A new hypergeometric representation of the confluent Heun equation resums infinite PM/PN correction series and yields the circular-orbit energy flux to 30PN order, matching independent numerical black-hole perturbation results to 10-14 digits.
The effect of resummation on retarded Green's function and greybody factor in $AdS$ black holes
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abstract
We investigate the retarded Green's function and the greybody factor in asymptotically AdS black holes. Using the connection coefficients of the Heun equation, expressed in terms of the Nekrasov-Shatashvili (NS) free energy of an $SU(2)$ supersymmetric gauge theory with four fundamental hypermultiplets, we derive asymptotic expansions for both the retarded Green's function and the greybody factor in the small horizon limit. Furthermore, we compute the corrections to these asymptotic expansions resulting from the resummation procedure of the instanton part of the NS function.
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Resumming Post-Minkowskian and Post-Newtonian gravitational waveform expansions
A new hypergeometric representation of the confluent Heun equation resums infinite PM/PN correction series and yields the circular-orbit energy flux to 30PN order, matching independent numerical black-hole perturbation results to 10-14 digits.