Lovelock tensor as generalized Einstein tensor

General Relativity and Gravitation

Volumn 41, Issue 1, 2009, Pages 117-129

  Farhoudi, Mehrdad ^a  

^a SHAHID BEHESHTI UNIVERSITY   (Iran)

Author keywords

Higher order gravity; Lovelock Einstein tensors; Trace operator

Indexed keywords

EID: 58149335521     PISSN: 00017701     EISSN: 15729532     Source Type: Journal    
DOI: 10.1007/s10714-008-0658-9     Document Type: Article

References (45)

1. Weyl, H.: Gravitation und Elektrizität. Preuss. Akad. Wiss. Berlin Sitz. 465-480 (1918)
2. H. Weyl 1919 Eine neue Erweiterung der Relativitätstheorie Ann. der Phys. 59 101 133
3. Weyl, H.: Raum-Zeit-Materie, (Springer-Verlag, Berlin, 1st ed. 1918, 4th ed. 1921). Its English version (of the 4th ed.) is: Space-Time-Matter, translated by: H. L. Brose (Dover Publications, New York, 1st ed. 1922, reprinted 1950)
4. H. Weyl 1921 Über die physikalischen Grundlagen der erweiterten Relativitätstheorie Phys. Zeitschr. 22 473 480
5. Eddington, A.: The Mathematical Theory of Relativity. (Cambridge University Press, 1st ed. 1923, 2nd ed. 1924, Chelsee Publishing Co., New York, 1975)
6. Farhoudi, M.: Non-linear Lagrangian Theories of Gravitation. Ph.D. Thesis. Queen Mary & Westfield College, University of London (1995)
7. Wheeler J.A. (1968). Einstein's Vision. Springer, Berlin
8. R. Utiyama B.S. DeWitt 1962 Renormalization of a classical gravitational interacting with quantized matter fields J. Math. Phys. 3 608 618
9. Birrell N.D. and Davies P.C.W. (1982). Quantum Fields in Curved Space. Cambridge University Press, London
10. Buchbinder I.L., Odintsov S.D. and Shapiro I.L. (1992). Effective Action in Quantum Gravity. Institute of Physics Publishing, Bristol
11. K.S. Stelle 1977 Renormalization of higher derivative quantum gravity Phys. Rev. D16 953 969
12. E.S. Fradkin A.A. Tseytalin 1982 Renormalizable asymptotically free quantum theory of gravity Nucl. Phys. B201 469 491
13. K.S. Stelle 1978 Classical gravity with higher derivatives Gen. Rel. Grav. 9 353 371
14. B. Zwiebach 1985 Curvature squared terms and string theories Phys. Lett. 156B 315 317
15. B. Zumino 1986 Gravity theories in more than four dimensions Phys. Rev. 137 109 114
16. D. Lovelock 1971 The Einstein tensor and its generalizations J. Math. Phys. 12 498 501
17. D. Lovelock 1972 The four dimensionality of space and the Einstein tensor J. Math. Phys. 13 874 876
18. Briggs, C.C.: Some possible features of general expressions for Lovelock tensors and for the coefficients of Lovelock Lagrangians up to the 15th order in curvature (and beyond), gr-qc/9808050
19. Misner C.W., Thorne K.S. and Wheeler J.A. (1973). Gravitation. W. H. Freeman & Company, San Francisco
20. Isham, C.J.: Quantum gravity. In: MacCallum M.A.H. (ed.) Proc. 11th General Relativity and Gravitation, Stockholm, 1986, pp. 99-129. Cambridge University Press, London (1987)
21. M. Farhoudi 2006 On higher order gravities, their analogy to GR, and dimensional dependent version of Duff's trace anomaly relation Gen. Rel. Grav. 38 1261 1284
22. S. Nojiri S.D. Odintsov 2007 Introduction to modified gravity and gravitational alternative for dark energy Int. J. Geom. Meth. Mod. Phys. 4 115 146
23. M. Farhoudi 2005 Classical trace anomaly Int. J. Mod. Phys. D14 1233 1250
24. S. Gottlöber H.-J. Schmidt A.A. Starobinsky 1990 Sixth-order gravity and conformal transformations Class. Quant. Grav. 7 893 900
25. 2 inflation Phys. Lett. B245 348 354
26. H.A. Buchdahl 1962 On the gravitational field equations arising from the square of a Gaussian curvature Nuovo Cim. 23 141 157
27. G.V. Bicknell 1974 Non-viability of gravitational theory based on a quadratic Lagrangian J. Phys. A: Math. Nucl. Gen. 7 1061 1069
28. K.S. Stelle 1978 Classical gravity with higher derivatives Gen. Rel. Grav. 9 353 371
29. W. Maluf 1987 Conformal invariance and torsion in general relativity Gen. Rel. Grav. 19 57 71
30. Dadhich, N.: On the derivation of the gravitational dynamics. gr-qc/0802.3034
31. Farhoudi, M. New derivation of Weyl invariants in six dimensions. Work in progress
32. G. Magnano M. Ferraris M. Francaviglia 1987 Non-linear gravitational Lagrangians Gen. Rel. Grav. 19 465 479
33. G. Magnano M. Ferraris M. Francaviglia 1990 Legendre transformation and dynamical structure of higher derivative gravity Class. Quant. Grav. 7 557 570
34. H. Sirousse Zia 1994 Singularity theorems and the general relativity + additional matter fields formulation of metric theories of gravitation Gen. Rel. Grav. 26 587 597
35. J.D. Barrow S. Cotsakis 1988 Inflation and the conformal structure of higher order gravity theories Phys. Lett. B214 515 518
36. A. Hindawi B.A. Ovrut D. Waldram 1996 Non-trivial vacua in higher derivative gravitation Phys. Rev. D53 5597 5608
37. Farhoudi, M.: Lovelock metric as a generalized metric. work in progress
38. M.J. Duff 1977 Observations on conformal anomalies Nucl. Phys. B125 334 348
39. S. Nojiri S.D. Odintsov M. Sasaki 2005 Gauss-Bonnet dark energy Phys. Rev. D71 123509
40. Cognola, G., Elizalde, E., Nojiri, S., Odintsov, S.D., Zerbini, S.: String-inspired Gauss-Bonnet gravity reconstructed from the universe expansion history and yielding the transition from matter dominance to dark energy. hep-th/0611198
41. T. Koivisto D.F. Mota 2007 Cosmology and astrophysical constraints of Gauss-Bonnet dark energy Phys. Lett. B644 104 108
42. S. Tsujikawa M. Sami 2007 String-inspired cosmology: a late time transition from scaling matter era to dark energy universe caused by a Gauss-Bonnet coupling JCAP 01 006
43. M. Sami A. Toporensky P.V. Tretjakov S. Tsujikawa 2005 The fate of (phantom) dark energy universe with string curvature corrections Phys. Lett. B619 193 200
44. S. Nojiri S.D. Odintsov M. Sami 2006 Dark energy cosmology from higher-order string-inspired gravity and its reconstruction Phys. Rev. D74 046004
45. G. Calcagni S. Tsujikawa M. Sami 2005 Dark energy and cosmological solutions in second-order string gravity Class. Quant. Grav. 22 3977 4006