On applications of Campbell's embedding theorem

Classical and Quantum Gravity

Volumn 14, Issue 4, 1997, Pages 865-879

  Lidsey, James E ^a   Romero, Carlos ^b   Tavakol, Reza ^a   Rippl, Steve ^a  

^a QUEEN MARY UNIVERSITY OF LONDON   (United Kingdom)

^b FEDERAL UNIVERSITY OF PARAÍBA   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040238307     PISSN: 02649381     EISSN: None     Source Type: Journal    
DOI: 10.1088/0264-9381/14/4/005     Document Type: Article

References (74)

1. Campbell J E 1926 A Course of Differential Geometry (Oxford: Clarendon)
2. Kaluza T 1921 Preus. Acad. Wiss. K1 966 Klein O 1926 Z. Phys. 37 895 Klein O 1926 Nature 118 516
3. Kaluza T 1921 Preus. Acad. Wiss. K1 966 Klein O 1926 Z. Phys. 37 895 Klein O 1926 Nature 118 516
4. Kaluza T 1921 Preus. Acad. Wiss. K1 966 Klein O 1926 Z. Phys. 37 895 Klein O 1926 Nature 118 516
5. Appelquist T, Chodos A and Freund PGO 1987 Modern Kaluza-Klein Theories (New York: Addison-Wesley)
6. Duff M J, Nilsson E W and Pope CN 1986 Phys. Rep. 130 1
7. Witten E 1981 Nucl. Phys. B 186 412 Duff M J 1994 Kaluza-Klein theories in perspective Preprint NI-94-015, hep-th/9410046 Maia M D 1995 Hypersurfaces of five dimensional vacuum spacetimes Preprint gr-qc/9512002
8. Witten E 1981 Nucl. Phys. B 186 412 Duff M J 1994 Kaluza-Klein theories in perspective Preprint NI-94-015, hep-th/9410046 Maia M D 1995 Hypersurfaces of five dimensional vacuum spacetimes Preprint gr-qc/9512002
9. Witten E 1981 Nucl. Phys. B 186 412 Duff M J 1994 Kaluza-Klein theories in perspective Preprint NI-94-015, hep-th/9410046 Maia M D 1995 Hypersurfaces of five dimensional vacuum spacetimes Preprint gr-qc/9512002
10. Green M B, Schwarz J H and Witten E 1988 Superstring Theory (Cambridge: Cambridge University Press)
11. Kolb E W and Turner M S 1990 The Early Universe (New York: Addison-Wesley)
12. Wesson P S and Ponce de Leon J 1992 J. Math. Phys. 33 3883 Wesson P S 1992 Phys. Lett. B 276 299 Liu H and Wesson P S 1992 J. Math. Phys. 33 3888 Wesson P S 1992 Mod. Phys. Lett. A 7 921
13. Wesson P S and Ponce de Leon J 1992 J. Math. Phys. 33 3883 Wesson P S 1992 Phys. Lett. B 276 299 Liu H and Wesson P S 1992 J. Math. Phys. 33 3888 Wesson P S 1992 Mod. Phys. Lett. A 7 921
14. Wesson P S and Ponce de Leon J 1992 J. Math. Phys. 33 3883 Wesson P S 1992 Phys. Lett. B 276 299 Liu H and Wesson P S 1992 J. Math. Phys. 33 3888 Wesson P S 1992 Mod. Phys. Lett. A 7 921
15. Wesson P S and Ponce de Leon J 1992 J. Math. Phys. 33 3883 Wesson P S 1992 Phys. Lett. B 276 299 Liu H and Wesson P S 1992 J. Math. Phys. 33 3888 Wesson P S 1992 Mod. Phys. Lett. A 7 921
16. Wesson P S 1992 Astrophys. J. 394 19
17. Billyard A and Wesson P S 1996 Gen. Rel. Grav. 28 129
18. Witten E 1988 Nucl. Phys. B 311 46 Mandai G, Sengupta A M and Wadia S R 1991 Mod Phys. Lett. A 6 1685 Witten E 1991 Phys. Rev. D 44 1991 Mann R B 1992 Gen. Rel. Grav. 24 433 Callan C G, Giddings S B, Harvey J A and Strominger A 1992 Phys. Rev. D 45 R1005 Russo J G, Susskind L and Thorlacius L 1992 Phys. Rev D 46 3444 Russo J G, Susskind L and Thorlacius L 1993 Phys Rev D 47 533 Mann R B and Ross S F 1993 Phys. Rev. D 47 3312 Gegenberg J and Kunstatter G 1993 Phys Rev. D 47 R4192 Mazzitelli F D and Russo J G 1993 Phys. Rev D 47 4490 Perry M J and Teo E 1993 Phys. Rev. Lett. 71 2669 Önder M and Tucker R W 1994 Class. Quantum Grav. 11 1243 Navarro-Salas J, Navarro M, Talavera C F and Aldaya V 1994 Phys. Rev 50 901 Mignemi S 1994 Phys. Rev. D 50 R4733 Lidsey J E 1995 Phys. Rev. D 51 1829 Tseytlin A A 1995 Class. Quantum Grav. 12 2365
19. Witten E 1988 Nucl. Phys. B 311 46 Mandai G, Sengupta A M and Wadia S R 1991 Mod Phys. Lett. A 6 1685 Witten E 1991 Phys. Rev. D 44 1991 Mann R B 1992 Gen. Rel. Grav. 24 433 Callan C G, Giddings S B, Harvey J A and Strominger A 1992 Phys. Rev. D 45 R1005 Russo J G, Susskind L and Thorlacius L 1992 Phys. Rev D 46 3444 Russo J G, Susskind L and Thorlacius L 1993 Phys Rev D 47 533 Mann R B and Ross S F 1993 Phys. Rev. D 47 3312 Gegenberg J and Kunstatter G 1993 Phys Rev. D 47 R4192 Mazzitelli F D and Russo J G 1993 Phys. Rev D 47 4490 Perry M J and Teo E 1993 Phys. Rev. Lett. 71 2669 Önder M and Tucker R W 1994 Class. Quantum Grav. 11 1243 Navarro-Salas J, Navarro M, Talavera C F and Aldaya V 1994 Phys. Rev 50 901 Mignemi S 1994 Phys. Rev. D 50 R4733 Lidsey J E 1995 Phys. Rev. D 51 1829 Tseytlin A A 1995 Class. Quantum Grav. 12 2365
20. Witten E 1988 Nucl. Phys. B 311 46 Mandai G, Sengupta A M and Wadia S R 1991 Mod Phys. Lett. A 6 1685 Witten E 1991 Phys. Rev. D 44 1991 Mann R B 1992 Gen. Rel. Grav. 24 433 Callan C G, Giddings S B, Harvey J A and Strominger A 1992 Phys. Rev. D 45 R1005 Russo J G, Susskind L and Thorlacius L 1992 Phys. Rev D 46 3444 Russo J G, Susskind L and Thorlacius L 1993 Phys Rev D 47 533 Mann R B and Ross S F 1993 Phys. Rev. D 47 3312 Gegenberg J and Kunstatter G 1993 Phys Rev. D 47 R4192 Mazzitelli F D and Russo J G 1993 Phys. Rev D 47 4490 Perry M J and Teo E 1993 Phys. Rev. Lett. 71 2669 Önder M and Tucker R W 1994 Class. Quantum Grav. 11 1243 Navarro-Salas J, Navarro M, Talavera C F and Aldaya V 1994 Phys. Rev 50 901 Mignemi S 1994 Phys. Rev. D 50 R4733 Lidsey J E 1995 Phys. Rev. D 51 1829 Tseytlin A A 1995 Class. Quantum Grav. 12 2365
21. Witten E 1988 Nucl. Phys. B 311 46 Mandai G, Sengupta A M and Wadia S R 1991 Mod Phys. Lett. A 6 1685 Witten E 1991 Phys. Rev. D 44 1991 Mann R B 1992 Gen. Rel. Grav. 24 433 Callan C G, Giddings S B, Harvey J A and Strominger A 1992 Phys. Rev. D 45 R1005 Russo J G, Susskind L and Thorlacius L 1992 Phys. Rev D 46 3444 Russo J G, Susskind L and Thorlacius L 1993 Phys Rev D 47 533 Mann R B and Ross S F 1993 Phys. Rev. D 47 3312 Gegenberg J and Kunstatter G 1993 Phys Rev. D 47 R4192 Mazzitelli F D and Russo J G 1993 Phys. Rev D 47 4490 Perry M J and Teo E 1993 Phys. Rev. Lett. 71 2669 Önder M and Tucker R W 1994 Class. Quantum Grav. 11 1243 Navarro-Salas J, Navarro M, Talavera C F and Aldaya V 1994 Phys. Rev 50 901 Mignemi S 1994 Phys. Rev. D 50 R4733 Lidsey J E 1995 Phys. Rev. D 51 1829 Tseytlin A A 1995 Class. Quantum Grav. 12 2365
22. Witten E 1988 Nucl. Phys. B 311 46 Mandai G, Sengupta A M and Wadia S R 1991 Mod Phys. Lett. A 6 1685 Witten E 1991 Phys. Rev. D 44 1991 Mann R B 1992 Gen. Rel. Grav. 24 433 Callan C G, Giddings S B, Harvey J A and Strominger A 1992 Phys. Rev. D 45 R1005 Russo J G, Susskind L and Thorlacius L 1992 Phys. Rev D 46 3444 Russo J G, Susskind L and Thorlacius L 1993 Phys Rev D 47 533 Mann R B and Ross S F 1993 Phys. Rev. D 47 3312 Gegenberg J and Kunstatter G 1993 Phys Rev. D 47 R4192 Mazzitelli F D and Russo J G 1993 Phys. Rev D 47 4490 Perry M J and Teo E 1993 Phys. Rev. Lett. 71 2669 Önder M and Tucker R W 1994 Class. Quantum Grav. 11 1243 Navarro-Salas J, Navarro M, Talavera C F and Aldaya V 1994 Phys. Rev 50 901 Mignemi S 1994 Phys. Rev. D 50 R4733 Lidsey J E 1995 Phys. Rev. D 51 1829 Tseytlin A A 1995 Class. Quantum Grav. 12 2365
23. Witten E 1988 Nucl. Phys. B 311 46 Mandai G, Sengupta A M and Wadia S R 1991 Mod Phys. Lett. A 6 1685 Witten E 1991 Phys. Rev. D 44 1991 Mann R B 1992 Gen. Rel. Grav. 24 433 Callan C G, Giddings S B, Harvey J A and Strominger A 1992 Phys. Rev. D 45 R1005 Russo J G, Susskind L and Thorlacius L 1992 Phys. Rev D 46 3444 Russo J G, Susskind L and Thorlacius L 1993 Phys Rev D 47 533 Mann R B and Ross S F 1993 Phys. Rev. D 47 3312 Gegenberg J and Kunstatter G 1993 Phys Rev. D 47 R4192 Mazzitelli F D and Russo J G 1993 Phys. Rev D 47 4490 Perry M J and Teo E 1993 Phys. Rev. Lett. 71 2669 Önder M and Tucker R W 1994 Class. Quantum Grav. 11 1243 Navarro-Salas J, Navarro M, Talavera C F and Aldaya V 1994 Phys. Rev 50 901 Mignemi S 1994 Phys. Rev. D 50 R4733 Lidsey J E 1995 Phys. Rev. D 51 1829 Tseytlin A A 1995 Class. Quantum Grav. 12 2365
24. Witten E 1988 Nucl. Phys. B 311 46 Mandai G, Sengupta A M and Wadia S R 1991 Mod Phys. Lett. A 6 1685 Witten E 1991 Phys. Rev. D 44 1991 Mann R B 1992 Gen. Rel. Grav. 24 433 Callan C G, Giddings S B, Harvey J A and Strominger A 1992 Phys. Rev. D 45 R1005 Russo J G, Susskind L and Thorlacius L 1992 Phys. Rev D 46 3444 Russo J G, Susskind L and Thorlacius L 1993 Phys Rev D 47 533 Mann R B and Ross S F 1993 Phys. Rev. D 47 3312 Gegenberg J and Kunstatter G 1993 Phys Rev. D 47 R4192 Mazzitelli F D and Russo J G 1993 Phys. Rev D 47 4490 Perry M J and Teo E 1993 Phys. Rev. Lett. 71 2669 Önder M and Tucker R W 1994 Class. Quantum Grav. 11 1243 Navarro-Salas J, Navarro M, Talavera C F and Aldaya V 1994 Phys. Rev 50 901 Mignemi S 1994 Phys. Rev. D 50 R4733 Lidsey J E 1995 Phys. Rev. D 51 1829 Tseytlin A A 1995 Class. Quantum Grav. 12 2365
25. Witten E 1988 Nucl. Phys. B 311 46 Mandai G, Sengupta A M and Wadia S R 1991 Mod Phys. Lett. A 6 1685 Witten E 1991 Phys. Rev. D 44 1991 Mann R B 1992 Gen. Rel. Grav. 24 433 Callan C G, Giddings S B, Harvey J A and Strominger A 1992 Phys. Rev. D 45 R1005 Russo J G, Susskind L and Thorlacius L 1992 Phys. Rev D 46 3444 Russo J G, Susskind L and Thorlacius L 1993 Phys Rev D 47 533 Mann R B and Ross S F 1993 Phys. Rev. D 47 3312 Gegenberg J and Kunstatter G 1993 Phys Rev. D 47 R4192 Mazzitelli F D and Russo J G 1993 Phys. Rev D 47 4490 Perry M J and Teo E 1993 Phys. Rev. Lett. 71 2669 Önder M and Tucker R W 1994 Class. Quantum Grav. 11 1243 Navarro-Salas J, Navarro M, Talavera C F and Aldaya V 1994 Phys. Rev 50 901 Mignemi S 1994 Phys. Rev. D 50 R4733 Lidsey J E 1995 Phys. Rev. D 51 1829 Tseytlin A A 1995 Class. Quantum Grav. 12 2365
26. Witten E 1988 Nucl. Phys. B 311 46 Mandai G, Sengupta A M and Wadia S R 1991 Mod Phys. Lett. A 6 1685 Witten E 1991 Phys. Rev. D 44 1991 Mann R B 1992 Gen. Rel. Grav. 24 433 Callan C G, Giddings S B, Harvey J A and Strominger A 1992 Phys. Rev. D 45 R1005 Russo J G, Susskind L and Thorlacius L 1992 Phys. Rev D 46 3444 Russo J G, Susskind L and Thorlacius L 1993 Phys Rev D 47 533 Mann R B and Ross S F 1993 Phys. Rev. D 47 3312 Gegenberg J and Kunstatter G 1993 Phys Rev. D 47 R4192 Mazzitelli F D and Russo J G 1993 Phys. Rev D 47 4490 Perry M J and Teo E 1993 Phys. Rev. Lett. 71 2669 Önder M and Tucker R W 1994 Class. Quantum Grav. 11 1243 Navarro-Salas J, Navarro M, Talavera C F and Aldaya V 1994 Phys. Rev 50 901 Mignemi S 1994 Phys. Rev. D 50 R4733 Lidsey J E 1995 Phys. Rev. D 51 1829 Tseytlin A A 1995 Class. Quantum Grav. 12 2365
27. Witten E 1988 Nucl. Phys. B 311 46 Mandai G, Sengupta A M and Wadia S R 1991 Mod Phys. Lett. A 6 1685 Witten E 1991 Phys. Rev. D 44 1991 Mann R B 1992 Gen. Rel. Grav. 24 433 Callan C G, Giddings S B, Harvey J A and Strominger A 1992 Phys. Rev. D 45 R1005 Russo J G, Susskind L and Thorlacius L 1992 Phys. Rev D 46 3444 Russo J G, Susskind L and Thorlacius L 1993 Phys Rev D 47 533 Mann R B and Ross S F 1993 Phys. Rev. D 47 3312 Gegenberg J and Kunstatter G 1993 Phys Rev. D 47 R4192 Mazzitelli F D and Russo J G 1993 Phys. Rev D 47 4490 Perry M J and Teo E 1993 Phys. Rev. Lett. 71 2669 Önder M and Tucker R W 1994 Class. Quantum Grav. 11 1243 Navarro-Salas J, Navarro M, Talavera C F and Aldaya V 1994 Phys. Rev 50 901 Mignemi S 1994 Phys. Rev. D 50 R4733 Lidsey J E 1995 Phys. Rev. D 51 1829 Tseytlin A A 1995 Class. Quantum Grav. 12 2365
28. Witten E 1988 Nucl. Phys. B 311 46 Mandai G, Sengupta A M and Wadia S R 1991 Mod Phys. Lett. A 6 1685 Witten E 1991 Phys. Rev. D 44 1991 Mann R B 1992 Gen. Rel. Grav. 24 433 Callan C G, Giddings S B, Harvey J A and Strominger A 1992 Phys. Rev. D 45 R1005 Russo J G, Susskind L and Thorlacius L 1992 Phys. Rev D 46 3444 Russo J G, Susskind L and Thorlacius L 1993 Phys Rev D 47 533 Mann R B and Ross S F 1993 Phys. Rev. D 47 3312 Gegenberg J and Kunstatter G 1993 Phys Rev. D 47 R4192 Mazzitelli F D and Russo J G 1993 Phys. Rev D 47 4490 Perry M J and Teo E 1993 Phys. Rev. Lett. 71 2669 Önder M and Tucker R W 1994 Class. Quantum Grav. 11 1243 Navarro-Salas J, Navarro M, Talavera C F and Aldaya V 1994 Phys. Rev 50 901 Mignemi S 1994 Phys. Rev. D 50 R4733 Lidsey J E 1995 Phys. Rev. D 51 1829 Tseytlin A A 1995 Class. Quantum Grav. 12 2365
29. Witten E 1988 Nucl. Phys. B 311 46 Mandai G, Sengupta A M and Wadia S R 1991 Mod Phys. Lett. A 6 1685 Witten E 1991 Phys. Rev. D 44 1991 Mann R B 1992 Gen. Rel. Grav. 24 433 Callan C G, Giddings S B, Harvey J A and Strominger A 1992 Phys. Rev. D 45 R1005 Russo J G, Susskind L and Thorlacius L 1992 Phys. Rev D 46 3444 Russo J G, Susskind L and Thorlacius L 1993 Phys Rev D 47 533 Mann R B and Ross S F 1993 Phys. Rev. D 47 3312 Gegenberg J and Kunstatter G 1993 Phys Rev. D 47 R4192 Mazzitelli F D and Russo J G 1993 Phys. Rev D 47 4490 Perry M J and Teo E 1993 Phys. Rev. Lett. 71 2669 Önder M and Tucker R W 1994 Class. Quantum Grav. 11 1243 Navarro-Salas J, Navarro M, Talavera C F and Aldaya V 1994 Phys. Rev 50 901 Mignemi S 1994 Phys. Rev. D 50 R4733 Lidsey J E 1995 Phys. Rev. D 51 1829 Tseytlin A A 1995 Class. Quantum Grav. 12 2365
30. Witten E 1988 Nucl. Phys. B 311 46 Mandai G, Sengupta A M and Wadia S R 1991 Mod Phys. Lett. A 6 1685 Witten E 1991 Phys. Rev. D 44 1991 Mann R B 1992 Gen. Rel. Grav. 24 433 Callan C G, Giddings S B, Harvey J A and Strominger A 1992 Phys. Rev. D 45 R1005 Russo J G, Susskind L and Thorlacius L 1992 Phys. Rev D 46 3444 Russo J G, Susskind L and Thorlacius L 1993 Phys Rev D 47 533 Mann R B and Ross S F 1993 Phys. Rev. D 47 3312 Gegenberg J and Kunstatter G 1993 Phys Rev. D 47 R4192 Mazzitelli F D and Russo J G 1993 Phys. Rev D 47 4490 Perry M J and Teo E 1993 Phys. Rev. Lett. 71 2669 Önder M and Tucker R W 1994 Class. Quantum Grav. 11 1243 Navarro-Salas J, Navarro M, Talavera C F and Aldaya V 1994 Phys. Rev 50 901 Mignemi S 1994 Phys. Rev. D 50 R4733 Lidsey J E 1995 Phys. Rev. D 51 1829 Tseytlin A A 1995 Class. Quantum Grav. 12 2365
31. Witten E 1988 Nucl. Phys. B 311 46 Mandai G, Sengupta A M and Wadia S R 1991 Mod Phys. Lett. A 6 1685 Witten E 1991 Phys. Rev. D 44 1991 Mann R B 1992 Gen. Rel. Grav. 24 433 Callan C G, Giddings S B, Harvey J A and Strominger A 1992 Phys. Rev. D 45 R1005 Russo J G, Susskind L and Thorlacius L 1992 Phys. Rev D 46 3444 Russo J G, Susskind L and Thorlacius L 1993 Phys Rev D 47 533 Mann R B and Ross S F 1993 Phys. Rev. D 47 3312 Gegenberg J and Kunstatter G 1993 Phys Rev. D 47 R4192 Mazzitelli F D and Russo J G 1993 Phys. Rev D 47 4490 Perry M J and Teo E 1993 Phys. Rev. Lett. 71 2669 Önder M and Tucker R W 1994 Class. Quantum Grav. 11 1243 Navarro-Salas J, Navarro M, Talavera C F and Aldaya V 1994 Phys. Rev 50 901 Mignemi S 1994 Phys. Rev. D 50 R4733 Lidsey J E 1995 Phys. Rev. D 51 1829 Tseytlin A A 1995 Class. Quantum Grav. 12 2365
32. Witten E 1988 Nucl. Phys. B 311 46 Mandai G, Sengupta A M and Wadia S R 1991 Mod Phys. Lett. A 6 1685 Witten E 1991 Phys. Rev. D 44 1991 Mann R B 1992 Gen. Rel. Grav. 24 433 Callan C G, Giddings S B, Harvey J A and Strominger A 1992 Phys. Rev. D 45 R1005 Russo J G, Susskind L and Thorlacius L 1992 Phys. Rev D 46 3444 Russo J G, Susskind L and Thorlacius L 1993 Phys Rev D 47 533 Mann R B and Ross S F 1993 Phys. Rev. D 47 3312 Gegenberg J and Kunstatter G 1993 Phys Rev. D 47 R4192 Mazzitelli F D and Russo J G 1993 Phys. Rev D 47 4490 Perry M J and Teo E 1993 Phys. Rev. Lett. 71 2669 Önder M and Tucker R W 1994 Class. Quantum Grav. 11 1243 Navarro-Salas J, Navarro M, Talavera C F and Aldaya V 1994 Phys. Rev 50 901 Mignemi S 1994 Phys. Rev. D 50 R4733 Lidsey J E 1995 Phys. Rev. D 51 1829 Tseytlin A A 1995 Class. Quantum Grav. 12 2365
33. Witten E 1988 Nucl. Phys. B 311 46 Mandai G, Sengupta A M and Wadia S R 1991 Mod Phys. Lett. A 6 1685 Witten E 1991 Phys. Rev. D 44 1991 Mann R B 1992 Gen. Rel. Grav. 24 433 Callan C G, Giddings S B, Harvey J A and Strominger A 1992 Phys. Rev. D 45 R1005 Russo J G, Susskind L and Thorlacius L 1992 Phys. Rev D 46 3444 Russo J G, Susskind L and Thorlacius L 1993 Phys Rev D 47 533 Mann R B and Ross S F 1993 Phys. Rev. D 47 3312 Gegenberg J and Kunstatter G 1993 Phys Rev. D 47 R4192 Mazzitelli F D and Russo J G 1993 Phys. Rev D 47 4490 Perry M J and Teo E 1993 Phys. Rev. Lett. 71 2669 Önder M and Tucker R W 1994 Class. Quantum Grav. 11 1243 Navarro-Salas J, Navarro M, Talavera C F and Aldaya V 1994 Phys. Rev 50 901 Mignemi S 1994 Phys. Rev. D 50 R4733 Lidsey J E 1995 Phys. Rev. D 51 1829 Tseytlin A A 1995 Class. Quantum Grav. 12 2365
34. Rippl S, Romero C and Tavakol R 1995 Class. Quantum Grav. 12 2411
35. Verbin Y 1994 Phys. Rev. D 50 7318
36. Giddings S, Abbott J and Kuchar K 1984 Gen. Rel. Grav. 16 751
37. Kramer D, Stephani H, MacCallum M and Herlt E 1980 Exact Solutions of Einstein's Field Equations (Cambridge: Cambridge University Press)
38. Fronsdal C 1959 Phys. Rev. 116 778
39. Eisenhart L P 1949 Riemannian Geometry (Princeton, NJ: Princeton University Press)
40. Friedman A 1961 J. Math. Mech. 10 625 Friedman A 1965 Rev. Mod Phys. 37 201
41. Friedman A 1961 J. Math. Mech. 10 625 Friedman A 1965 Rev. Mod Phys. 37 201
42. Schouten J A and Struik D J 1921 Am. J. Math. 43 213
43. Kasner E 1921 Am. J. Math. 43 126 Kasner E 1921 Am. J. Math. 43 130
44. Kasner E 1921 Am. J. Math. 43 126 Kasner E 1921 Am. J. Math. 43 130
45. See for example Misner C W, Thorne K S and Wheeler J A 1973 Gravitation (San Francisco, CA: Freeman)
46. See for example Wald RM 1984 General Relativity (Chicago, IL: University of Chicago Press)
47. Magaard L 1963 Zur einbettung riemannscher raume in Einstein-raume und konforeuclidische raume PhD Thesis Kiel
48. Goenner H 1980 General Relativity and Gravitation One Hundred Years after the Birth of Albert Einstein vol I (New York: Plenum) p 441
49. Romero C, Tavakol R and Zalaletdinov R 1996 Gen. Rel. Grav 28 365
50. Brinkman H W 1925 Math. Ann. 94 119
51. Baldwin O R and Jeffery G B 1926 Proc. R. Soc. A 111 95
52. Penrose R 1965 Rev. Mod Phys. 37 215
53. Guven R 1987 Phys. Lett. 191B 275 Amati D and Klimcik C 1989 Phys. Lett. B 219 443
54. Guven R 1987 Phys. Lett. 191B 275 Amati D and Klimcik C 1989 Phys. Lett. B 219 443
55. Horowitz G T and Steif A R 1990 Phys. Rev. Lett. 64 260 Horowitz G T and Steif A R 1990 Phys. Rev. D 42 1950
56. Horowitz G T and Steif A R 1990 Phys. Rev. Lett. 64 260 Horowitz G T and Steif A R 1990 Phys. Rev. D 42 1950
57. Brinkman H W 1923 Proc. Natl Acad. Sci. 9 1
58. Friedan D 1980 Phys. Rev. Lett. 45 1057 Jack I, Jones D and Mohammedi N 1989 Nucl. Phys. B 322 431 Callan C, Friedan D, Martinec E and Perry M 1985 Nucl. Phys. B 262 593
59. Friedan D 1980 Phys. Rev. Lett. 45 1057 Jack I, Jones D and Mohammedi N 1989 Nucl. Phys. B 322 431 Callan C, Friedan D, Martinec E and Perry M 1985 Nucl. Phys. B 262 593
60. Friedan D 1980 Phys. Rev. Lett. 45 1057 Jack I, Jones D and Mohammedi N 1989 Nucl. Phys. B 322 431 Callan C, Friedan D, Martinec E and Perry M 1985 Nucl. Phys. B 262 593
61. Hawking S W and Ellis G F R 1973 The Large Scale Structure of Spacetime (Cambridge: Cambridge University Press)
62. Clarke C J S 1970 Proc. R. Soc. A 314 417
63. Horowitz G T and Steif A R 1991 Phys. Lett. B 258 91
64. Deser S, Jackiw R and t'Hooft G 1984 Ann. Phys. 152 220
65. Vilenkin A 1981 Phys. Rev. D 23 852
66. Hiscock W A 1985 Phys. Rev. D 31 3288
67. Starobinsky A A 1980 Phys. Lett. 91B 99 Guth A H 1981 Phys. Rev. D 23 347 Sato K 1981 Mon. Not. R. Astron. Soc. 195 467 Linde A D 1982 Phys. Lett. 108B 389 Albrecht A and Steinhardt P J 1982 Phys. Rev. Lett. 48 1220
68. Starobinsky A A 1980 Phys. Lett. 91B 99 Guth A H 1981 Phys. Rev. D 23 347 Sato K 1981 Mon. Not. R. Astron. Soc. 195 467 Linde A D 1982 Phys. Lett. 108B 389 Albrecht A and Steinhardt P J 1982 Phys. Rev. Lett. 48 1220
69. Starobinsky A A 1980 Phys. Lett. 91B 99 Guth A H 1981 Phys. Rev. D 23 347 Sato K 1981 Mon. Not. R. Astron. Soc. 195 467 Linde A D 1982 Phys. Lett. 108B 389 Albrecht A and Steinhardt P J 1982 Phys. Rev. Lett. 48 1220
70. Starobinsky A A 1980 Phys. Lett. 91B 99 Guth A H 1981 Phys. Rev. D 23 347 Sato K 1981 Mon. Not. R. Astron. Soc. 195 467 Linde A D 1982 Phys. Lett. 108B 389 Albrecht A and Steinhardt P J 1982 Phys. Rev. Lett. 48 1220
71. Starobinsky A A 1980 Phys. Lett. 91B 99 Guth A H 1981 Phys. Rev. D 23 347 Sato K 1981 Mon. Not. R. Astron. Soc. 195 467 Linde A D 1982 Phys. Lett. 108B 389 Albrecht A and Steinhardt P J 1982 Phys. Rev. Lett. 48 1220
72. Olive K A 1990 Phys. Rep. 190 307 Liddle A R and Lyth D H 1993 Phys. Rep. 231 1
73. Olive K A 1990 Phys. Rep. 190 307 Liddle A R and Lyth D H 1993 Phys. Rep. 231 1
74. Mashhoon B, Liu H and Wesson P S 1994 Phys. Lett. B 331 305