{"id":408603,"date":"2026-04-20T17:43:07","date_gmt":"2026-04-20T17:43:07","guid":{"rendered":"https:\/\/www.newsbeep.com\/ie\/408603\/"},"modified":"2026-04-20T17:43:07","modified_gmt":"2026-04-20T17:43:07","slug":"jonathan-luk-tackles-the-mathematics-of-black-holes","status":"publish","type":"post","link":"https:\/\/www.newsbeep.com\/ie\/408603\/","title":{"rendered":"Jonathan Luk tackles the mathematics of black holes"},"content":{"rendered":"

Albert Einstein\u2019s theory of general relativity has a math problem, several problems actually. They have to do with black holes and are extremely complex and difficult to solve\u2014just the kind of problems that have always fascinated\u00a0Jonathan Luk<\/a>.<\/p>\n

This fascination led the Stanford mathematician to a long collaboration with Princeton\u2019s Mihalis Dafermos that disproved the \u201cstrong cosmic censorship conjecture,\u201d the hypothesis that sought to save general relativity from the loss of determinism. What Luk and Dafermos showed is that determinism, or the idea that the future is always predicated by past data, does not always hold true within certain types of black holes.<\/p>\n

Their achievement was recently recognized with a\u00a02026 B\u00f4cher Memorial Prize<\/a>, the American Mathematical Society\u2019s top prize for mathematical analysis. Their work also pokes a hole in determinism, leaving open the possibility of unpredictable futures\u2014at least deep within some black holes. This has troubling implications, but for Luk, it just means there is more work to be done.<\/p>\n

\u201cI think the important thing is to first understand what happens inside black holes; then we can try to understand what it means,\u201d said Luk, professor of mathematics in Stanford\u2019s\u00a0School of Humanities and Sciences<\/a>.\u00a0<\/p>\n

The search for solutions<\/p>\n

When Einstein wrote the theory of general relativity in 1915, he included a set of equations describing how the gravity of large objects curves space-time\u2014and physicists and mathematicians have been trying to find solutions to those equations ever since.<\/p>\n

The equations suggested the existence of black holes, areas where gravity becomes so strong not even light can escape. Evidence of black holes was gathered in the ensuing 100 years, but it wasn\u2019t until 2019 that astrophysicists captured the image of one.\u00a0<\/p>\n

Using the Event Horizon Telescope, scientists obtained the first picture of a black hole in 2019.\u00a0Photo by Event Horizon Telescope Collaboration\u00a0<\/p>\n

Yet the search for solutions to Einstein\u2019s equations also found some problems: namely that inside some rotating black holes, there is a location, called the Cauchy horizon, after which determinism breaks down. In other words, beyond that horizon the past doesn\u2019t predict the future \u2014an idea that challenges our understanding of the universe.\u00a0<\/p>\n

To save determinism, the physicist Roger Penrose proposed the strong cosmic censorship conjecture in 1979. He argued that the Cauchy horizon was unstable and any gravitational wave that made it past would just cause a crushing singularity, a point at which matter is condensed into an infinite density. This singularity would end space-time and protect the theory from producing unpredictable futures.<\/p>\n

Through their work, Luk and Dafermos found that there is no crushing singularity, as Penrose proposed, even when space-time is \u201cperturbed\u201d or distorted by gravitational waves. That means that space-time could still be unpredictable beyond the Cauchy horizon within a black hole. The mathematicians essentially found a new aspect of Einstein\u2019s equations.<\/p>\n

\u201cLuk and Dafermos really achieved something that was very unexpected,\u201d said\u00a0Rafe Mazzeo<\/a>, the Cassius Lamb Kirk Professor of the Natural Sciences and professor of mathematics in H&S. \u201cIn terms of the mathematical understanding of relativity, it\u2019s really a huge advance.\u201d<\/p>\n

The intersection of physics and mathematics<\/p>\n

This discovery, like a lot of things in mathematics or science, took many years. Luk describes solving complex problems like this as a process that has many obstacles.<\/p>\n

\u201cIn mathematics, I think you are always stuck,\u201d he said.<\/p>\n

That frustration doesn\u2019t deter Luk. In fact, the more difficult a problem is, the more fascinating he finds it. This has been true ever since he faced his first challenging, nonstandard math problem as a fourth grader.<\/p>\n","protected":false},"excerpt":{"rendered":"Albert Einstein\u2019s theory of general relativity has a math problem, several problems actually. They have to do with…\n","protected":false},"author":2,"featured_media":408604,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[61,60,82],"class_list":{"0":"post-408603","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-science","8":"tag-ie","9":"tag-ireland","10":"tag-science"},"_links":{"self":[{"href":"https:\/\/www.newsbeep.com\/ie\/wp-json\/wp\/v2\/posts\/408603","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.newsbeep.com\/ie\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.newsbeep.com\/ie\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/ie\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/ie\/wp-json\/wp\/v2\/comments?post=408603"}],"version-history":[{"count":0,"href":"https:\/\/www.newsbeep.com\/ie\/wp-json\/wp\/v2\/posts\/408603\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/ie\/wp-json\/wp\/v2\/media\/408604"}],"wp:attachment":[{"href":"https:\/\/www.newsbeep.com\/ie\/wp-json\/wp\/v2\/media?parent=408603"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.newsbeep.com\/ie\/wp-json\/wp\/v2\/categories?post=408603"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.newsbeep.com\/ie\/wp-json\/wp\/v2\/tags?post=408603"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}