A new study explores how the behavior of light around extremely compact objects may change when Einstein’s theory of gravity is modified at very short distances. The work focuses on pseudo-complex General Relativity (pcGR), an extension of Einstein’s theory that introduces a repulsive gravitational effect in regions where gravity becomes exceptionally strong. SDSU Physics Professor Fridolin Weber is a co-author of the study, which was carried out with collaborators from Algeria, Mexico, Brazil, and Italy.

One of the most recognizable features of a black hole is its shadow. The boundary of this shadow is closely connected to the photon sphere, a region where gravity is strong enough for light to travel along circular paths around the object. The researchers found that, in pcGR, an event horizon and a photon sphere do not necessarily disappear at the same time. Remarkably, there is a range of conditions in which an object can have no event horizon but still retain a photon sphere. Such an object could therefore produce some of the strong gravitational lensing and shadow-like features normally associated with a black hole.

The study also identifies a precise transition at which the photon sphere itself disappears. Using methods from dynamical-systems theory, the researchers show that stable and unstable circular light orbits merge and vanish together as the strength of the repulsive correction increases. Beyond this point, light that would normally be captured by a black hole can instead be turned around by the strongly modified gravitational field.

The authors further examine what happens as such a compact object loses energy through Hawking radiation. Within the semiclassical model considered in the paper, evaporation stops at a stable, zero-temperature remnant before the photon sphere can disappear. The remnant would therefore retain the light-orbit structure responsible for a shadow.

These results suggest that a black-hole-like shadow does not by itself prove the existence of an event horizon. Future observations with instruments such as the Event Horizon Telescope and next-generation gravitational-wave detectors may provide ways to distinguish conventional black holes from alternative compact objects predicted by modified theories of gravity.

View PDF of the publication: Maghlaoui et al. 2026, Classical and Quantum Gravity