Revisiting the matching of black hole tidal responses: a systematic study of relativistic and logarithmic corrections

Understand

The worldline effective field theory (EFT) gives a gauge-invariant definition of black hole conservative tidal responses (Love numbers), dissipation numbers, and their spin-0 and spin-1 analogs.

• In the first part of this paper we show how the EFT allows us to circumvent the source/response ambiguity without having to use the analytic continuation prescription.
• The source/response ambiguity appears if Post-Newtonian (PN)corrections to external sources overlap with the response.
• However, these PN corrections can be clearly identified and isolated using the EFT.