Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A ∗

You have one photograph: a single blurry orange ring, roughly fifty microarcseconds across, hovering against the darkness at the center of our galaxy. From that one image, physicists are now trying to rule out entire branches of theoretical physics — extra dimensions, quantum gravity corrections, wormholes, naked singularities, and scalar fields clutching black holes like a second skin. They are not metaphorically ruling them out; they are actually eliminating them with numbers. That is what Vagnozzi and colleagues set out to do with the Event Horizon Telescope image of Sagittarius A-star, and the scope of what one blurry ring can say about the universe turns out to be genuinely staggering. The method is elegant in its simplicity. For any static, spherically symmetric spacetime, photon orbits are governed by an effective potential — think of it as a landscape that light rolls through. At the peak of that landscape sits the photon sphere, and the shadow radius is determined directly from where that peak sits and what the metric looks like there. In the standard Schwarzschild case, the shadow radius equals three times the square root of three times the mass. In angular units, that becomes six times the square root of three times the angular gravitational radius, which is just the mass divided by the distance. So if you know the mass-to-distance ratio with high precision, you know exactly what size shadow general relativity predicts, and you can compare it to what the telescope actually sees. Vagnozzi and colleagues use stellar dynamics measurements from the Keck Observatory and the Very Large Telescope Interferometer, known as the VLTI, as their precision anchor. Keck gives a mass of about three point nine five million solar masses at a distance of seven point nine five kiloparsecs. VLTI gives four point three million solar masses at eight point three kiloparsecs. By folding those into the Event Horizon Telescope measurement, they define a fractional deviation delta, which describes how much the observed shadow radius departs from the Schwarzschild prediction. They find that delta equals negative zero point zero four, plus or minus about zero point zero nine or ten, depending on which stellar-orbit prior you use. That number is the lever that pries open the entire landscape of alternative theories. One immediate consequence follows: theories that predict a shadow larger than Schwarzschild are pushed hardest against that measurement. The Event Horizon Telescope data sit, on average, slightly below the Schwarzschild prediction. Bigger shadows have nowhere to hide. The first wave of alternatives involves regular black holes and string-inspired spacetimes. Regular black holes — the Bardeen and Hayward solutions — were constructed to remove the singularity at the center, replacing it with a finite core. The Bardeen metric is controlled by a magnetic charge, while the Hayward metric is governed by a short-distance length scale that encodes an effective cosmological constant at the core. Both are characterized by what Vagnozzi and colleagues call a hair parameter — a single number capturing how far the spacetime departs from Schwarzschild. For both models, increasing the hair shrinks the shadow, which means they sit on the less-constrained side of the Schwarzschild threshold. The results show that both Bardeen and Hayward black holes remain fully consistent with the Event Horizon Telescope image across their entire allowed parameter range, including the extremal values. String-inspired solutions present a different story. The Sen black hole is a solution of low-energy heterotic string theory carrying a dilaton charge and a Kalb-Ramond field. It is constrained to a charge of no more than about zero point six times the mass at one sigma, and no more than zero point seven five times the mass at two sigma. The extremal Sen hole, sitting at a charge of the square root of two times the mass, is ruled out. The Einstein-Maxwell-dilaton solution fares similarly: the dilaton charge is limited to below about zero point eight times the mass at one sigma, again excluding the extremal configuration. For the Gauss-Bonnet coupling, the shadow changes are too small to be meaningful — binary black hole observations constrain that parameter to levels orders of magnitude tighter than the shadow ever could. The next category is where the physics gets philosophically interesting: modifications to gravity itself, not just to the black hole solution. Vagnozzi and colleagues test the Randall-Sundrum braneworld scenario, where our four-dimensional universe is a membrane embedded in a five-dimensional spacetime, allowing gravity to leak into the extra dimension. The tidal charge parameter in that model can be negative, which increases the shadow size, placing it squarely in the regime that the Event Horizon Telescope constrains most tightly. The result is a meaningful upper bound on how much extra-dimensional gravity can leak. Loop quantum gravity introduces corrections to the metric at the Planck scale, encoding quantum geometry through a minimum area parameter. The shadow shifts are modest but calculable, and the Event Horizon Telescope places limits on the quantum parameter at the level of order-one times the mass squared. Horndeski scalar-tensor theories — the broadest class of scalar-field modifications to gravity with second-order equations of motion — contribute black hole solutions with scalar hair that can either enlarge or shrink the shadow depending on the coupling. Where the hair enlarges the shadow, the Event Horizon Telescope provides some of the first direct horizon-scale constraints on those couplings. In several cases, Vagnozzi and colleagues note that the shadow-based limits surpass cosmological constraints, which is remarkable because cosmological observations span the entire observable universe. Now for the strangest chapter. What if the object at the center of the galaxy has no event horizon at all? Vagnozzi and colleagues catalogue what they call black hole mimickers: horizonless compact objects that cast a shadow-like feature purely because they concentrate spacetime curvature strongly enough to trap photon orbits, even without a horizon to define a point of no return. The Janis-Newman-Winicour spacetime is a naked singularity — a singularity not hidden behind a horizon, which technically violates what is called cosmic censorship. It only casts a shadow when a scalar parameter nu lies between zero and one-half. The Event Horizon Telescope constrains nu to below about zero point four at one sigma, barely excluding the extremal value. That naked singularity is one of the most compatible objects in the entire catalogue with the Event Horizon Telescope data. The JMN-1 family is stranger still. When its collapse parameter chi exceeds two-thirds, the JMN-1 spacetime supports a photon sphere — and in that regime, the shadow radius is exactly three times the square root of three times the mass, identical to Schwarzschild. The Event Horizon Telescope cannot distinguish it from a classical black hole. However, for chi below two-thirds, there is no photon sphere, and instead a bright full-moon image fills the center — which is directly inconsistent with the dark interior the Event Horizon Telescope observes. That portion of the parameter space is ruled out. Some mimickers fare far worse. The null naked singularity and the Casimir wormhole — a traversable wormhole supported by Casimir energy, with a throat radius and an ADM mass tied together — predict a shadow radius equal to just the mass, far smaller than the observed ring. Vagnozzi and colleagues report that these are excluded at greater than five sigma. The universe, apparently, is not a Casimir wormhole. Stepping back, the picture that emerges is asymmetric and precise. Models predicting larger shadows than Schwarzschild are tightly constrained; the Event Horizon Telescope measurement sits slightly below Schwarzschild, and there is not much room above it. Models predicting smaller shadows have more space. Across more than fifty scenarios tested, dimensional parameters are typically bounded at the level of a tenth of some power of the mass, while dimensionless parameters are constrained at the ten-percent level or better. Future measurements will sharpen all of this considerably. GRAVITY-Plus will improve the mass-to-distance prior for Sagittarius A-star, tightening the anchor that the entire test depends on. The next-generation Event Horizon Telescope, with roughly double the antennas and commissioning not targeted earlier than 2027, will improve sensitivity and dynamic range enough to resolve finer structure in the ring. Space-based interferometry could push angular resolution an order of magnitude further. X-ray interferometry, planned further in the future — most likely not before 2060 — could reach sub-microarcsecond scales; though that would probe the inner disk edge and carry more spin dependence. One blurry ring. And already, an enormous swath of theoretical physics has had to conform to it or be set aside. The ring will only get sharper. This lecture was created by ennepō. Go to https://ennepo.ai to Discover, Create and Follow the latest research in your field. Read when you can. Listen when you want to.