Impact of mass transfer on the orbital evolution of a white dwarf close to an intermediate-mass black hole

ABSTRACT Extreme mass-ratio inspirals of low-mass white dwarfs (WDs; 0.1–0.3 $\text{M}_{\odot }$) around spinning intermediate-mass black holes (IMBHs; $10^{3}$–$10^{5}$ $\text{M}_{\odot }$) offer unique opportunities for multimessenger astronomy, emitting both gravitational waves (GWs) and electromagnetic signals. Yet, despite their astrophysical relevance, theoretical models often omit key interactions between relativistic dynamics and phase-dependent mass transfer (MT). In this study, we integrate a perturbed Keplerian formalism with post-Newtonian corrections to simulate the relativistic orbit of a WD around a rotating IMBH, explicitly resolving the narrow phase near pericentre where Roche-lobe overflow initiates MT. We find that GW emission and MT exert competing influences on the orbit: MT episodes can increase both orbital period and eccentricity, potentially enabling the WD to avoid complete tidal disruption and even escape. We further quantify the GW phase evolution induced by MT, identifying parameter regimes in which GW detectors could observe a 1 rad phase shift over observational time-scales. Finally, we propose that the orbital expansion driven by MT may lead to the disappearance of quasi-periodic eruptions. Our results underscore the necessity of jointly modelling relativistic effects and dynamic MT in WD–IMBH systems.