Classical space–times from the S-matrix

By D. Neill, I. Rothstein. 2013

268 citations recorded by the source corpus.

Abstract We show that classical space–times can be derived directly from the S-matrix for a theory of massive particles coupled to a massless spin two particle. As an explicit example we derive the Schwarzchild space–time as a series in G N . At no point of the derivation is any use made of the Einstein–Hilbert action or the Einstein equations. The intermediate steps involve only on-shell S-matrix elements which are generated via BCFW recursion relations and unitarity sewing techniques. The notion of a space–time metric is only introduced at the end of the calculation where it is extracted by matching the potential determined by the S-matrix to the geodesic motion of a test particle. Other static space–times such as Kerr follow in a similar manner. Furthermore, given that the procedure is action independent and depends only upon the choice of the representation of the little group, solutions to Yang–Mills (YM) theory can be generated in the same fashion. Moreover, the squaring relation between the YM and gravity three point functions shows that the seeds that generate solutions in the two theories are algebraically related. From a technical standpoint our methodology can also be utilized to calculate quantities relevant for the binary inspiral problem more efficiently then the more traditional Feynman diagram approach.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1ccf7731ad0b3f42021ebb0a643c7ffa22e9a1ae

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Citations in the corpus

An effective field theory for forward scattering and factorization violation (2016, background): “For a discussion on this point see [117].”
From boundary data to bound states. Part II. Scattering angle to dynamical invariants (with twist) (2019, background): “Therefore, provided the matching discussed in [15–18] carries over to spin, as suggested in [19–26], the existence of this gauge is guarantee to all PM orders.”
The tune of love and the nature(ness) of spacetime (2016, background): “[59], the search for a more efficient computational scheme within the EFT framework has also become an important goal in the field [15,60,61].”
Revisiting the second post-Minkowskian eikonal and the dynamics of binary black holes (2019, methodology): “The technique of deriving the relativistic interaction of two massive objects from an amplitude approach has recently attracted renewed attention [9, 10, 11, 12, 13, 14, 15, 16] since it links directly to the post-Minkowskian approximation of the classical gravitational dynamics relevant for the ins”
Double copy for massive quantum particles with spin (2019, methodology): “Focusing on analytical methods that use scattering amplitudes, there are by now a number of impressive results and techniques relevant to black-hole scattering [3–13].”
Type D spacetimes and the Weyl double copy (2018, unknown): “The success of the double copy for scattering amplitudes motivated the investigation of its manifestation for solutions of the classical ﬁeld equations, with early steps given in [45–47].”
Perturbative spacetimes from Yang-Mills theory (2016, methodology): “[68, 69], which used tree-level amplitudes to construct perturbatively the Schwarszchild spacetime.”
Spinning black hole binary dynamics, scattering amplitudes, and effective field theory (2020, methodology): “As we will see in detail in the next section and used in earlier literature [11, 12, 22, 23, 33, 36, 37], the new physical information in this amplitude arises from triangle integrals.”
Scattering of spinning black holes from exponentiated soft factors (2018, background): “The reason that this leads to classical effects is that the O(t0) piece, which is dropped, is ultralocal after a Fourier transform [25, 53].”
Classical and quantum scattering in post-Minkowskian gravity (2019, background): “[17, 22, 24, 25] might exacerbate the classicalquantum conflict by making the usual, non relativistic Coulomb coupling constant GE1E2 ~ v parametrically larger than the natural dimensionless quantum coupling constant αg = GE1E2 ~ entering the loop expansion of M.”
On-shell techniques and universal results in quantum gravity (2013, unknown): “[5] which appeared near the end of our work, also uses on-shell methods to derive corrections to the scattering potential, but there only the classical correction terms are considered).”
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