Near-horizon perturbation of Kerr black holes (arXiv:2512.07937)

• We derive a convergent source term for linear gravitational perturbation associate with the spin s=+2 perturbation

• We validate the derivation by calculating the shear perturbation and the fluxes of a generic EMRI. Both of results agree with calculation in Teukolsky formalism very well.

• See GeneralizedSasakiNakamura.jl for our code implementation.

High performance EMRI waveform generation based on Sasaki-Nakamura formalism (arXiv:2511.08673)

• Benefiting from the short-range nature of the Sasaki–Nakamura (SN) formalism, we can use it to compute gravitational-wave waveforms from point particles on both bound and unbound orbits.
• The difficulties in solving the inhomogeneous SN source term and evaluating the Green’s function integral can be avoided by applying the integration-by-parts (IBP) technique.
• See GeneralizedSasakiNakamura.jl for our code implementation.

Binary extreme-mass-ratio inspiral (b-EMRI) waveform modeling (arXiv:2410.08673)

• B-EMRIs are hierarchical triple systems consisting of a supermassive bleck hole (SMBH) and two staller mass black holes.

• We carried out a waveform model based on black hole perturbation theory and relativistic three-body dynamics.

• What’s interesting is that the small binary could resonantly excite the quasi-normal modes of the SMBH, leading to some distinguishable features.