the transform for three and four-point amplitudes in a classical limit, recovering both stationary and dynamical solutions in GR as parametrized by their tower of multipole moments, including the Kerr black hole. As a corollary, this provides a link between the Kerr-Schild classical double copy and the QFT double copy.

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“…Generally, a much less ambiguous option is to ultraboost the source of the initial metric, then feed the result back into the Einstein equations to obtain a metric. 6 The source of the Kerr metric was investigated long ago by Israel, who argued that Kerr is sourced by an equatorial disk of mass M whose radius is given by the spin parameter a [59,60]. 7 This description was also confirmed in a precise distributional analysis by Balasin and Nachbagauer some years later [69].…”

Section: Ultraboosting the Source Of Kerrmentioning

confidence: 92%

“…The first attempt in this direction goes back to work by Duff [1], where the Schwarzschild solution in harmonic coordinates was derived to order G 2 N . This approach can also be implemented through unitarity techniques [2], and similar methods can be used to obtain other solutions such as Reissner-Nordström and Kerr [3] as well as quantum corrections, higher-order corrections and higher-dimensional generalizations [4][5][6]. Other approaches have focused instead on effective field theory techniques for the derivation of these solutions [7,8] or the use of one-point functions for the extraction of the large distance behaviour [9].…”

Section: Introductionmentioning

confidence: 99%

The ultrarelativistic limit of Kerr

Adamo

Cristofoli

Tourkine

2023

J. High Energ. Phys.

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The massless (or ultrarelativistic) limit of a Schwarzschild black hole with fixed energy was determined long ago in the form of the Aichelburg-Sexl shockwave, but the status of the same limit for a Kerr black hole is less clear. In this paper, we explore the ultrarelativistic limit of Kerr in the class of Kerr-Schild impulsive pp-waves by exploiting a relation between the metric profile and the eikonal phase associated with scattering between a scalar and the source of the metric. This gives a map between candidate metrics and tree-level, 4-point scattering amplitudes. At large distances from the source, we find that all candidates for the massless limit of Kerr in this class do not have spin effects. This includes the metric corresponding to the massless limit of the amplitude for gravitational scattering between a scalar and a massive particle of infinite spin. One metric, discovered by Balasin and Nachbagauer, does have spin and finite size effects at short distances, leading to a remarkably compact scattering amplitude with many interesting properties. We also discuss the classical single copy of the ultrarelativistic limit of Kerr in electromagnetism.

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Schwarzschild-Tangherlini metric from scattering amplitudes

Cited by 16 publications

References 18 publications

Classical solutions and their double copy in split signature

Classical solutions and their double copy in split signature

Reconstructing Classical Spacetimes from the S-Matrix in Twistor Space

The ultrarelativistic limit of Kerr

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