In the centers of many galaxies slumber supermassive black holes, surrounded by accretion disks and the activity of active galactic nuclei. When a compact object — such as a stellar-mass black hole — orbits them, a gravitational duet is born. Its music spreads across the Universe via gravitational waves. The space-based observatory LISA, set to launch in the coming years, will be the perfect listener: over a year it will capture up to a hundred thousand orbital cycles — like notes in a symphony, where each revolution slightly shifts the pitch. Deciphering this music means peering into the very heart of warped space and, perhaps, hearing new physical instruments not written in Einstein's score.

Researchers constructed a signal model combining rigorous self-force calculations in the Schwarzschild metric with leading contributions from a hypothetical scalar field and post-adiabatic corrections. These corrections are like subtle overtones, born from the back-reaction of waves on the orbit. Numerical simulations and Bayesian spectroscopy of the signal showed: if overtones are neglected, mass and initial radius estimates deviate by tens of standard deviations, but the scalar charge — a characteristic of the additional field — remains remarkably robust. Only at extremely large charges or mass ratios does it begin to shift. Pure Einsteinian templates that ignore the charge produce colossal systematic errors. Recall: according to the no-hair theorem of Hawking and others, black holes in GR lack scalar charge, so its detection would be a breakthrough.

These results are good news for tests of general relativity. It turns out that to detect scalar charge, simpler adiabatic models can be used without overburdening calculations with subtle overtones. But real astrophysics demands full precision: without post-adiabatic corrections, the true mass of the black hole or its distance cannot be determined. A pleasant surprise: even the simplest dipole approximation for scalar flux works excellently — as if nature deliberately cracks open a door to new physics, paving the way for rapid scanning of extended gravity theories, including models of dark energy and axions. Correlating future observations of gravitational lensing and interferometric data from LISA promises to shed light on the nature of dark energy.

Up next — accounting for the rotation of the central black hole (Kerr metric) and eccentric orbits, where scalar overtones might ring louder. The addition of post-adiabatic contributions from the scalar field itself, not yet complete, will definitively pinpoint the sensitivity limits of LISA to 'new physics.' This work sets a data analysis strategy for future missions and is directly linked to quantizing gravity: scalar fields naturally arise in string theories and dark energy models. Precise measurement or constraints on the scalar charge in the strong-field regime will become a crucial test on the path to a unified theory.