The constraint on modified black holes with extreme mass ratio inspirals

The low-energy effective action of String Theory introduces corrections to the dilaton-graviton sector, resulting in deformed black holes beyond general relativity. We analyze extreme mass-ratio inspiral systems (EMRIs), where a stellar-mass object spirals into a slowly rotating supermassive black hole including a distinct deviation parameter. This study examines the effects of this deformation on the rate of change of orbital energy and angular momentum, orbital evolution, and phase dynamics, incorporating leading-order post-Newtonian corrections. The String theory parameter $$\alpha $$ α will accelerate the EMRI merger because of the extra energy and angular momentum fluxes carried away by corrections to the dilaton-graviton sector. With 1-year observations of EMRIs, we employ the Fisher information matrix method to evaluate the potential for detecting deviations from general relativity through space-based gravitational wave detectors that utilize time-delay interferometry to suppress laser noise. The constraint on modified black holes, $$\varDelta \alpha \preceq 10^{-5}$$ Δ α ⪯ 10 - 5 , is almost the same with and without the time-delay interferometry combination. This analysis enhances our understanding and underscores the crucial role of observations in advancing gravitational phenomena within String Theory.