The original version of this story appeared in Quanta Magazine. At both the beginning of time and the core of every black hole, a singularity—a point of infinite density—exists. In the quest to understand these mysteries, scientists apply known principles of space, time, gravity, and quantum mechanics to contexts where such concepts typically collapse. Few phenomena in the universe challenge human imagination more intensely. Many physicists trust that achieving a coherent explanation of events occurring in and around singularities could potentially lead to groundbreaking insights, perhaps even a new understanding of the fundamental composition of space and time.
In the late 1960s, some physicists hypothesized that singularities might be encircled by chaotic regions where space and time unpredictably expand and contract. Charles Misner from the University of Maryland termed this a “Mixmaster universe,” named after a then-popular line of kitchen appliances. Nobel Laureate physicist Kip Thorne later illustrated it by imagining an astronaut falling into a black hole, suggesting the chaos would mix the astronaut’s body parts as a mixer blends eggs.
Albert Einstein’s general theory of relativity, which elucidates black hole gravity, employs a single field equation to explain the curvature of space and momentum of matter. This equation, however, utilizes a mathematical shorthand known as a tensor to encapsulate 16 intricate, interwoven equations. Scientists like Misner developed helpful simplifying assumptions to investigate scenarios such as the Mixmaster universe.
Absent those assumptions, Einstein’s equation cannot be solved analytically, and even with them, it remained too complex for the numerical simulations available at the time. Similar to the appliance namesake, these ideas eventually fell out of vogue. Gerben Oling, a postdoctoral researcher at the University of Edinburgh, commented that these dynamics represent a pervasive phenomenon in gravitational theory but had become neglected over time.
Recently, physicists have revisited the chaos around singularities employing advanced mathematical tools. Their objectives are twofold: to validate the approximations made by Misner and others as accurate representations of Einsteinian gravity, and to approach singularities more closely, hoping their extreme conditions might aid in reconciling general relativity with quantum mechanics into a quantum gravity theory, a long-standing goal for physicists. Sean Hartnoll from the University of Cambridge remarked, “The time is ripe now for these ideas to be fully developed.”
Kip Thorne described the late 1960s as a “golden age” for black hole research, noting that the term “black hole” had just gained widespread adoption. During a visit to Moscow in September 1969, Thorne received a manuscript from Evgeny Lifshitz, a prominent Ukrainian physicist. Lifshitz, along with Vladimir Belinski and Isaak Khalatnikov, had devised a new solution to Einstein’s gravitational equations near a singularity, using their own assumptions. Fearing Soviet censorship, which could delay the publication of this result as it contradicted an earlier proof he had coauthored, Lifshitz requested Thorne to disseminate it in the West.
Previous black hole models presumed perfect symmetries that do not naturally occur, such as assuming a star was a perfect sphere before forming a black hole, or was devoid of electrical charge. These assumptions facilitated solving Einstein’s equations in simpler forms, as demonstrated by Karl Schwarzschild shortly after Einstein’s publication. The solution by Belinski, Khalatnikov, and Lifshitz, later dubbed the BKL solution, described a more realistic scenario where black holes emerge from irregularly shaped structures, leading to a tumultuous environment of space and time stretching and compressing in various directions.
Thorne discreetly brought the manuscript to the United States and forwarded a copy to Misner, aware that he too was exploring similar concepts. Both Misner and the Soviet team independently arrived at comparable ideas through distinct methodologies and assumptions. The BKL group’s work, moreover, addressed a major unresolved issue of that time in mathematical relativity concerning “generic” singularities. Belinski, the last remaining member of the BKL group, noted via email that Misner’s vivid accounts aided his understanding of the chaotic conditions near singularities revealed by their collective work.
