“Gravity can exist without mass.” It’s a statement that upends a century of astrophysical dogma and, for some, sounds as plausible as finding a unicorn in a particle accelerator. But in a series of recent articles, physicist Richard Lieu at the University of Alabama in Huntsville has presented a mathematically strict argument for just such an eventuality, and has proposed that unresolvable densities of zero-mass shells topological defects in space and time can produce gravitational fields indistinguishable from dark matter’s.
The theory, released in the Monthly Notices of the Royal Astronomical Society, relies on the premise of a “shell singularity.” Gravity, in Lieu’s expression, is not generated from mass but from an arrangement of spacetime in which mass, strangely, does not exist. As he explains, “With a sufficient number of such unresolvably closely spaced singular shells, the potential Φ is effectively a continuous function.” The gravitational field in this case is maintained by a lattice of concentric, massless shells each made up of a thin inner shell of positive mass and an equally thin outer shell of negative mass. The combined mass adds up to zero, but the shells as a group gravitate toward stars and light, duplicating the effects credited to dark matter.
The process is not some mathematical trick. Lieu’s shells are a type of topological defect local distortions in the texture of spacetime, possibly created during the universe’s earliest phase transitions. These imperfections, he explains, “are very compact regions of space with a very high density of matter, usually in the form of linear structures known as cosmic strings, although 2-D structures such as spherical shells are also possible.” The structure of the shells positive and negative mass layers guarantees that even though the net mass is zero, so is not the gravitational potential. As Lieu describes it, “when a star sits on this shell it feels a tremendous gravitational force pushing it to the center of the shell.”
The model neatly explains two of the most confounding observations in contemporary astrophysics: the flat rotation curves of galaxies and the gravitational lensing observed in clusters. Both effects in normal cosmology are explained by massive dark matter halos that are invisible. Yet as Lieu shows, a galaxy or cluster made up of a stack of dense massless shells can duplicate these effects. “Gravitational bending of light by a collection of concentric singular shells making up a galaxy or cluster is the result of a beam of light being slightly deflected inward. when passing through one shell.” The net total effect of passing through multiple shells is a finite, measurable overall deflection which simulates the presence of lots of dark matter much as the speed of stellar orbits,” Lieu explains
Implications are profound. If gravity can be the result of spacetime topology instead of mass, then the hunt for dark matter so far unsuccessful at particle accelerators and underground detectors could be pursuing a ghost. As Stacy McGaugh, head of astronomy at Case Western Reserve, points out in the context of rival theories, “Either dark matter halos are much bigger than we expected, or the whole paradigm is wrong… perhaps the evidence for it is pointing to some new theory of gravity beyond what Einstein taught us.”
Lieu’s hypothesis is not the only one vying for space in this arena. Theoretical physicists are looking at a range of possibilities from emergent models of gravity, where gravity emerges from quantum data or thermodynamic laws, to quantum gravity models that avoid the requirement for dark matter by altering the fabric of spacetime itself. Others, such as Oppenheim’s “wobbly spacetime” model, explain the missing gravity energy as arising from random fluctuations in the passage of time and in the geometry of space.
However, Lieu’s method is distinctive in its technicality. The shell singularity solution arises directly from the Poisson equation and Einstein’s field equations and results in a stable, time-independent metric. The model can also duplicate observed galactic rotation curves, explain gravitational lensing, and even reproduce the observed temperature and density profiles of baryonic gas in clusters and galaxies all without any exotic particles. The individual shells, at sub-astronomical separations, are themselves unresolved by present telescopes, but their combined gravitational effect is, in principle, testable via meticulous mapping of lensing anomalies and the distribution of ring- and shell-like galaxy morphology.
While Lieu admits that his theory does not eliminate dark matter completely, nor does it explain all of cosmology’s enigmas like the cosmic microwave background or nucleosynthesis, it offers a definite, testable alternative. As he mentions, “the availability of a second solution, even if it is highly suggestive, is not by itself sufficient to discredit the dark matter hypothesis it could be an interesting mathematical exercise at best. But it is the first proof that gravity can exist without mass.”
The next few years might host a new generation of observation tests probing for the telltale marks of shell-caused lensing, or the faint imprints of topological defects on the largest scales of the cosmos. Until then, however, the notion that gravity’s hold may be spun from the very fabric of spacetime itself, and not from hidden mass, remains one of the most exciting and technically substantial criticisms of the dark matter hypothesis ever put forward.
