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#### From Scattering in Black Hole Backgrounds to Higher-Spin Amplitudes: Part I

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2107.10179.pdf

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JHEP03(2023)136.pdf

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##### Citation

Bautista, Y. F., Guevara, A., Kavanagh, C., & Vines, J. (2023). From Scattering
in Black Hole Backgrounds to Higher-Spin Amplitudes: Part I.* Journal of High Energy Physics,*
*2023*(3): 136. doi:10.1007/JHEP03(2023)136.

Cite as: https://hdl.handle.net/21.11116/0000-0008-E76E-9

##### Abstract

The scattering of massless waves of helicity $|h|=0,\frac{1}{2},1$ in

Schwarzschild and Kerr backgrounds is revisited in the long-wavelenght regime.

Using a novel description of such backgrounds in terms of gravitating massive

particles, we compute classical wave scattering in terms of $2\to 2$ QFT

amplitudes in flat space, to all orders in spin. The results are Newman-Penrose

amplitudes which are in direct correspondence with solutions of the

Regge-Wheeler/Teukolsky equation. By introducing a precise prescription for the

point-particle limit, in Part I of this work we show how both agree for $h=0$

at finite values of the scattering angle and arbitrary spin orientation.

Associated classical observables such as the scattering cross sections, wave

polarizations and time delay are studied at all orders in spin. The effect of

the black hole spin on the polarization and helicity of the waves is found in

agreement with previous analysis at linear order in spin. In the particular

limit of small scattering angle, we argue that wave scattering admits a

universal, point-particle description determined by the eikonal approximation.

We show how our results recover the scattering eikonal phase with spin up to

second post-Minkowskian order, and match it to the effective action of null

geodesics in a Kerr background. Using this correspondence we derive classical

observables such as polar and equatorial scattering angles.

This study serves as a preceding analysis to Part II, where the Gravitational

Wave ($h=2$) case will be studied in detail.

Schwarzschild and Kerr backgrounds is revisited in the long-wavelenght regime.

Using a novel description of such backgrounds in terms of gravitating massive

particles, we compute classical wave scattering in terms of $2\to 2$ QFT

amplitudes in flat space, to all orders in spin. The results are Newman-Penrose

amplitudes which are in direct correspondence with solutions of the

Regge-Wheeler/Teukolsky equation. By introducing a precise prescription for the

point-particle limit, in Part I of this work we show how both agree for $h=0$

at finite values of the scattering angle and arbitrary spin orientation.

Associated classical observables such as the scattering cross sections, wave

polarizations and time delay are studied at all orders in spin. The effect of

the black hole spin on the polarization and helicity of the waves is found in

agreement with previous analysis at linear order in spin. In the particular

limit of small scattering angle, we argue that wave scattering admits a

universal, point-particle description determined by the eikonal approximation.

We show how our results recover the scattering eikonal phase with spin up to

second post-Minkowskian order, and match it to the effective action of null

geodesics in a Kerr background. Using this correspondence we derive classical

observables such as polar and equatorial scattering angles.

This study serves as a preceding analysis to Part II, where the Gravitational

Wave ($h=2$) case will be studied in detail.