Linking waves to particles

13 January 2017

Gravitational waves could also shed light on the microscopic world.

Black holes are arguably humankind’s most intriguing intellectual construction. Featuring a curvature singularity where space–time “ends” and tidal forces are infinite, black-hole interiors cannot be properly understood without a quantum theory of gravity. They are defined by an event horizon – a surface beyond which nothing escapes to the outside – and an exterior region called a photosphere, which is able to trap light rays. These uncommon properties explain why black holes were basically ignored for half a century, considered little more than a bizarre mathematical solution of Einstein’s equations but one without counterpart in nature.

LIGO’s discovery of gravitational waves provides the strongest evidence to date for the existence of black holes, but these tiny distortions of space–time have much more to tell us. Gravitational waves offer a unique way to test the basic tenets of general relativity, some of which have been taken for granted without observations. Are black holes the simplest possible macroscopic objects? Do event horizons and black holes really exist, or is their formation halted by some as-yet unknown mechanism? In addition, gravitational waves can tell us if gravitons are massless and if extra-light degrees of freedom fill the universe, as predicted in the 1970s by Peccei and Quinn in an attempt to explain the smallness of the neutron electric-dipole moment, and more recently by string theory. Ultralight fields affect the evolution of black holes and their gravitational-wave emission in a dramatic way that should be testable with upcoming gravitational-wave observatories.

The existence of black holes

The standard criterion with which to identify a black hole is straightforward: if an object is dark, massive and compact, it’s a black hole. But are there other objects which could satisfy the same criteria? Ordinary stars are bright, while neutron stars have at most three solar masses and therefore neither is able to explain observations of very massive dark objects. In recent years, however, unknown physics and quantum effects in particular have been invoked that change the structure of the horizon, replacing it by a hard surface. In this scenario, the exterior region – including the photosphere – would remain unchanged, but black holes would be replaced by very compact, dark stars. These stars could be made of normal matter under extraordinary quantum conditions or of exotic matter such as new scalar particles that may form “boson stars”.

Unfortunately, the formation of objects invoking poorly understood quantum effects is difficult to study. The collapse of scalar fields, on the other hand, can theoretically allow boson stars to form, and these may become more compact and massive through mergers. Interestingly, there is mounting evidence that compact objects without horizons but with a photosphere are unstable, ruling out entire classes of alternatives that have been put forward.

Gravitational waves might soon provide a definite answer to such questions. Although current gravitational-wave detections are not proof for the existence of black holes, they are a strong indicator that photospheres exist. Whereas observations of electromagnetic processes in the vicinities of black holes only probe the region outside of the photosphere, gravitational waves are sensitive to the entire space–time and are our best probe of strong-field regions.

A typical gravitational-wave signal generated by a small star falling head-on into a massive black hole looks like that in figure 1. As the star crosses the photosphere, a burst of radiation is emitted and a sequence of pulses dubbed  “quasinormal ringing” follow, determined by the characteristic modes of the black hole. But if the star falls into a quantum-corrected or exotic compact object with no horizon, part of the burst generated during the crossing of the photosphere reflects back at the object surface. The resulting signal in a detector would thus initially look the same, but be followed by lower amplitude “echoes” trapped between the photosphere and the surface of the object (figure 1, lower panel). These echoes, although tricky to dig out in noisy data, would be a smoking gun for new physics. With increasing sensitivity in detectors such as LIGO and Virgo, observations will be pushing back the object’s surface closer to the horizon, perhaps even to the point where we can detect the echo of quantum effects.

Dark questions

Understanding strong-field gravity with gravitational waves can also test the nature of dark matter. Although dark matter may interact very feebly with Standard Model particles, according to Einstein’s equivalence principle it must fall just like any other particle. If dark matter is composed of ultralight fields, as recent studies argue, then black holes may serve as excellent dark-matter detectors. You might ask how a monstrous, supermassive black hole could ever be sensitive to ultralight fields. The answer lies in superradiant resonances. When black holes rotate, as most do, they display an interesting effect discovered in the 1970s called superradiance: if one shines a low-frequency lamp on a rotating black hole, the scattered beam is brighter. This happens at the expense of the hole’s kinetic energy, causing the spin of the black-hole to decrease.

Not only electromagnetic waves, but also gravitational waves and any other bosonic field can be amplified by a rotating black hole. In addition, if the field is massive, low-energy fluctuations are trapped near the horizon and are forced to interact repeatedly with the black hole, producing an instability. This instability extracts rotational energy and transfers it to the field, which grows exponentially in amplitude and forms a rotating cloud around the black hole. For a one-million solar-mass black hole and a scalar field with a mass of 10–16 eV, the timescale for this to take place is less than two minutes. Therefore, the very existence of ultralight fields is constrained by the observation of spinning black holes. With this technique, one can place unprecedented bounds on the mass of axion-like particles, another popular candidate for dark matter. For example, we know from current astrophysical observations that the mass of dark photons must be smaller than 10–20 eV, which is 100 times better than accelerator bounds. The technique relies only on measurements of the mass and spin of black holes, which will be known with unprecedented precision with future gravitational-wave observations.

Superradiance, together with current electromagnetic observations of spinning black holes, can also be used to constrain the mass of the graviton, since any massive boson would trigger superradiant instabilities. Spin measurements of the supermassive black hole in galaxy Fairall 9 requires the mass of the graviton to be lighter than 5 × 10–23 eV – an impressive number which is even more stringent than the bound recently placed by LIGO.

Gravitational lighthouses

Furthermore, numerical simulations suggest that the superradiant instability mechanism eventually causes a slowly evolving and non-symmetric cloud to form around the black hole, emitting periodic gravitational waves like a gravitational “lighthouse”. This would not only mean that black holes are not as simple as we thought, but lead to a definite prediction: some black holes should be emitting nearly monochromatic gravitational waves whose frequency is dictated only by the field’s mass. This raises terrific opportunities for gravitational-wave science: not only can gravitational waves provide the first direct evidence of ultralight fields and of possible new effects near the horizon, but they also carry detailed information about the black-hole mass and spin. If light fields exist, the observation of a few hundred black holes should show “gaps” in the mass-spin plane corresponding to regions where spinning black holes are too unstable to exist.

This is a surprising application of gravitational science, which can be used to investigate the existence of new particles such as those possibly contributing to the dark matter. The idea of using observations of supermassive black holes to provide new insights not accessible in laboratory experiments would certainly be exciting. Perhaps these new frontiers in gravitational-wave astrophysics, in addition to probing the most extreme objects, will also give us a clearer understanding of the microscopic universe.

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