Scattering amplitudes, black holes and leading singularities in cubic theories of gravity

Emond, William T.; Moynihan, Nathan

doi:10.1007/jhep12(2019)019

Cited by 58 publications

(53 citation statements)

References 36 publications

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“…The extra terms do not introduce modifications of the three-graviton interaction [46,47], and do not affect the three-and four-point graviton amplitudes. However, the R µνα β R βγ νσ R σ µγα term modifies the scalar potential, as shown recently in [51] and discussed at the end of Section 2.…”

Section: Graviton Bending In the Bosonic String Theorymentioning

confidence: 53%

“…While we discussed so far the effects of the interaction I 1 = R αβ µν R µν ρσ R ρσ αβ , there exists a second independent contraction R µνα β R βγ νσ R σ µγα . Corrections to the Newton potential due to this interaction were recently studied in [51]. These two structures combine naturally into…”

Section: R 3 Corrections To the Gravitational Potentialmentioning

confidence: 99%

“…Finally, the recent paper [51] computed corrections to the Newton potential due to a coupling of the form R µνα β R βγ νσ R σ µγα . A natural combination to consider is G 3 := I 1 − 2R µνα β R βγ νσ R σ µγα , which also appears in the low-energy effective action of the bosonic string, and is a topological invariant in six dimensions.…”

Section: Introductionmentioning

confidence: 99%

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On higher-derivative effects on the gravitational potential and particle bending

Brandhuber¹,

Travaglini²

2020

J. High Energ. Phys.

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Using modern amplitude techniques we compute the leading classical and quantum corrections to the gravitational potential between two massive scalars induced by adding an R 3 term to Einstein gravity. We then study the scattering of massless scalars, photons and gravitons off a heavy scalar in the presence of the same R 3 deformation, and determine the bending angle in the three cases from the non-analytic component of the scattering amplitude. Similarly to the Einstein-Hilbert case, we find that the classical contribution to the bending angle is universal, but unlike that case, universality is preserved also by the first quantum correction. Finally we extend our analysis to include a deformation of the form ΦR 2 , where Φ is the dilaton, which arises in the low-energy effective action of the bosonic string in addition to the R 3 term, and compute its effect on the graviton bending. α {a.brandhuber, g.travaglini}@qmul.ac.uk arXiv:1905.05657v2 [hep-th]

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Section: Graviton Bending In the Bosonic String Theorymentioning

confidence: 53%

Section: R 3 Corrections To the Gravitational Potentialmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On higher-derivative effects on the gravitational potential and particle bending

Brandhuber¹,

Travaglini²

2020

J. High Energ. Phys.

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“…The classical terms of the one-loop amplitude have been given elsewhere [6][7][8][25][26][27][28]. They can be decomposed in terms of scalar integrals with coefficients that are independent of the exchanged three-momentum q,…”

Section: Post-minkowskian Hamiltoniansmentioning

confidence: 99%

Post-Minkowskian Hamiltonians in general relativity

et al. 2019

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We describe the computation of post-Minkowskian Hamiltonians in General Relativity from scattering amplitudes. Using a relativistic Lippmann-Schwinger equation, we relate perturbative amplitudes of massive scalars coupled to gravity to the post-Minkowskian Hamiltonians of classical General Relativity to any order in Newton's constant. We illustrate this by deriving an Hamiltonian for binary black holes without spin up to 2nd order in the post-Minkowskian expansion and demonstrate explicitly the equivalence with the recently proposed method based on an effective field theory matching. PACS numbers: 04.60.-m, 04.62.+v, 04.80.Cc 1 arXiv:1906.01579v1 [hep-th] 4 Jun 2019daring angle of attack is to treat the bound state problem as not expanded in momentum while still expanding to fixed order in Newton's constant. Such an approach has recently been proposed by Cheung, Rothstein and Solon [8], and it has already been pushed one order higher in the expansion in Newton's constant [9] (and compared to the post-Newtonian expansions in [10]). Here the method of effective field theory is used to extract the interaction Hamiltonian: the underlying Einstein-Hilbert action coupled to matter produces the classical part of the scattering amplitude while an effective theory of two massive objects define the interaction Hamiltonian. The correct matching between the two theories is performed

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“…In addition to this more or less structural properties, GQTGs have been considered in various contexts, and many interesting additional properties and applications explored -see e.g., [45,[81][82][83][84][85][86][87][88][89][90][91]. At cubic order in curvature, the most general (nontrivial) GQTG can be written as…”

mentioning

confidence: 99%

All higher-curvature gravities as Generalized quasi-topological gravities

Bueno

Cano

Moreno

et al. 2019

J. High Energ. Phys.

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Generalized quasi-topological gravities (GQTGs) are higher-curvature extensions of Einstein gravity characterized by the existence of non-hairy generalizations of the Schwarzschild black hole which satisfy g tt g rr = −1, as well as for having secondorder linearized equations around maximally symmetric backgrounds. In this paper we provide strong evidence that any gravitational effective action involving highercurvature corrections is equivalent, via metric redefinitions, to some GQTG. In the case of theories involving invariants constructed from contractions of the Riemann tensor and the metric, we show this claim to be true as long as (at least) one non-trivial GQTG invariant exists at each order in curvature -and extremely conclusive evidence suggests this is the case in general dimensions. When covariant derivatives of the Riemann tensor are included, the evidence provided is not as definitive, but we still prove the claim explicitly for all theories including up to eight derivatives of the metric as well as for terms involving arbitrary contractions of two covariant derivatives of the Riemann tensor and any number of Riemann tensors. Our results suggest that the physics of generic higher-curvature gravity black holes is captured by their GQTG counterparts, dramatically easier to characterize and universal. As an example, we map the gravity sector of the Type-IIB string theory effective action in AdS 5 at order O(α 3 ) to a GQTG and show that the thermodynamic properties of black holes in both frames match.ArXiv ePrint: 190n.nnnnn arXiv:1906.00987v1 [hep-th]

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Scattering amplitudes, black holes and leading singularities in cubic theories of gravity

Cited by 58 publications

References 36 publications

On higher-derivative effects on the gravitational potential and particle bending

On higher-derivative effects on the gravitational potential and particle bending

Post-Minkowskian Hamiltonians in general relativity

All higher-curvature gravities as Generalized quasi-topological gravities

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