Bulletin of the American Mathematical Society

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Book Information:

Author: Theodore Frankel
Title: Gravitational curvature, an introduction to Einstein's theory
Additional book information: W. H. Freeman and Co., San Francisco, California, 1979, xviii + 172 pp., $8.95. ISBN 0-7167-1062-5.

Author: Hans Stephani
Title: General relativity, an introduction to the theory of the gravitational field
Additional book information: (edited by John Stewart; translated from German by Martin Pollock and John Stewart) Cambridge Univ. Press, New York, New York, 1982, xvi + 298 pp., $49.50. ISBN 0-521-24008-5.

Author: Robert M. Wald
Title: General relativity
Additional book information: University of Chicago Press, Chicago, Illinois, 1984, xiii + 491 pp., $50.00 HB; $30.00 PB. ISBN 0-266-87033-2.

1.

H. Bateman, The transformation of coordinates which can be used to transform one physical problem into another, Proc. London Math. Soc. 8 (1910), 469-488.

H. Bondi, F. A. E. Pirani, and I. Robinson, Gravitational waves in general relativity. III. Exact plane waves, Proc. Roy. Soc. London Ser. A 251 (1959), 519–533. MR 106747, DOI 10.1098/rspa.1959.0124

3.

E. Cartan, Sur les espaces conformes généralisés et l'Univers optique, C. R. Acad. Sci. Paris 174 (1922), 857-859.

4.

E. Cartan, Sur les variétés à connexion affine et la théorie de la relativité généralisée I; I (suite); II, Ann. Sci. École Norm. Sup. 40 (1923), 325-412; 41 (1924), 1-25; 42 (1925), 17-88. English translation by A. Ashtekar and A. Magnon-Ashtekar, Bibliopolis, Naples, 1985.

Subrahmanyan Chandrasekhar, The mathematical theory of black holes, International Series of Monographs on Physics, vol. 69, The Clarendon Press, Oxford University Press, New York, 1983. Oxford Science Publications. MR 700826

S. S. Chern and J. K. Moser, Real hypersurfaces in complex manifolds, Acta Math. 133 (1974), 219–271. MR 425155, DOI 10.1007/BF02392146

7.

W. K. Clifford, The common sense of the exact sciences, D. Appleton and Co., New York, 1885.

S. Deser and B. Zumino, Consistent supergravity, Phys. Lett. B 62 (1976), no. 3, 335–337. MR 411531, DOI 10.1016/0370-2693(76)90089-7

S. K. Donaldson, Self-dual connections and the topology of smooth $4$-manifolds, Bull. Amer. Math. Soc. (N.S.) 8 (1983), no. 1, 81–83. MR 682827, DOI 10.1090/S0273-0979-1983-15090-5

10.

A. Einstein and N. Rosen, On gravitational waves, J. Franklin Inst. 223 (1937), 43-54.

Daniel Z. Freedman, P. van Nieuwenhuizen, and S. Ferrara, Progress toward a theory of supergravity, Phys. Rev. D (3) 13 (1976), no. 12, 3214–3218. MR 462449, DOI 10.1103/PhysRevD.13.3214

12.

A. Friedmann, Über die Krümmung des Raumes, Z. Phys. 10 (1922), 377-386.

13.

R. P. Geroch, What is a singularity in general relativity?, Ann. Physics 48 (1968), 526-540.

Kurt Gödel, An example of a new type of cosmological solutions of Einstein’s field equations of gravitation, Rev. Modern Physics 21 (1949), 447–450. MR 0031841, DOI 10.1103/revmodphys.21.447

J. N. Goldberg and R. K. Sachs, A theorem on Petrov types, Acta Phys. Polon. 22 (1962), no. suppl., 13–23. MR 156679

André Haefliger, Structures feuilletées et cohomologie à valeur dans un faisceau de groupoïdes, Comment. Math. Helv. 32 (1958), 248–329 (French). MR 100269, DOI 10.1007/BF02564582

S. W. Hawking and G. F. R. Ellis, The large scale structure of space-time, Cambridge Monographs on Mathematical Physics, No. 1, Cambridge University Press, London-New York, 1973. MR 0424186

S. W. Hawking and R. Penrose, The singularities of gravitational collapse and cosmology, Proc. Roy. Soc. London Ser. A 314 (1970), 529–548. MR 264959, DOI 10.1098/rspa.1970.0021

19.

R. P. Kerr and A. Schild, A new class of vacuum solutions of the Einstein field equations, Atti del Convegno sulla Relatività Generale: Probleme dell'energia e onde gravitazionali, G. Barbèra, Editore, Florence, 1965.

T. W. B. Kibble, Lorentz invariance and the gravitational field, J. Mathematical Phys. 2 (1961), 212–221. MR 127952, DOI 10.1063/1.1703702

D. Kramer, H. Stephani, E. Herlt, and M. MacCallum, Exact solutions of Einstein’s field equations, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge-New York, 1980. Edited by Ernst Schmutzer. MR 614593

Hans Lewy, An example of a smooth linear partial differential equation without solution, Ann. of Math. (2) 66 (1957), 155–158. MR 88629, DOI 10.2307/1970121

A. Lichnerowicz, Théories relativistes de la gravitation et de l’électromagnétisme. Relativité générale et théories unitaires, Masson et Cie, Paris, 1955 (French). MR 0071917

Charles W. Misner, Kip S. Thorne, and John Archibald Wheeler, Gravitation, W. H. Freeman and Co., San Francisco, Calif., 1973. MR 0418833

Ezra Newman and Roger Penrose, An approach to gravitational radiation by a method of spin coefficients, J. Mathematical Phys. 3 (1962), 566–578. MR 141500, DOI 10.1063/1.1724257

S. P. Novikov, The topology of foliations, Trudy Moskov. Mat. Obšč. 14 (1965), 248–278 (Russian). MR 0200938

István Ozsváth and Engelbert L. Schücking, The finite rotating universe, Ann. Physics 55 (1969), 166–204. MR 252015, DOI 10.1016/0003-4916(69)90311-X

Roger Penrose, Gravitational collapse and space-time singularities, Phys. Rev. Lett. 14 (1965), 57–59. MR 172678, DOI 10.1103/PhysRevLett.14.57

R. Penrose, Twistor algebra, J. Mathematical Phys. 8 (1967), 345–366. MR 216828, DOI 10.1063/1.1705200

Roger Penrose, Techniques of differential topology in relativity, Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, No. 7, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1972. MR 0469146

Roger Penrose, Physical space-time and nonrealizable CR-structures, Bull. Amer. Math. Soc. (N.S.) 8 (1983), no. 3, 427–448. MR 693958, DOI 10.1090/S0273-0979-1983-15109-1

R. Penrose and M. A. H. MacCallum, Twistor theory: an approach to the quantisation of fields and space-time, Phys. Rep. 6C (1973), no. 4, 241–315. MR 475660, DOI 10.1016/0370-1573(73)90008-2

Roger Penrose and Wolfgang Rindler, Spinors and space-time. Vol. 1, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, 1984. Two-spinor calculus and relativistic fields. MR 776784, DOI 10.1017/CBO9780511564048

Ivor Robinson, Null electromagnetic fields, J. Mathematical Phys. 2 (1961), 290–291. MR 127369, DOI 10.1063/1.1703712

Ivor Robinson and Andrzej Trautman, Integrable optical geometry, Lett. Math. Phys. 10 (1985), no. 2-3, 179–182. MR 815241, DOI 10.1007/BF00398155

36.

I. Robinson and A. Trautman, A generalization of Mariot 's theorem on congruences of null geodesics, Proc. Roy. Soc. London (to appear).

D. W. Sciama, On the analogy between charge and spin in general relativity, Recent developments in general relativity, Pergamon, Oxford; PWN—Polish Scientific Publishers, Warsaw, 1962, pp. 415–439. MR 0164767

A. H. Taub, Empty space-times admitting a three parameter group of motions, Ann. of Math. (2) 53 (1951), 472–490. MR 41565, DOI 10.2307/1969567

Andrzej Trautman, Deformations of the Hodge map and optical geometry, J. Geom. Phys. 1 (1984), no. 2, 85–95. MR 794981, DOI 10.1016/0393-0440(84)90005-6

40.

S. Weinberg, Gravitation and cosmology, J. Wiley, New York, 1972.

R. O. Wells Jr., The Cauchy-Riemann equations and differential geometry, Bull. Amer. Math. Soc. (N.S.) 6 (1982), no. 2, 187–199. MR 640945, DOI 10.1090/S0273-0979-1982-14976-X

C. N. Yang and R. L. Mills, Conservation of isotopic spin and isotopic gauge invariance, Phys. Rev. (2) 96 (1954), 191–195. MR 65437

1.

H. Bateman, The transformation of coordinates which can be used to transform one physical problem into another, Proc. London Math. Soc. 8 (1910), 469-488.

2.

H. Bondi, F. A. E. Pirani and I. Robinson, Gravitational waves in general relativity III. Exact plane waves, Proc. Roy. Soc. London A251 (1959), 519-533. MR 0106747

3.

E. Cartan, Sur les espaces conformes généralisés et l'Univers optique, C. R. Acad. Sci. Paris 174 (1922), 857-859.

4.

E. Cartan, Sur les variétés à connexion affine et la théorie de la relativité généralisée I; I (suite); II, Ann. Sci. École Norm. Sup. 40 (1923), 325-412; 41 (1924), 1-25; 42 (1925), 17-88. English translation by A. Ashtekar and A. Magnon-Ashtekar, Bibliopolis, Naples, 1985.

5.

S. Chandrasekhar, The mathematical theory of black holes, Clarendon Press, Oxford, 1983. MR 700826

6.

S. S. Chern and J. K. Moser, Real hypersurfaces in complex manifolds, Acta Math. 133 (1974), 219-271. MR 425155

7.

W. K. Clifford, The common sense of the exact sciences, D. Appleton and Co., New York, 1885.

8.

S. Deser and B. Zumino, Consistent supergravity, Phys. Lett. 62B (1976), 335-337. MR 411531

9.

S. K. Donaldson, Self-dual connections and the topology of smooth 4-manifolds, Bull. Amer. Math. Soc. (N.S.) 8 (1983), 81-83. MR 682827

10.

A. Einstein and N. Rosen, On gravitational waves, J. Franklin Inst. 223 (1937), 43-54.

11.

D. Z. Freedman, P. Van Nieuwenhuizen and S. Ferrara, Progress toward a theory of supergravity, Phys. Rev. D13 (1976), 3214-18. MR 462449

12.

A. Friedmann, Über die Krümmung des Raumes, Z. Phys. 10 (1922), 377-386.

13.

R. P. Geroch, What is a singularity in general relativity?, Ann. Physics 48 (1968), 526-540.

14.

K. Gödel, An example of a new type of cosmological solutions of Einstein's field equations of gravitation, Rev. Modern Phys. 21 (1949), 447-450. MR 31841

15.

J. N. Goldberg and R. K. Sachs, A theorem on Petrov types, Acta Phys. Polon. 22 Suppl. (1962), 13-23. MR 156679

16.

A. Haefliger, Structures feuilletées et cohomologie à valeur dans un faisceau de groupoïdes, Comment. Math. Helv. 32 (1958), 248-329. MR 100269

17.

S. W. Hawking and G. F. R. Ellis, The large scale structure of space-time, Cambridge Univ. Press, Cambridge, 1973. MR 424186

18.

S. W. Hawking and R. Penrose, The singularities of gravitational collapse and cosmology, Proc. Roy. Soc. London A314 (1970), 529-548. MR 264959

19.

R. P. Kerr and A. Schild, A new class of vacuum solutions of the Einstein field equations, Atti del Convegno sulla Relatività Generale: Probleme dell'energia e onde gravitazionali, G. Barbèra, Editore, Florence, 1965.

20.

T. W. B. Kibble, Lorentz invariance and the gravitational field, J. Math. Phys. 2 (1961), 212-221. MR 127952

21.

D. Kramer, H. Stephani, M. MacCallum and E. Herlt, Exact solutions of Einstein's field equations, Cambridge Univ. Press and Deutsch Verlag der Wissenschaften, Cambridge and Berlin, 1980. MR 614593

22.

H. Lewy, An example of a smooth linear partial differential equation without solution, Ann. of Math. (2) 66 (1957), 155-158. MR 88629

23.

A. Lichnerowicz, Théories relativistes de la gravitation et de l'électromagnétisme, Masson et Cie, Paris, 1955. MR 71917

24.

C. W. Misner, K. S. Thorne and J. A. Wheeler, Gravitation, W. H. Freeman and Co., San Francisco, 1973. MR 418833

25.

E. T. Newman and R. Penrose, An approach to gravitational radiation by a method of spin coefficients, J. Math. Phys. 3 (1962), 566-578; Errata: Ibid. 4 (1963), 998. MR 141500

26.

S. P. Novikov, Topology of foliations, Trudy Moskov. Mat. Obšč 14 (1965), 248-278 = Trans. Moscow Math. Soc. (1965), 268-304. MR 200938

27.

I. Ozsvàth and E. Schücking, The finite rotating universe, Ann. Physics 55 (1969), 166-204. MR 252015

28.

R. Penrose, Gravitational collapse and space-time singularities, Phys. Rev. Lett. 14 (1965), 57-59. MR 172678

29.

R. Penrose, Twistor algebra, J. Math. Phys. 8 (1967), 345-366. MR 216828

30.

R. Penrose, Techniques of differential topology in relativity, SIAM, Philadelphia, 1972. MR 469146

31.

R. Penrose, Physical space-time and nonrealizable CR-structures, Bull. Amer. Math. Soc. (N.S.) 8 (1983), 427-448. MR 693958

32.

R. Penrose and M. A. H. MacCallum, Twistor theory: An approach to the quantisation of fields and space-time, Phys. Rep. 6 (1972), 241-316. MR 475660

33.

R. Penrose and W. Rindler, Spinors and space-time, Cambridge Univ. Press, Cambridge, vol. I: 1984, vol. II: to appear. MR 776784

34.

I. Robinson, Null electromagnetic fields, J. Math. Phys. 2 (1961), 290-291. MR 127369

35.

I. Robinson and A. Trautman, Integrable optical geometry, Lett. Math. Phys. 10 (1985), 179-182. MR 815241

36.

I. Robinson and A. Trautman, A generalization of Mariot 's theorem on congruences of null geodesics, Proc. Roy. Soc. London (to appear).

37.

D. W. Sciama, On the analogy between charge and spin in general relativity, Recent developments in General Relativity, Pergamon Press and PWN, Oxford and Warsaw, 1962. MR 164767

38.

A. H. Taub, Empty space-times admitting a three-parameter group of motions, Ann. of Math. 53 (1951), 472-490. MR 41565

39.

A. Trautman, Deformations of the Hodge map and optical geometry, J. Geometry and Physics (Florence) 1 (1984), 85-95. MR 794981

40.

S. Weinberg, Gravitation and cosmology, J. Wiley, New York, 1972.

41.

R. O. Wells, Jr., The Cauchy-Riemann equations and differential geometry, Bull. Amer. Math. Soc. (N.S.) 6 (1982), 187-199. MR 640945

42.

C. N. Yang and R. L. Mills, Conservation of isotopic spin and isotopic gauge invariance, Phys. Rev. 96 (1954), 191-195. MR 65437