# Study solves mysteries in gravitational collapse of gravitational waves

× Close

The strength of a gravitational wave as a function of distance from the origin (horizontal axis) and a specific scale of time (vertical axis). The two panels represent results from two different codes, and the team found that they agreed well. The data is displayed in such a way that precise self-similarity produces perfectly repeatable patterns in this image. While the researchers clearly observed recurring patterns, it is also clear that they repeat only roughly, not frequently. Credit: Baumgart et al., *Physical review letters* (2023). doi: 10.1103/PhysRevLett.131.181401

Black holes are regions in space where gravity is so strong that nothing, not even light, can escape. These fascinating regions have been the focus of countless studies, but some of the physics behind their formation is not yet fully understood.

Black holes form in what is known as gravitational collapse. This is essentially the contraction of a cosmic body, driven by its own gravity that pulls matter inward (i.e. towards the body’s center of gravity).

Whether or not this collapsed object forms a black hole depends on the specific properties of this object. In some cases, the object may be so close to the threshold that it has difficulty determining whether it will form a black hole or not. This type of collapse results in so-called critical phenomena.

Physicists have tried to understand the critical phenomena in gravitational collapse for decades, as some of its properties are shared with other known physical systems. A recent paper published in *Physical review letters* Through an international research collaboration based at Bowdoin College in the US and other institutes in Germany, Prague, the UK and Portugal, they reached agreement between three independently conducted numerical simulations of these phenomena and solved some long-standing puzzles in this field of study.

“Critical phenomena in gravitational collapse, near the beginning of black hole formation, were first reported by Matt Choptwick about 30 years ago,” Thomas W. Baumgart, co-author of the paper, told Phys.org.

“Partly because these effects share many properties with critical phenomena in other fields of physics (e.g., phase transitions in statistical physics) and partly because they address fundamental questions regarding the properties of general relativity, they immediately attracted the attention of many researchers from different fields of “Physics.”

Two of the most fascinating properties of critical gravitational collapse are universality and self-similarity. In this context, universality refers to the idea that no matter how the calculation begins, as the black hole begins to form, the solution will always be the same. On the other hand, self-similarity means that this global solution will repeat the same patterns as the physical scale decreases.

“While Choptwick’s calculations included the so-called scalar field as the source of matter, Andrew Abrahams and Chuck Evans shortly thereafter reported similar effects of the collapse of gravitational waves (i.e. pure gravity in the absence of any matter),” Baumgart explained. .

“Another difference is that Choptwick was able to assume spherical symmetry, whereas gravitational waves cannot exist in spherical symmetry, so Abrahams and Evans had to relax the spherical symmetry assumption. Unfortunately, these latter results have been very difficult to reproduce.” , because some digital codes failed completely in this case, or provided results that seemed contradictory to those of Abrahams and Evans.

Following the apparently contradictory results obtained in the 1990s, the nature of the dangerous collapse of “pure gravity” remained an unsolved mystery for almost three decades. However, recently, three different research groups have performed independent numerical simulations of this collapse, using independently developed codes.

“All three of these codes solve Einstein’s equations in general relativity, but they use completely different numerical strategies (e.g., spectral versus finite difference methods),” Baumgart said. “Cartesian coordinates versus spherical polar coordinates, different measurement conditions, etc. All three codes also make different choices of the so-called ‘slicing condition’ (i.e. they make different choices of the rate of time progression in the codes).”

The main goal of the latest study by Baumgart and colleagues was to collectively examine the three numerical simulations recently conducted by the three different research teams. Their paper was thus a joint effort between the two teams, aiming to link their independent research efforts to shed new light on the nature of gravitational collapse.

“As a first discovery, we report that despite all the numerical differences, our codes produce completely consistent results for the critical collapse of gravitational waves,” Baumgart said. “This gives us confidence that these results are correct, and not numerical artifacts. It turns out that the appropriate choice of the discretization condition is crucial: another very popular option is one that has succeeded in many other numerical relativistic simulations, but fails. This is the case, which explains the failure of some previous attempts to solve this problem.”

It is worth noting that in the three independent numerical simulations, the researchers found no evidence to support the universality property. In other words, they found that starting numerically with different initial data led to different values during the approach to black hole formation.

“Our findings explain another piece of the puzzle,” Baumgart said. “Some previous studies have reported differences from the results of Abrahams and Evans, which therefore appeared to be conflicting. However, those studies also used different raw data. Disagreement between the results therefore only constitutes a contradiction under the assumption of universality – which we do. I see no evidence.” ”

While the researchers found no evidence of universality, they did find rough evidence of self-similarity. However, interestingly, in contrast to what was observed for the critical breakdown in spherical symmetry, the self-similarity they observed did not appear to be precise.

Going back to the 1990s, Abrahams and Evans also reported imprecise self-similarity. Thus, these latter results are in line with previous findings, which may indicate that instances of departures from precise self-similarity can be linked to the absence of spherical symmetry.

The latest work by Baumgart and colleagues could soon pave the way for new numerical and theoretical studies aimed at further studying and reworking the critical collapse of gravitational waves. This could bring physicists closer to revealing the nature and secrets of this interesting physical phenomenon, which is known to precede the formation of black holes.

“While we believe our work has resolved many open questions in the context of critical gravitational wave collapse, many follow-up questions remain,” Baumgart added. “For example, we found nearly similar solutions for some initial data families, but not for others, and the nature of the ‘threshold solution’ for those other families remains unclear.

“It would also be desirable to perform simulations with better tuning of the onset of black hole formation (e.g., using better-resolution numerical codes and/or other improvements) to explore whether a global decisive solution will emerge to tune this.” Better than anyone has achieved so far.

“Finally, we plan to investigate the causes of deviation from exact self-similarity and determine whether these deviations are directly related to the lack of spherical symmetry.”

**more information:**

Thomas W. Baumgarty et al., Critical Phenomena in Gravitational Wave Collapse, *Physical review letters* (2023). doi: 10.1103/PhysRevLett.131.181401