PI: Ulrich Sperhake

Black holes are one of the most fundamental and exciting predictions of Einstein’s theory of general relativity and have played a key role in understanding the phenomenology and mathematical structure of relativity almost right from the time Einstein first published his theory – Schwarzschild found his famous black-hole solution little more than a month after Einstein’s publication. Starting in the early 1960s with astronomical observations of X-ray sources, like Cygnus X-1, and quasars, like 3C 273, and their eventual identification with accretion onto compact objects, black holes acquired an equally prominent status as common astrophysical objects in our Universe. More recently, this status has been further cemented by numerous gravitational-wave observations by LIGO and Virgo, all compatible with the predictions for black holes and neutron stars in general relativity, and observations of black-hole shadows by the Event Horizon Telescope.

From a mathematical viewpoint, the most characteristic feature of a black hole is its event horizon, the outer boundary of a region from which nothing, not even light, can escape to an outside observer. In terms of their observational features, however, the decisive property of a black hole is its light ring located outside the horizon; for a Schwarzschild black hole of mass  , the horizon is at radius   whereas the light ring is at  , 50% further out. The shape of black-hole shadows, accretion dynamics and the characteristic gravitational-wave ringdown of a black hole are closely related to the light ring, rather than the horizon. This raises the intriguing question whether the observed compact objects really are black holes. Even if we accept Occam’s razor by which black holes are the simplest and, hence, most likely explanation, there remains the exciting possibility that a population of ultra-compact objects of black-hole mimickers, is hiding inside a more conventional black-hole population. These mimickers, in turn may provide us with clues about the nature of dark matter and the structure of spacetime in regions of extreme gravity.

These considerations have sparked an intensive theoretical search for candidate objects that may possess a light but no event horizon. This search has identified ultra-compact boson stars, stellar objects composed of dark-matter fields, as one of the most promising type of mimickers. One of the prerequisites for any viable mimicker candidate, however, is long-term stability – otherwise, they would cease to exist before playing a significant role in astrophysical processes in our Universe. Mathematical and numerical investigations, in turn, have questioned the stability of ultracompact boson stars, based mainly on the realization that if they have a light ring but no horizon, they must have a second light ring with the additional property that it can trap light. In our project, we have investigated a specific class, so-called Thin Shell Boson Stars (TSBS) using a combination of numerical simulations, an analytic perturbative investigation and the tracing of light rays in TSBS spacetimes. Our three-pronged investigation uniformly supports the hypothesis that TSBS are stable mimickers of black holes. Our perturbative analysis demonstrates that these specific stars have the same division into stable and unstable branches as known for the classic Tolman-Oppenheimer-Volkoff neutron-star models as well as other boson-star families. Our ray tracing confirms the trapping capacity of the second light ring, but shows that light rays are only trapped if they originate near the light ring; light incident from the outside is not trapped. Our numerical time evolutions of these TSBSs fully confirm this picture, revealing the two light rings at the expected locations, exhibiting small-amplitude radial oscillations with exactly the frequency spectrum predicted by perturbation theory, and revealing no evolution besides these oscillations. Our work thus provides the first concrete evidence of a long-term stable class of black-hole mimickers.

The figure displays the respective shadows of a TSBS (left) and a Schwarzschild black hole (right) of equal mass, either surrounded by a geometrically thin accretion disk. Both exhibit the same light ring just outside the shadow but the TSBS exhibits a second light ring which may provide us with observational signatures to distinguish the two types of objects in future, more accurate, shadow observations.