The original version of this story appeared in Quanta Magazine.

At the beginning of the universe, and at the heart of every black hole, lies a peculiar and mysterious point known as a singularity. This singularity is where the laws of physics as we know them break down, characterized by a density that approaches infinity. To delve into these enigmatic phenomena, physicists harness our understanding of space, time, gravity, and quantum mechanics, attempting to apply this knowledge to environments where conventional theories simply cannot hold. The nature of singularities presents one of the most profound challenges to human imagination and scientific inquiry, raising questions that could fundamentally reshape our understanding of reality.

In the late 1960s, a group of physicists began to ponder the possibility that singularities might be encased in a tumultuous region of chaotic activity. This conjecture was vividly articulated by Charles Misner from the University of Maryland, who coined the term Mixmaster universe, drawing an analogy to the popular kitchen appliance known for its ability to blend ingredients. The idea was that if an astronaut were to fall into a black hole, their body could be mixed and distorted in a manner akin to how a mixmaster whips together eggs. Kip Thorne, a Nobel Prize-winning physicist, elaborated on this notion, capturing the unsettling and chaotic potential of black holes.

Einstein's groundbreaking general theory of relativity serves as the mathematical framework for understanding the gravitational forces at play in black holes. It uses a single field equation to illustrate how space bends and how matter behaves under this curvature. However, this prominent equation conceals a more complex reality, encapsulating 16 distinct yet interconnected equations through a mathematical shorthand known as a tensor. To navigate this complexity, various scientists, including Misner, developed simplifying assumptions that allowed them to model scenarios akin to the Mixmaster universe.

Despite these theoretical advancements, the intricate nature of Einsteins equations meant that they could not be solved analytically without these assumptions. Even with the simplifications, the equations proved too convoluted for the computational simulations of the era. Consequently, these dynamics, which were once believed to be a common occurrence in gravitational physics, gradually faded from scholarly focus. According to Gerben Oling, a postdoctoral researcher at the University of Edinburgh, These dynamics are supposed to be a very general phenomenon in gravity, but its something that fell off the map.

In recent years, however, physicists have begun to revisit the chaotic phenomena surrounding singularities, armed with new mathematical tools and methodologies. Their research endeavors are driven by two primary objectives: first, to validate the approximations made by Misner and his contemporaries as reflections of Einsteinian gravity, and second, to inch closer to the singularity itself. This pursuit is essential, as it may finally bridge the longstanding divide between general relativity and quantum mechanics, an objective that has eluded physicists for over a century. As Sean Hartnoll from the University of Cambridge aptly stated, The time is ripe now for these ideas to be fully developed.

The Birth of Mixmaster Chaos

Kip Thorne characterized the late 1960s as a golden age for black hole research. It was during this period that the term black hole gained widespread acceptance within the scientific community. In September of 1969, while visiting Moscow, Thorne was handed a manuscript by Evgeny Lifshitz, a distinguished Ukrainian physicist. Lifshitz, alongside colleagues Vladimir Belinski and Isaak Khalatnikov, had discovered a novel solution to Einsteins equations of gravity in the vicinity of a singularity, employing a set of assumptions they crafted. Concerned that Soviet censors might delay the publication of their groundbreaking work, as it conflicted with an earlier proof he had co-authored, Lifshitz entrusted Thorne with the responsibility of sharing their findings in the West.

Prior models of black holes often relied on idealized symmetries that do not reflect the complexity of the natural world. These models suggested that a star might be a perfect sphere before undergoing gravitational collapse, or that it possessed no net electrical charge. Such simplifications were necessary for Karl Schwarzschild to derive a solution to Einstein's equations shortly after their publication. However, the BKL solution, named after Belinski, Khalatnikov, and Lifshitz, offered a more realistic portrayal of black hole formation, demonstrating that rather than a smooth, continuous stretching of space and time, black holes could be the result of a chaotic interplay of forces, resulting in the twisting and turning of spacetime in multiple directions.

Thorne clandestinely returned the manuscript to the United States, forwarding a copy to Misner, aware that Misner was exploring similar concepts. Remarkably, both Misner and the Soviet physicists had independently arrived at similar conclusions using related assumptions but different methodologies. The BKL team's findings played a pivotal role in addressing what Thorne described as the biggest unsolved problem of that era in mathematical relativity, namely the existence of what is termed a generic singularity. Recently, Belinski, the last surviving member of the BKL trio, expressed in an email how Misners vivid depictions significantly aided him in visualizing the chaotic scenarios surrounding singularities they both uncovered.