Gravitational Faraday effect from on-shell amplitudes

Abstract

A bstract Effects of massive object’s spin on massive-massless 2 → 2 classical scattering is studied. Focus is set on the less-considered dimensionless expansion parameter λ/b , where λ is the massless particle’s wavelength and b is the impact parameter. Corrections in λ/b start to appear from $$ \mathcal{O} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> </mml:math> ( G 2 ), with leading correction terms tied to the gravitational Faraday effect, which is a special case of the Lense-Thirring effect. We compute the eikonal phase up to $$ \mathcal{O} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> </mml:math> ( G 2 ) and extract spin effect on the scattering angle and time delay up to 14th order in spin. The gravitational Faraday effect at linear order in spin [1] is reproduced by λ/b correction terms, which we compute to higher orders in spin. We find that the equivalence principle, or universality, holds up to NLO for general spinning bodies, i.e. away from geometric optics limit. Furthermore, in the black hole limit, we confirm the absence of particular spin structure observed [2–8], along with the associated shift symmetry [7], and argue that it holds to arbitrary spin order at $$ \mathcal{O} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> </mml:math> ( G 2 ) in the massless probe limit.

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