Abstract
In this Letter, we present the first multiparticle solutions to Einstein's field equations in the presence of matter. These solutions are iteratively obtained via the perturbiner method, which can circumvent gravity's infinite number of vertices with the definition of a multiparticle expansion for the inverse spacetime metric as well. Our construction provides a simple layout for the computation of tree level field theory amplitudes in D spacetime dimensions involving any number of gravitons and matter fields, with or without supersymmetry.
Highlights
Overview.—Gravity is still in many ways the least understood of the fundamental forces of nature, arguably at the macroscopic but definitely at the microscopic level
In this Letter, we present the first multiparticle solutions to Einstein’s field equations in the presence of matter
These solutions are iteratively obtained via the perturbiner method, which can circumvent gravity’s infinite number of vertices with the definition of a multiparticle expansion for the inverse spacetime metric as well
Summary
Rμν 1⁄4 0; ð5Þ which can be used to analyze linearized solutions around a given background, i.e., the gravitons These single-particle solutions around flat space (with metric ημν) are given by gμνðxÞ 1⁄4 ημν þ hμνeik·x; ð6Þ. In work order with to gμν ðfxinÞdsathtiesfsyoinlugtigoμnρsgρfνor1⁄4HδPμνμ.νF, owr ethheaevxepaalnssoioton In this gauge, the multiparticle currents of the Ricci tensor RPμν are computed to be RPμν sP 2. HPμν is symmetric in the exchange of any two single-particle labels This symmetry is lifted to the amplitude Mn, which is symmetric in the exchange of any two graviton legs, only (n − 1) are manifest through H2.::nμν. In order to see this, we can examine the residual gauge transformations preserving Eq (13) They lead to a recursion for the currents ΛPμ in Eq (11) given by ΛPμ kνP sP
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