{"id":30356,"date":"2026-11-05T13:59:12","date_gmt":"2026-11-05T18:59:12","guid":{"rendered":"https:\/\/www.clarku.edu\/news\/?post_type=story&#038;p=30356"},"modified":"2026-11-05T17:43:18","modified_gmt":"2026-11-05T22:43:18","slug":"unlocking-the-cosmos-darkest-secrets","status":"publish","type":"story","link":"https:\/\/www.clarku.edu\/news\/2026\/11\/05\/unlocking-the-cosmos-darkest-secrets\/","title":{"rendered":"Unlocking the cosmos\u2019 darkest secrets"},"content":{"rendered":"\n\n\n<h2 class=\"wp-block-heading\" id=\"h-mathematician-s-research-into-black-holes-traces-back-to-einstein\">Mathematician\u2019s research into black holes traces back to Einstein<\/h2>\n\n\n\n<p>The Event Horizon Telescope research collaboration captured the first images of supermassive black holes within the last seven years. But scientists have been trying to unlock the mathematical mysteries behind black holes since Albert Einstein published his theory of relativity in 1915.<\/p>\n\n\n\n<p>Clark mathematician <a href=\"https:\/\/www.clarku.edu\/faculty\/profiles\/aghil-alaee-khangha\/\">Aghil Alaee Khangha<\/a> continues down a path laid by physicists from Robert Oppenheimer and Hartland Snyder in the 1930s to Stephen Hawking in the \u201970s, as well as 2020 Nobel laureates Roger Penrose, Reinhard Genzel, and Andrea Ghez. According to the <a href=\"https:\/\/www.genealogy.math.ndsu.nodak.edu\/index.php\">Mathematics Genealogy Project<\/a> \u2014 an online tool tracing the Ph.D. advising \u201croots\u201d of mathematicians back to the 14th century \u2014 Alaee, in fact, is directly \u201cconnected\u201d to Hawking.<\/p>\n\n\n\n<aside class=\"wp-block-group alignright boxout has-light-blue-background-color has-background is-content-justification-left is-layout-constrained wp-container-core-group-is-layout-6ad1ded9 wp-block-group-is-layout-constrained\" style=\"padding-top:var(--wp--preset--spacing--30);padding-bottom:var(--wp--preset--spacing--30)\">\n<h3 class=\"wp-block-heading\" id=\"h-explore-space\">Explore space<\/h3>\n\n\n\n<p><a href=\"https:\/\/www.clarku.edu\/programs\/major\/mathematics-bs\/\">Major in mathematics<\/a><\/p>\n\n\n\n<p><a href=\"https:\/\/www.clarku.edu\/programs\/major\/physics-bs\/\">Major in physics<\/a><\/p>\n<\/aside>\n\n\n\n<p>Applying differential geometry and geometric analysis (as seen in his calculations above), Alaee studies the relationship among a black hole\u2019s energy, spin, charge, and its boundary, called the \u201cevent horizon.\u201d A \u201cpoint of no return,\u201d this boundary has \u201ca gravitational pull so strong that nothing, not even light, can escape it,\u201d according to NASA.<\/p>\n\n\n\n<p>\u201cIf the density of matter is very large in a very small region of space, it creates a kind of well \u2014 you can call that a gravity well \u2014 and that\u2019s a black hole,\u201d explains Alaee, who served as a fellow for Harvard\u2019s Black Hole Initiative and Center of Mathematical Sciences and Applications before joining Clark\u2019s <a href=\"https:\/\/www.clarku.edu\/mathematics\/\">Mathematics Department<\/a>. A black hole\u2019s extreme curvature \u201cwill bend space and time so much that even if you\u2019re moving at the speed of light, if you are very close to that well, you will just go inside.\u201d<\/p>\n\n\n\n<p>Since childhood, Alaee has been fascinated by space and black holes. But it wasn\u2019t until college that he determined that mathematics \u2014 specifically, geometric analysis, which applies rigorous mathematical calculations to prove the conjectures of physicists \u2014 could best answer his questions.<\/p>\n\n\n\n<figure class=\"wp-block-image alignleft size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"720\" height=\"720\" src=\"https:\/\/www.clarku.edu\/news\/wp-content\/uploads\/sites\/37\/Aghil-Alaee-Khangha-720x720-1.avif\" alt=\"Aghil Alaee Khangha\" class=\"wp-image-30361\" style=\"width:300px\" srcset=\"https:\/\/www.clarku.edu\/news\/wp-content\/uploads\/sites\/37\/Aghil-Alaee-Khangha-720x720-1.avif 720w, https:\/\/www.clarku.edu\/news\/wp-content\/uploads\/sites\/37\/Aghil-Alaee-Khangha-720x720-1-300x300.avif 300w, https:\/\/www.clarku.edu\/news\/wp-content\/uploads\/sites\/37\/Aghil-Alaee-Khangha-720x720-1-150x150.avif 150w\" sizes=\"auto, (max-width: 720px) 100vw, 720px\" \/><figcaption class=\"wp-element-caption\">Aghil Alaee Khangha, associate professor of mathematics<\/figcaption><\/figure>\n\n\n\n<p>\u201cThe universe around us has a very particular language, and I believe that language is math,\u201d says Alaee, who has been funded by a National Science Foundation LEAPS-MPS grant. \u201cMathematicians say, \u2018If you impose these assumptions, then the claim is correct or the claim is false.\u2019 \u201d<\/p>\n\n\n\n<p>Alaee has studied and published six articles with Shing-Tung Yau, the Harvard professor emeritus and Black Hole Institute researcher credited with developing the field of modern differential geometry and geometric analysis.<\/p>\n\n\n\n<p>In 1979, Yau, with his student Richard Schoen, \u201csolved a longstanding question in Albert Einstein\u2019s theory of relativity by proving that the sum of the energy in the universe is positive; their proof has provided an important tool for understanding how black holes form,\u201d according to Harvard. For that, Yau received the Field Medal, the highest award in mathematics. In 2022, he left Harvard to establish the Yau Mathematical Sciences Center at Tsinghua University in China.<\/p>\n\n\n\n<p>Alaee and a new generation of mathematicians aim to investigate the existence, uniqueness, stability, geometric inequalities, and evolution of black holes, continuing Yau and Schoen\u2019s positive energy theorem.<\/p>\n\n\n\n<p>More recently, Alaee and his collaborators \u2014 Yau, along with Marcus Khuri of Stony Brook University in New York \u2014 have studied mathematical questions about quasi-local energy and mass.<\/p>\n\n\n\n<p>\u201cThese quantities are designed to measure how much energy and mass are contained in a finite region of curved space, rather than in the entire space,\u201d Alaee explains.<\/p>\n\n\n\n<p>The researchers introduced a new notion of quasi-local energy \u201cwith several important properties: It is nonnegative, it detects when the geometry is flat, and as the region becomes larger and eventually fills the whole space, it approaches the total energy of the system,\u201d he says. Unlike many earlier definitions, the new definition of energy can also be applied to more complicated boundary shapes and surfaces such as \u201ctori,\u201d which are doughnut-shaped, according to Alaee.<\/p>\n\n\n\n<p>Published in the article, <a href=\"https:\/\/link.springer.com\/article\/10.1007\/s00220-024-04976-x\">\u201cA Quasi-Local Mass,\u201d<\/a> in <em>Communications in Mathematical Physics<\/em>, their work also provided \u201ca genuinely quasi-local proof of positivity, addressing an open problem posed by Richard Schoen in 2018,\u201d he adds, \u201cand may provide an answer to Penrose\u2019s longstanding problem in 1982 of finding the right notion of quasi-local mass and energy.\u201d<\/p>\n\n\n\n<p>In his research, Alaee says, he is especially interested in applying the tools of geometric analysis \u201cto the problem of energy minimization \u2014 identifying the lowest-energy states in general relativity and extending these ideas to higher dimensions and theories such as string theory.\u201d<\/p>\n\n\n\n<p>Last summer, two undergraduate students \u2014 mathematics major Reevu Majumdar \u201927 and mathematics and computer science major Rahban Yoftahe \u201927 \u2014 got a taste of this research when they worked with Alaee to unpack these fundamental questions: How does spacetime bend around an object of enormous mass, and what can the geometry of that curvature tell researchers about the object\u2019s mass and other properties?<\/p>\n\n\n\n<p>They also took a directed study with Alaee on differential geometry, which Majumdar described as \u201cthe hardest thing ever\u201d and \u201ctruly, truly mind-bending.\u201d Once they began studying geometric analysis and tackling black-hole computations, they better understood the material.<\/p>\n\n\n\n<p>\u201cIt\u2019s very nice to see the math that we\u2019re doing has a tangible application,\u201d said Majumdar, who presented a poster with Yoftahe at <a href=\"https:\/\/www.clarku.edu\/news\/2026\/09\/03\/deciphering-black-holes-problematic-proteins-and-intelligent-bacteria-75-undergraduates-experience-clarks-summer-of-science\/\">Clark\u2019s \u201cSummer of Science\u201d event <\/a>in July. \u201cWe can see how it\u2019s working, and it makes sense.\u201d<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/www.clarku.edu\/news\/wp-content\/uploads\/sites\/37\/STEM_Send_Off_Celebration_Jul_2026-22-web-2-1024x683.avif\" alt=\"Students showing their posters at the STEM send-off celebration\" class=\"wp-image-29355\" srcset=\"https:\/\/www.clarku.edu\/news\/wp-content\/uploads\/sites\/37\/STEM_Send_Off_Celebration_Jul_2026-22-web-2-1024x683.avif 1024w, https:\/\/www.clarku.edu\/news\/wp-content\/uploads\/sites\/37\/STEM_Send_Off_Celebration_Jul_2026-22-web-2-300x200.avif 300w, https:\/\/www.clarku.edu\/news\/wp-content\/uploads\/sites\/37\/STEM_Send_Off_Celebration_Jul_2026-22-web-2-768x512.avif 768w, https:\/\/www.clarku.edu\/news\/wp-content\/uploads\/sites\/37\/STEM_Send_Off_Celebration_Jul_2026-22-web-2-1536x1024.avif 1536w, https:\/\/www.clarku.edu\/news\/wp-content\/uploads\/sites\/37\/STEM_Send_Off_Celebration_Jul_2026-22-web-2-2048x1365.avif 2048w, https:\/\/www.clarku.edu\/news\/wp-content\/uploads\/sites\/37\/STEM_Send_Off_Celebration_Jul_2026-22-web-2-1200x800.avif 1200w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">Reevu Majumdar \u201927 discusses his research at Clark\u2019s \u201cSummer of Science\u201d event. <\/figcaption><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Applying differential geometry and geometric analysis, Professor Aghil Alaee Khangha studies the relationship among a black hole\u2019s energy, spin, charge, and its boundary, called the \u201cevent horizon.\u201d 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