A gravitational singularity is a point experiencing such extreme gravity that it breaks the structure of spacetime itself, at least as we understand it. At the singularity, our current best model of gravity – general relativity – predicts infinite gravity and some other crazy artefacts. The most known example of a singularity is the centre of a black hole, where matter theoretically compresses to an infinite density with infinite gravity.

Physicists are very curious as to what is actually happening at these singularities, but the universe, as shy as it is, hides all of its black hole singularities behind event horizons. The event horizon is the point of no return for anything near a black hole – not even objects moving at the speed of light can escape its gravity. Since light cannot escape past the event horizon, we’re unable to observe any of these singularities. How convenient! This leads to an uneasy truce between physicists; maybe our theory of gravity breaks down in some places, but those places have been effectively swept under the rug, so maybe things are all okay for now? However, if we want a complete theory of gravity, it must be true throughout all of spacetime. Some modern alternative gravity theories have a bold solution to this issue: what if there is no horizon and no singularity? Could we have objects that behave like black holes but with no event horizon? This paper seeks these horizonless compact objects (HCOs) using the gravitational waves they emit upon collision.

Gravitational waves have already become an instrumental tool for studying some of the most extreme events taking place in our universe, such as black hole mergers. When two black holes merge, they go through 3 phases: an inspiral phase, where they spin around one another as they get closer and closer, a merger phase, and a ringdown phase, where the new black hole (created by the merge) wiggles around a bit as it settles down to be stable. The author of the paper, Dr. Maggio, argues that this ringdown phase is key to determining whether the new black hole has a horizon or not.

So how do we tell if our resulting object is a black hole or a HCO? Systems which oscillate (wiggle) tend to have what's known as normal modes. A normal mode is when all parts of the system oscillate at the same frequency and do not fall out of sync. They’re extra special because if you know them, you can use them to describe any oscillation the system does! The problem is that we know our black hole won't oscillate forever – it'll eventually settle down. Therefore, we need to find "quasi-normal modes," and we can do this by using the Schwarzschild metric. This is just a mathematical object that describes the curvature of spacetime around a non-spinning black hole. Dr. Maggio takes the Schwarzschild metric and tests what happens when you nudge spacetime just a bit. In doing so, she derives the frequencies of the quasi-normal modes and which ones are the most common. She can then repeat the process for a theoretical HCO.

The HCO differs from a black hole in two key ways. Firstly, its lack of an event horizon means that it's no longer immediately clear how big it should be, so Dr. Maggio defines a free parameter called the "compactness" of the object which is directly related to its size. Secondly, while a black hole absorbs everything that crosses its event horizon, a HCO could have some reflectivity, so she leaves that as a free parameter in the model. Repeating the calculations for the HCO, one finds that the quasi-normal modes are different to the ones found from a black hole! Generally, it's found that HCO quasi-normal modes will be of lower frequency and take longer to settle down.

We can now tell the difference between a black hole and HCO using these oscillations, and we can do this through gravitational waves. The author proceeds to explore the potential observations if the gravitational wave signal of a HCO in its ringdown phase were identified. To comprehend this distinct signal, it's necessary to explore the concept of a "photon ring" encircling a black hole. This ring, essentially just a spherical structure of light surrounding a black hole, denotes the radius at which photons can enter a stable circular orbit around the black hole. Beyond this, it is particularly difficult for light to escape the black hole's pull. In the wave signal of a black hole, gravitational waves that cannot overcome this hill are reabsorbed when they are reflected back and contact the event horizon of the black hole. However, as we discussed, a HCO has no horizon that would suck these waves back up, meaning that these gravitational waves can get trapped between the surface of the object and light ring. They may bounce around in this trapped state for a while before finally getting out at a later time, meaning that a HCO may produce a gravitational wave "echo" following the initial detection of waves.

Can we detect this echo? Well, so far, no detections of gravitational wave echoes have been made by any of the gravitational wave detectors currently online. However, planned next generation detectors like LISA or the Einstein Telescope will likely be powerful enough to either detect or rule out HCOs.

published: 04/02/24 by kaan evcimen