Robert Geroch

{{Short description|American mathematical physicist}}

{{External links|date=April 2025}}

{{Infobox scientist

| name = Robert Geroch

| image =

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| birth_date = {{Birth date and age|1942|06|01|df=y}}

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| nationality = American

| fields = Physics
Mathematics

| workplaces = University of Chicago

| alma_mater =

| doctoral_advisor = John Archibald Wheeler

| doctoral_students = Abhay Ashtekar
Gary Horowitz
Basilis C. Xanthopoulos

| known_for = Geroch energy
Geroch's splitting theorem
Geroch group

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}}

Robert Geroch (born 1 June 1942 in Akron, Ohio)American Men and Women of Science, Thomson Gale, 2004 is an American theoretical physicist and professor at the University of Chicago. He has worked prominently on general relativity and mathematical physics and has promoted the use of category theory in mathematics and physics. He was the Ph.D. supervisor for Abhay Ashtekar, Basilis Xanthopoulos and Gary Horowitz. He also proved an important theorem in spin geometry.{{Citation

|author-first=Robert

|author-last=Geroch

|author-link =

|title =Spinor Structure of Space-Times in General Relativity. I

|trans-title=

|journal =Journal of Mathematical Physics

|volume =9

|issue=11

|pages =1739–1743

|year =1968

|language =

|url =

|doi =10.1063/1.1664507

|jfm =

|bibcode=1968JMP.....9.1739G

}}

{{Citation

|author-first=Phillip E.

|author-last=Parker

|author-link =

|title =On some theorems of Geroch and Stiefel

|trans-title=

|journal =Journal of Mathematical Physics

|volume =25

|issue=3

|pages =597–599

|year =1984

|language =

|doi =10.1063/1.1665067

|jfm =

}}

Education

Geroch obtained his Ph.D. degree from Princeton University in 1967 under the supervision of John Archibald Wheeler, with a thesis on Singularities in the spacetime of general relativity: their definition, existence, and local characterization.{{MathGenealogy |id=92456}}

Writings

= Chapters =

  • {{cite book | last=Geroch | first=Robert |editor-last1=Esposito|editor-first1=F. P.|editor-last2=Witten|editor-first2=L.| title=Asymptotic Structure of Space-Time | chapter=Asymptotic Structure of Space-Time | publisher=Springer US | publication-place=Boston, MA | date=1977 | isbn=978-1-4684-2345-7 | doi=10.1007/978-1-4684-2343-3_1}}
  • Horowitz, G.T and Geroch, R.P. (1979) "Global structure of spacetimes", p. 212–293. In Hawking S.W. and Israel, W (eds): General Relativity: An Einstein Centenary Survey. Cambridge University Press 1979 ({{ISBN|9780521299282}})

= Articles =

  • {{cite journal | last=Geroch | first=R. P. | title=Singularities in Closed Universes | journal=Physical Review Letters | volume=17 | issue=8 | date=1966-08-22 | issn=0031-9007 | doi=10.1103/PhysRevLett.17.445 | pages=445–447}}
  • {{cite journal | last=Geroch | first=Robert P. | title=Topology in General Relativity | journal=Journal of Mathematical Physics | volume=8 | issue=4 | date=1967-04-01 | issn=0022-2488 | doi=10.1063/1.1705276 | pages=782–786}}
  • {{Citation

|author-first=Robert

|author-last=Geroch

|author-link =

|title =Spinor Structure of Space-Times in General Relativity. I

|trans-title=

|journal =Journal of Mathematical Physics

|volume =9

|issue=11

|pages =1739–1743

|year =1968

|language =

|url =

|doi =10.1063/1.1664507

|jfm =

|bibcode=1968JMP.....9.1739G

}}

  • {{cite journal | last=Geroch | first=Robert | title=Multipole Moments. I. Flat Space | journal=Journal of Mathematical Physics | volume=11 | issue=6 | date=1970-06-01 | issn=0022-2488 | doi=10.1063/1.1665348 | pages=1955–1961}}
  • {{cite journal | last=Geroch | first=Robert | title=Domain of Dependence | journal=Journal of Mathematical Physics | volume=11 | issue=2 | date=1970-02-01 | issn=0022-2488 | doi=10.1063/1.1665157 | pages=437–449}}
  • Geroch, R.P. (1971) "Space-time structure from a global viewpoint," Rend. Scu. Int. Fis. Enrico Fermi 47: 71-103(1971); in B.K.Sachs, ed., General Relativity and Cosmology (New York, Academic Press, 1971).
  • {{cite journal | last=Geroch | first=Robert | title=A Method for Generating Solutions of Einstein's Equations | journal=Journal of Mathematical Physics | volume=12 | issue=6 | date=1971-06-01 | issn=0022-2488 | doi=10.1063/1.1665681 | pages=918–924}}
  • {{cite journal | last=Geroch | first=Robert | title=A Method for Generating New Solutions of Einstein's Equation. II | journal=Journal of Mathematical Physics | volume=13 | issue=3 | date=1972-03-01 | issn=0022-2488 | doi=10.1063/1.1665990 | pages=394–404}}
  • {{cite journal | last=Geroch | first=Robert | title=Einstein algebras | journal=Communications in Mathematical Physics | volume=26 | issue=4 | date=1972 | issn=0010-3616 | doi=10.1007/BF01645521 | pages=271–275}}
  • {{cite journal |last1=Geroch|first1=R. P.|last2=Kronheimer|first2=E. H.|last3=Penrose|first3=R.| title=Ideal points in space-time | journal=Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences | volume=327 | issue=1571 | date=1972-04-25 | issn=0080-4630 | doi=10.1098/rspa.1972.0062 | pages=545–567}}
  • {{cite journal | last=Ashtekar | first=A | last2=Geroch | first2=R | title=Quantum theory of gravitation | journal=Reports on Progress in Physics | volume=37 | issue=10 | date=1974-10-01 | issn=0034-4885 | doi=10.1088/0034-4885/37/10/001 | pages=1211–1256}}

= Books =

  • {{cite book | author = R. Geroch | title = General Relativity from A to B | publisher = University of Chicago Press | year = 1981 | isbn = 0-226-28863-3 | url-access = registration | url = https://archive.org/details/generalrelativit00gero }}
  • {{cite book | author = R. Geroch | title = Mathematical Physics (Lectures in Physics)| publisher = University of Chicago Press | year=1985 | isbn=0-226-28862-5}}
  • {{cite book | author = R. Geroch | title = Perspectives in computation| publisher = University of Chicago Press | year=2009 | isbn=978-0-226-28855-0}}
  • {{cite book | author = R. Geroch | title = Geometrical Quantum Mechanics: 1974 Lecture Notes (Lecture Notes Series) (Volume 3)

| publisher = Minkowski Institute Press; 1 edition | year = 2013| isbn = 978-1927763049}}

Unpublished notes

  • [http://home.uchicago.edu/~geroch Course Notes, Problem Sets, and Short Topics], for Lecture courses at the University of Chicago, primarily in the 1970s.
  • Suggestions For Giving Talks, Notes on giving scientific talks, 1973. Available at: arXiv:gr-qc/9703019

See also

Notes

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