Compton Amplitude for Rotating Black Hole from QFT

We construct a candidate tree-level gravitational Compton amplitude for a rotating Kerr black hole, for any quantum spin <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>s</a:mi><a:mo>=</a:mo><a:mn>0</a:mn><a:mo>,</a:mo><a:mn>1</a:mn><a:mo>/</a:mo><a:mn>2</a:mn><a:mo>,</a:mo><a:mn>1</a:mn><a:mo>,</a:mo><a:mo>…</a:mo><a:mo>,</a:mo><a:mi>∞</a:mi></a:mrow></a:math>, from which we extract the corresponding classical amplitude to all orders in the spin vector <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msup><c:mi>S</c:mi><c:mi>μ</c:mi></c:msup></c:math>. We use multiple insights from massive higher-spin quantum field theory, such as massive gauge invariance and improved behavior in the massless limit. A chiral-field approach is particularly helpful in ensuring correct degrees of freedom, and for writing down compact off-shell interactions for general spin. The simplicity of the interactions is echoed in the structure of the spin-<e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>s</e:mi></e:math> Compton amplitude, for which we use homogeneous symmetric polynomials of the spin variables. Where possible, we compare to the general-relativity results in the literature, available up to eighth order in spin. Published by the American Physical Society 2024