Star Harp: How Orbits Around a Black Hole Weigh the Graviton ✛ ✦

At the center of the Milky Way, shrouded in dust and glare, lurks a supermassive black hole — Sagittarius A*. Around it, like moths around a flame, swarm dozens of guide stars. Two of them, S2 and S38, with eccentric orbits and periods of just a few years, have become the protagonists in testing the fundamental laws of the cosmos. Einstein gifted us general relativity — a flawless melody of gravity. But in this melody, overtones of the unknown are heard. If the graviton, the quantum of the gravitational field, has mass, then the harmony is disrupted, as if one string on a giant harp had gone slightly out of tune. The stars' orbits are the strings of a cosmic harp, and their precession, the slow rotation of the ellipse, betrays the slightest deviations from Schwarzschildian purity. If the graviton's mass were even a jot larger, these strings would snap — the orbits would become unstable, and the Galactic Center would turn into a chaotic carousel. The very architecture of the Milky Way sets an upper limit on the graviton mass.

Scientists used two approaches to capture this disharmony. The first is the analysis of the measured precession of S2's orbit, obtained by the GRAVITY collaboration using the VLTI interferometer. A Yukawa correction exp(-r/λ) was introduced into the Newtonian potential, where λ is the Compton wavelength of the graviton. Just as sound fades with distance, the gravity of a massive quantum weakens faster than the inverse-square law prescribes. Comparing with the classical precession predicted by general relativity allowed an upper limit on the mass to be extracted. The second method is direct numerical simulation of trajectories with χ² minimization, where the graviton mass became yet another free parameter of the orbit. This work is a triumph of precision astronomy: by measuring a star's position to an accuracy of microarcseconds, we weigh a ghost, as if hearing the breath of an infant on another continent.

Both methods yielded consistent results: the graviton mass does not exceed 1.25 × 10⁻²² eV/c² based on S2 data, and for S38 the limit is even lower — around 0.77 × 10⁻²² eV/c². These values are about five times weaker than the limits obtained from gravitational waves from black hole mergers by the LIGO-Virgo collaboration, but the principle here is different: not ripples in spacetime, but an almost Keplerian dance. Nature gives us two independent witnesses. Moreover, the Yukawa correction always increases precession, so any observed excess periastron shift automatically points to a massive graviton. This turns the Galactic Center into a natural laboratory for quantum gravity, where stars are test particles, and the black hole is the field source.

Ahead lies the era of the GRAVITY+ interferometer, which will boost astrometric accuracy by another order of magnitude, allowing more stars with different orbits to be included in the analysis. Merging with data from planetary ephemerides and future gravitational-wave observatories like LISA will create a multichannel test of gravity theories. Weighing the graviton is not just a hunt for an elusive number. It is an attempt to hear the quantum breath of spacetime, to connect dark energy and the accelerated expansion of the Universe with the microscopic properties of the field. Perhaps stellar orbits will show us the way to a unified theory where gravity ceases to be an exception and joins the ranks of the other interactions. The cosmic harp keeps sounding, and we are learning to discern its quietest overtone.