The discovery of gravitational waves in 2015 by LIGO and Virgo collaborations is one of the most recent experimental breakthroughs that concerns the fundamentals of our Universe.
Next year, we should be celebrating 10 years of this discovery, and without a doubt, gravitational wave physics will remain one of the best tools for learning about the Universe and fundamental physics in the coming years. The gravitational wave experiments require a lot of theoretical support, which has already led to many important advances and more to come. A curious fact is that black holes behave a lot like elementary particles, and one can use the tools developed initially for elementary particles to describe dynamics of black holes, and we explain why and how in this article.
Why can’t we just measure some signals and be happy? What are the main challenges for theoretical physics?
The basic problem looks simple to formulate at first sight. The dynamics of black holes should be completely described by Einstein’s equations. One needs to solve them with two black holes far away from each other as an input. The solution should describe the whole evolution of this binary system that emits gravitational waves all the time. It starts from the so-called inspiral phase, where the two black holes orbit each other and are well separated. Eventually, the system approaches the merger stage, where two horizons merge together. After this, there is a period of settling down to a single undisturbed black hole, known as a ringdown. Of course, there is no sharp separation between the stages.
No single theoretical tool exists that can handle this problem! Indeed, the present analytical tools prefer the first stage, where the black holes are relatively far apart, and the amount of gravitational radiation is small compared to their masses. Yet, there is no exact solution to this problem either! The merger stage has to be treated using numerical tools, and different stages of the ringdown can be tackled using analytical/numerical tools.
Why can’t everything be done via numerical tools?
The answer is that it is just too much data to handle. Einstein’s equations are complicated nonlinear equations and, if we wish to discretise space and time, we need too much memory and computer time to get a reasonable precision.
On the other hand, black holes are the most simple and ideal objects in the Universe. This property is formulated as the ‘no-hair’ theorem, which states that the only characteristics that a black hole can have are its mass, angular momentum and electric charge. Given that the electromagnetic forces are very strong compared to the gravitational ones, it is difficult to have macroscopical objects with non-negligible electric charge, and we can neglect it. Therefore, in practice, a black hole has a mass, and it spins with some angular velocity.
The no-hair theorem makes black holes very reminiscent of elementary particles. In fact, they do not have to be elementary. If a composite of several elementary particles is stable enough, it can be thought of as an elementary particle as well. One can think of neutrons and protons that consist of three quarks. The analogy can be extended further: nuclei, which are composites of neutrons and protons, can also be considered elementary in some approximation. In fact, everything that can be considered small in some approximation will lack features other than mass, charge and angular momentum. For example, the Earth from far away looks very round and rotates, but as we get closer, we can see it is not a perfect sphere, has mountains, etc.
To summarise, black holes share some properties with elementary particles and can be modelled as such once we are not close to the merger stage.
What does it mean in practice?
It implies that every object that can be considered compact can be modelled by replacing it with an elementary particle with the corresponding mass and spin. While the mass is the usual mass, the spin is more subtle. For quantum particles, the spin is quantised, but the associated amount of the angular momentum is expressed in terms of the Planck constant, which is quite small. Therefore, the angular momentum of something macroscopic, like a spinning top or a black hole, is a huge number in terms of spin. This way, we are led to a problem of how to describe the dynamics of (thought of as) elementary massive particles of arbitrary spin.
When black holes are viewed/modelled as particles, a more natural question to ask is how they scatter instead of how they orbit each other. The two problems: the scattering of two objects due to gravitational interactions and the evolution of the binary system, are closely related to each other. The former one was dubbed the black hole scattering problem.
As a side remark, the spectrum of physical states of string theory is populated by massive states with arbitrarily large spin. Such (usually called higher-spin) states make string theory a promising candidate for the solution of the quantum gravity problem since their presence is crucial for removing the ultraviolet divergences of Einstein gravity. The string theory itself was born while investigating the properties of (higher-spin) hadrons (unstable composite particles that can have any value of spin, in principle).
Surprisingly, the problem of constructing interactions of massive and massless higher-spin particles is one of the oldest, dating back to Dirac, Fierz and Pauli. At present, there are very few known solutions. The key mechanism behind the standard model of elementary particles is the Brout-Englert-Higgs mechanism that gives masses to spin-one particles (W and Z bosons). A peculiar family of theories known as massive gravity and bi-gravity gives masses to a spin-two particle. Beyond that, not so much is known. It is generally believed that a fully quantum-consistent theory with massive higher-spin fields needs infinitely many of them, as seen in string theory. However, if we do not want to quantise ‘all of it’, like in the black hole scattering problem, more consistent solutions should be possible. For example, bi-gravity is not a fully quantum-consistent theory since it contains gravity, the quantisation of which is the notorious quantum gravity problem.
Now that the problem of dynamics of black holes and other compact objects is reformulated as a problem to find a consistent theory of massive higher-spin particles interacting with gravity:
What makes a black hole be a black hole or what makes the higher-spin particle behave like a black hole?
It turns out that many different types of interactions exist between higher-spin particles and gravity; to be more precise, these are the first terms of yet unknown complete interactions. Remarkably, but perhaps not too surprisingly, black holes pick the simplest interaction, which bears the name ‘minimal’.
The relation between higher-spin particles, gravitational waves and black holes has given a new impulse to solve old problems (Guevara et al., 2019). Also, new techniques have been developed by the amplitude and higher-spin communities that were not previously available. In recent works (Cangemi et al., 2024a, 2024b, 2023; Ochirov and Skvortsov, 2022), two complementary approaches were tried: one based on a massive higher-spin gauge symmetry and another based on a novel formulation of massive fields called the chiral approach.
Gauge symmetry is a powerful principle. It says there is some redundancy in how we describe physics; for example, we usually choose a four-component gauge potential to describe photons with only two degrees of freedom, the other two to be eaten by the gauge symmetry. For it to work, the interactions must be constrained by the gauge symmetry. The gauge symmetry for massive higher-spin fields was initially developed by Zinoviev and Cangemi et al. (2024b, 2023) and shows that it can be used to constrain interactions, particularly to land on the one that describes black holes.
As an alternative, an approach that does not have the problem of redundancy of description has been proposed by Ochirov and Skvortsov (2022). Within this chiral approach, it is very easy to construct interactions. However, one needs to make sure they describe a parity invariant theory, which replaces the principle of minimality. The culmination of these ideas is the so-called Compton amplitude found in Cangemi et al. (2024a), which is the best we can say about the relation between black holes and higher-spin particles.
What about other objects in our Universe that can orbit each other while emitting gravitational waves?
For example, neutron stars are perhaps second to only black holes since they are very compact and dense leftovers of stars’ evolution. Neutron stars can also rotate very fast, which makes them interesting detectors of spin effects.
In the first approximation, they are characterised by the same data: mass and angular momentum (spin), but their imperfectness will lead to other effects, which must be smaller than the ‘black hole/elementary particle’ approximation.
From the higher-spin particle perspective, such corrections are provided by ‘more complicated’ (called non-minimal) interactions and can also be efficiently dealt with. However, the difference with the pure black hole is that some additional information is needed to fix the ambiguity since it depends on what type of compact object we are dealing with. In the first approximation, black holes and bricks scatter in the same way, but if more precision is needed, there is a difference, of course. The coefficients will be different for neutron stars and bricks and should not have any simple form. On the contrary, the theory that describes black hole scattering does not seem to require any input and can be found by following the principles of beauty and simplicity.
Summary
To summarise, in many situations, the motion of various physical systems, from elementary particles to black holes and stars, can be reproduced and modelled by the efficient techniques initially developed for particle physics—everything sufficiently far away looks like a massive particle with some (usually very large) spin. Black holes play a role of the most elementary objects from this particle point of view since their dynamics are reproduced by the simplest, minimal interactions. This particle physics philosophy is quite efficient and, combined with the ‘elementarity’ of black holes, should allow one to solve Einstein equations for the dynamics of black holes orbiting each other and emitting gravitational waves without actually solving them. It would also be very interesting to have a look at the ‘theory of black holes’ and uncover its underlying symmetry principles.
References
Cangemi, L., Chiodaroli, M., Johansson, H., Ochirov, A., Pichini, P. and Skvortsov, E. (2023) ‘Kerr Black Holes From Massive Higher-Spin Gauge Symmetry’, Physical Review Letters, 131(22), p. 221401. doi: 10.1103/PhysRevLett.131.221401.
Cangemi, L., Chiodaroli, M., Johansson, H., Ochirov, A., Pichini, P. and Skvortsov, E. (2024a) ‘Compton Amplitude for Rotating Black Hole from QFT’, Physical Review Letters, 133(7), p. 071601. doi: 10.1103/ PhysRevLett.133.071601.
Cangemi, L., Chiodaroli, M., Johansson, H., Ochirov, A., Pichini, P. and Skvortsov, E. (2024b) ‘From higher-spin gauge interactions to Compton amplitudes for root-Kerr’, Journal of High Energy Physics, 09, p. 196. doi: 10.1007/JHEP09(2024)196.
Guevara, A., Ochirov, A. and Vines, J. (2019) ‘Scattering of Spinning Black Holes from Exponentiated Soft Factors’, Journal of High Energy Physics, p. 56. doi: 10.1007/JHEP09(2019)056.
Ochirov, A. and Skvortsov, E. (2022) ‘Chiral Approach to Massive Higher Spins’, Physical Review Letters, 129(24), p. 241601. doi: 10.1103/PhysRevLett.129.241601.
PROJECT NAME
Higher Spin Symmetry in Quantum Gravity, Condensed Matter and Mathematics (HiSS)
PROJECT SUMMARY
The main goal of the HiSS project is to approach quantum gravity from a completely new direction—by providing the first working example of higher-spin gravity (HiSGRA). HiSS will construct new consistent models of quantum gravity along the higher-spin gravity lines, and explore and prove dualities in the condensed matter systems, which can be explained by higher-spin symmetry and deduced from HiSGRA.
PROJECT LEAD PROFILE
Dr Skvortsov is a research associate at Université de Mons, focussing on higher-spin gravities and applications thereof to the quantum gravity problem. Skvortsov graduated from Moscow Institute of Physics and Technology in 2005, obtained a PhD from Lebedev Institute of Physics in 2010 with a thesis on gauge fields in Minkowski and (anti)-de Sitter spaces within the unfolded formulation, and went on to spend time at Albert Einstein Insitute (Max Planck Institute for Gravitational Physics), Potsdam and Ludwig Maximilian University of Munich.
PROJECT CONTACT
Dr Evgeny Skvortsov
Tel: +32 (0)65 373899
Email: evgeny.skvortsov@umons.ac.be
FUNDING
This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 101002551.
Figure legends
Figure 1: Black holes, macroscopical objects, (elementary) particles, stars/planets, etc., in the first approximation, have the same basic characteristics: mass and angular momentum. For black holes, there are no other features (neglecting the charge).
Figure 2: Two spinning tops representing two higher-spin particles interacting with the gravitational field, which models the dynamics of black holes.
