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{{Short description|Australian mathematician}}
{{Use dmy dates|date=July 2019}}
'''Robert Bartnik''' (1956 – 2022) was an Australian [[mathematician]] based at [[Monash University]]. He
{{blockquote|Professor Bartnik is renowned internationally for the application of geometric analysis to mathematical problems arising in Einstein's theory of general relativity. His work is characterised by his ability to uncover new and anticipated phenomena in space-time geometry, often employing sophisticated tools from linear and nonlinear partial differential equations as well as elaborate numerical computations. He has contributed greatly to our understanding of the properties of the Einstein equations and gravitation.}}
His work with John McKinnon has been widely studied in the physics literature. They show that there is a discrete set of static solutions to the coupled Einstein/Yang-Mills equations which are geodesically complete and asymptotically flat. This is interesting since such solutions are known not to exist in the cases of the Einstein vacuum equations, the coupled Einstein/Maxwell equations, and the Yang-Mills equations. Although Bartnik and McKinnon's work was numerical, their observed phenomena has been mathematically justified by [[Joel Smoller]], Arthur Wasserman, [[Shing-Tung Yau]], and Joel McLeod.<ref>Smoller, Joel A.; Wasserman, Arthur G.; Yau, S.-T.; McLeod, J.B. ''Smooth static solutions of the Einstein/Yang-Mills equations.'' Comm. Math. Phys. 143 (1991), no. 1, 115–147.</ref>
In the mathematics literature, he
He was a visiting scholar at the [[Institute for Advanced Study]] in 1980–81.<ref>[http://www.ias.edu/people/cos/frontpage?page=10 Institute for Advanced Study: A Community of Scholars] {{webarchive|url=https://web.archive.org/web/20100527171235/http://www.ias.edu/people/cos/frontpage?page=10 |date=2010-05-27 }}</ref>
==Major publications==
As of 2022, Bartnik
{{refbegin}}
*{{cite journal|first1=Robert|last1=Bartnik|first2=Leon|author-link2=Leon Simon|last2=Simon|title=Spacelike hypersurfaces with prescribed boundary values and mean curvature|journal=[[Communications in Mathematical Physics]]|volume=87|year=1982|zbl=0512.53055|issue=1|pages=131–152|doi=10.1007/bf01211061|bibcode=1982CMaPh..87..131B |url=https://projecteuclid.org/journals/communications-in-mathematical-physics/volume-87/issue-1/Spacelike-hypersurfaces-with-prescribed-boundary-values-and-mean-curvature/cmp/1103921909.full|mr=0680653|s2cid=55672824 }}
*{{cite journal|first1=Robert|last1=Bartnik|title=Existence of maximal surfaces in asymptotically flat spacetimes|journal=[[Communications in Mathematical Physics]]|volume=94|year=1984|issue=2|zbl=0548.53054|pages=155–175|doi=10.1007/BF01209300|bibcode=1984CMaPh..94..155B |url=https://projecteuclid.org/journals/communications-in-mathematical-physics/volume-94/issue-2/Existence-of-maximal-surfaces-in-asymptotically-flat-spacetimes/cmp/1103941280.full|mr=0761792|s2cid=120000484 }}
*{{cite journal|first1=Robert|last1=Bartnik|title=The mass of an asymptotically flat manifold|journal=[[Communications on Pure and Applied Mathematics]]|volume=39|year=1986|issue=5|pages=661–693|doi=10.1002/cpa.3160390505|citeseerx=10.1.1.625.6978|mr=0849427|zbl=0598.53045}}
*{{cite journal|first1=Robert|last1=Bartnik|first2=John|last2=McKinnon|title=Particlelike solutions of the Einstein–Yang–Mills equations|journal=[[Physical Review Letters]]|volume=61|year=1988|issue=2|pages=141–144|doi=10.1103/PhysRevLett.61.141|pmid=10039043 |bibcode=1988PhRvL..61..141B |mr=0948143}}
*{{cite encyclopedia|mr=2098912|last1=Bartnik|first1=Robert|last2=Isenberg|first2=Jim|title=The constraint equations|encyclopedia=The Einstein equations and the large scale behavior of gravitational fields: 50 years of the Cauchy problem in general relativity|editor-first1=Piotr T.|isbn=3-7643-7130-7|zbl=1073.83009|editor-last1=Chruściel|editor-first2=Helmut|editor-last2=Friedrich|pages=1–38|publisher=[[Birkhäuser]]|location=Basel|year=2004|author-link2=James Isenberg|doi=10.1007/978-3-0348-7953-8_1|arxiv=gr-qc/0405092|s2cid=118082763 }}
{{refend}}
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{{DEFAULTSORT:Bartnik, Robert}}
[[Category:1956 births]]▼
[[Category:Fellows of the Australian Academy of Science]]
[[Category:Institute for Advanced Study visiting scholars]]
[[Category:Mathematicians from Melbourne]]
▲[[Category:Living people]]
[[Category:University of Melbourne alumni]]
[[Category:Princeton University alumni]]
▲[[Category:1956 births]]
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