On higher order gravities, their analogy to GR, and dimensional dependent version of Duff's trace anomaly relation

General Relativity and Gravitation

Volumn 38, Issue 8, 2006, Pages 1261-1284

  Farhoudi, Mehrdad ^a  

^a SHAHID BEHESHTI UNIVERSITY   (Iran)

Author keywords

Higher order gravity; Non linear Lagrangian; Weyl anomaly

Indexed keywords

EID: 33748310806     PISSN: 00017701     EISSN: 15729532     Source Type: Journal    
DOI: 10.1007/s10714-006-0304-3     Document Type: Article

References (202)

1. Isham, C.J.: Quantum gravity. In: MacCallum, M.A.H. (ed.) Proceeding 11th General Relativity and Gravitation, Stockholm, 1986, Cambridge University Press, 1987, pp. 99-129: Structural issues in quantum gravity, gr-qc/9510063
2. Newman, E.T., Goenner, H.: Classical and quantum alternatives to gravitational theories. In: Bertotti, B., de Felice, F., Pascolini, A. (eds.) Proceeding 10th General Relativity and Gravitation, Padua, Italy, 1983, D Reidel Publishing Company, Holland, 1984, pp. 199-21.1;
3. Goenner, H.: Alternative theories of gravity. In: MacCallum, M.A.H. (ed.) Proceedings 11th General Relativity and Gravitation, Stockholm, 1986, Cambridge University Press (1987), pp. 262-273;
4. Francaviglia, M.: Alternative gravity theories. In: Ashby, N., Bartlett, D.F., Wyss, W. (eds.)Proceeding 12th General Relativity and Gravitation, Boulder, 1989, Cambridge University Press, 1990, pp. 99-104
5. Hilbert, D.: Die Grundlagen der Physik. I & II, Nachr. Gesel. Wiss. Göttingen, 395-407 (1915) and 53-76 (1917) respectively.
6. These were consolidated with the same title into: Math. Annalen 92, 1-32 (1924)
7. Weyl, H.: Gravitation und Elektrizität Preuss. Akad. Wiss. Berlin, Sitz. 465-480 (1918);
8. Eine neue Erweiterung der Relativitätstheorie, Ann. der Phys. 59, 101-133 (1919);
9. Raum-Zeit-Materie, Springer Berlin Heidelberg New York, 1st edn. 1918, 4th edn. 1921. Its English version (of the 4th edn.) is translated by: Brose, H.L.: Space-Time-Matter, Dover Publications, New York, 1st edn. 1922, reprinted 1950;
10. Über die physikalischen Grundlagen der erweiterten Relativiätstheorie. Phys. Zeitschr. 22, 473-480 (1921)
11. Eddington, A.: The Mathematical Theory of Relativity. Cambridge University Press, Cambridge 1st edn. (1923), 2nd edn. (1924) Chelsee Publishing Co., New York, 1975
12. Stelle, K.S.: Classical gravity with higher derivatives. Gen. Rel. Grav. 9, 353-371 (1978)
13. Maluf, W.: Conformal invariance and torsion in general relativity. Gen. Rel. Grav. 19, 57-71 (1987)
14. Bach, R.: Zur Weylschen Relativitätstheorie und der Weylschen Erweiterung des Krümmungstensorbegriffs. Math. Zeitschr. 9, 110-135 (1921.)
15. Lanczos, C: Elektromagnetismus als natürliche Eigenschaft der Riemanns chen Geometrie. Zeits. Phys. 73, 147-168 (1931);
16. Electricity and general relativity. Rev. Mod. Phys. 29, 337-350 (1957)
17. Buchdahl, H.A.: On the gravitational field equations arising from the square of a Gaussian curvature. Nuovo Cim. 23, 141-157 (1962);
18. Bicknell, G.V.: Non-viability of gravitational theory based on a quadratic Lagrangian. J. Phys. A: Math. Nucl. Gen. 7, 1061-1069 (1974)
19. Clifton. T., Barrow, J.D.: The power of general relativity. Phys. Rev. D 72, 103005 (2005) gr-qc/0509059
20. Barrow, J.D., Clifton, T.: Exact cosmological solutions of scale-invariant gravity theories. Class, Quantum Grav. 23, L1-L7 (2006) gr-qc/0509085
21. Buchdahl, H.A.: Non-linear Lagrangians and cosmological theory. Mon. Not. R. Astr. Soc. 150, 1-8 (1970)
22. Wheeler, J.A.: Einstein's Vision. Springer, Berlin Heidelberg New York (1968)
23. Isham, C.J: Structural issues in quantum gravity, gr-qc/9510063, (lectures delivered at the GR14 Conference, Florence, August 1995)
24. Cecotti, S., Ferrara, S., Girardello, L., Porrati, M., Pasquinucci, A.: Matter coupling in higher derivative supergravity. Phys. Rev. D 33, R2504-R2507 (1986)
25. Birrell, N.D., Davies, P.C.W.: Quantum Fields in Curved Space. Cambridge University Press, Cambridge (1982);
26. Buchbinder, I.L., Odintsov, S.D., Shapiro, I.L.: Effective Action in Quantum Gravity. Institute of Physics Publishing Bristol and Philadelphia (1992)
27. Utiyama, R., DeWitt, B.S.: Renormalization of a classical gravitational interacting with quantized matter fields. J. Math. Phys. 3, 608-618 (1962);
28. Pechlaner, E., Sexl, R.: On quadratic Lagrangians in general relativity. Commun. Math. Phys. 2, 165-175 (1966)
29. Chern, S-S.: A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds. Ann. Math 45, 747-752 (1944);
30. On the curvatura integra in a Riemannian manifold, Ann. Math ibid. 46, 674-684 (1945);
31. Kobayashi, S., Nomizu, K.: Foundations of Differential Geometry, vol. II. Wiley Interscience, New York (1969);
32. Spivak, M.: A Comprehensive Introduction to Differential Geometry, 2nd edn, vol. 5. Publish or Perlish Inc., Delaware (1979)
33. Stelle, K.S.: Renormalization of higher derivative quantum gravity. Phys. Rev. D 16, 953-969 (1977)
34. Fradkin, E.S., Tseytalin, A.A.: Renormalizable asymptotically free quantum theory of gravity. Nucl. Phys. B 201, 469-491 (1982)
35. Candelas, P., Horowitz, G.T., Strominger, A., Witten, E.: Vacuum configurations for superstrings. Nucl. Phys. B 258, 46-74 (1985);
36. Metsaev, R.R., Tseytlin, A.A.: Curvature cubed terms in string theory effective actions. Phys. Lett. B 185, 52-58 (1987);
37. Green, M.B., Schwarz, J.H., Witten, E.: Superstring Theory, vols. 1, 2. Cambridge University Press, Cambridge (1987);
38. Lust, D., Theusen, S.: Lectures on String Theory. Springer, Berlin Heidelberg New York (1989);
39. Ketov, S.V.: The string generated correction to Einstein gravity from the sigma model approach. Gen. Rel. Grav. 22, 193-202 (1990);
40. Polchinski, I: String Theory. Cambridge University Press, Cambridge (1998)
41. Deser, S.: Gravity from strings. Phys. Scripta T15, 138-142 (1987)
42. Lovelock, D.: The Einstein tensor and its generalizations. I Math. Phys. 12, 498-501 (1971);
43. The four dimensionality of space and the Einstein tensor, I Math. Phys. ibid. 13, 874-876 (1972)
44. Briggs, C.G: 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
45. Wald, R.M.: General Relativity. The University of Chicago Press (1984)
46. Zwiebach, B.: Curvature squared terms and string theories. Phys. Lett. B 156, 315-317 (1985);
47. Zumino, B.: Gravity theories in more than four dimensions. Phys. Rep. 137, 109-114 (1986)
48. Duff, M.J., Nilsson, B.E.W., Ripe, C.N.: Gauss-Bonnet from Kaluza-Klein. Phys. Lett. B 173, 69-72 (1986)
49. Chamseddine, A.H.: Topological gauge theory of gravity in five and all odd dimensions. Phys. Lett. B 233, 291-294 (1989);
50. Müller-Hoissen, F.: From Chern-Simons to Gauss-Bonnet. Nucl. Phys. B 346, 235-252 (1990)
51. Allemandi, G., Francaviglia, M., Raiteri, M.: Charges and energy in Chern-Simons theories and Lovelock gravity. Class. Quantum Grav. 20, 5103-5120 (2003)
52. Nojiri, S., Odintsov, S.D.: Where new gravitational physics comes from M-theory? Phys. Lett. B 576, 5-11 (2003)
53. Simon, J.Z.: Higher derivative Lagrangians, non-locality, problems, and solutions. Phys. Rev. D 41, 3720-3733 (1990)
54. Cnockaert, S., Henneaux, M.: Lovelock terms and BRST cohomology. Class. Quantum Grav. 22, 2797-2810 (2005)
55. Madore, X: Cosmological applications of the Lanczos Lagrangian. Class. Quantum Grav. 3, 361-371 (1986);
56. Deruelle, N., Madore, J.: Kaluza-Klein cosmology with the Lovelock Lagrangian. In: Origin and early history of the universe, Proceeding 26th Liège International Astrophysical Colloquium, Belgium, July 1986, pp. 277-283 Cointe-Ougree, Belgium. (1987);
57. Mena Marugán, O.A.: Classical and quantum Lovelock cosmology. Phys. Rev. D 42, 2607-2620 (1990);
58. Lovelock gravity and classical wormholes. Class. Quantum Grav. 8, 935-946 (1991);
59. Poisson, E.: Quadratic gravity and the black hole singularity. Phys. Rev. D 43, 3923-3928 (1991);
60. Cotsakis, S.: Cosmological models in higher order gravity. Ph.D. Thesis, Sussex University (1990);
61. Fariña-Busto, L.: Non-linear gravitational Lagrangians in cosmology. Ph.D. Thesis, Queen Mary & Westfield College, University of London (1990)
62. n gravity. Class. Quantum Grav. 22, 4839-4868 (2005)
63. 2 inflation. Phys. Lett. B 245, 348-354 (1990)
64. Schmidt, H-J.: Variational derivatives of arbitrarily high order and multi-inflation cosmological models. Class. Quantum Grav. 7, 1023-1031 (1990);
65. Berkin, A.L., Maeda, K.: Inflation in generalized Einstein theories. Phys. Rev. D 44, 1691-1704 (1991)
66. 3 and RR terms. Astron. Nachr. 312, 291-297 (1991)
67. Dehghani, M.H.: Magnetic branes in Gauss-Bonnet gravity. Phys. Rev. D 69, 064024 (2004);
68. Meng, X.-H., Wang, P.: Inflationary attractor in Gauss-Bonnet brane cosmology. Class Quantum Grav. 21, 2527-2536 (2004)
69. Allemandi, G., Borowiec, A., Francaviglia, M.: Accelerated cosmological models in Ricci squared gravity. Phys. Rev. D 70, 103503 (2004);
70. Dehghani, M.H.: Accelerated expansion of the universe in Gauss-Bonnet gravity. Phys. Rev. D 70, 064009 (2004);
71. Carroll, S.M., Duvvuri, V., Trodden, M., Turner, M.S.: Is cosmic speed-up due to new gravitational physics? Phys. Rev. D 70, 043528 (2004);
72. Capozziello, S., Cardone, V.F., Carloni, S., Troisi, A.: Curvature quintessence matched with observational data. Int. J. Mod. Phys. D 12, 1969-1982 (2003);
73. Higher order curvature theories of gravity matched with observations: a bridge between dark energy and dark matter problems, astro-ph/0411114;
74. Poplawski, N.J.: The present and late universe in the Einstein frame, metric-affine 1/R gravity, gr-qc/0511071;
75. Atazadeh, K., Sepangi, H.R.: Accelerated expansion in modified gravity with a Yukawa-like term, gr-qc/0602028
76. Nojiri, S., Odintsov, S.D.: Modified gravity with 1nR terms and cosmic acceleration. Gen. Rel. Grav. 36, 1765-1780 (2004)
77. Nojiri, S., Odintsov, S.D.: Modified gravity with negative and positive powers of the curvature: unification of the inflation and of the cosmic acceleration. Phys. Rev. D 68, 123512 (2003);
78. Poplawski, N.J.: Acceleration of the universe in the Einstein frame of a metric-affine f (R) gravity. Class. Quantum Grav. 23, 2011-2020 (2006) gr-qc/0510007
79. Chiba, T.: 1/R gravity and scalar-tensor gravity. Phys. Lett. B 575, 1-3 (2003)
80. Soussa, M.E., Woodard, R.P.: The force of gravity from a Lagrangian containing inverse powers of the Ricci scalar. Gen. Rel. Grav. 36, 855-862 (2004)
81. Dolgov, A.D., Kawasaki, M.: Can modified gravity explain accelerated cosmic expansion? Phys. Lett. B 573, 1-4 (2003)
82. Nojiri, S., Odintsov, S.D.: The minimal curvature of the universe in modified gravity and conformal anomaly resolution of the instabilities. Mod. Phys. Lett. A 19, 627-638 (2004)
83. Riess, A.G., et al.: Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astro. J. 116, 1009-1038 (1998);
84. Perlmutter, S., et al.: Measurements of omega and lambda from 42 high-redshift supernovae. Astrophys. J. 517, 565-586 (1999);
85. Tonry, J.L., et al.: Cosmological results from high-z supernovae. Astrophys. J. 594, 1-24 (2003)
86. Lee, A.T., et al.: A high spatial resolution analysis of the MAXIMA-1 cosmic microwave background anisotropy data. Astrophys. J. 561, L1-L6 (2001);
87. Netterfield, C.B., et al.: A measurement by BOOMERANG of multiple peaks in the angular power spectrum of the cosmic microwave background. Astrophys. J. 571, 604-614 (2002);
88. Halverson, N.W., et al.: DASI first results: a measurement of the cosmic microwave background angular power spectrum. Astrophys. J. 568, 38-45 (2002);
89. Spergel, D.N., et al.: First year Wilkinson microwave anisotropy probe (WMAP) observations: determination of cosmological parameters. Astrophys. J. Suppl. 148, 175-225 (2003)
90. Madsen, M.S., Barrow, J.D.: De Sitter ground states and boundary terms in generalized gravity. Nucl. Phys. B 323, 242-252 (1989)
91. Mardones, A., Zanelli, J.: Lovelock-Cartan theory of gravity. Class. Quantum Grav. 8, 1545-1558 (1991)
92. Palatini, A.: Deduzione invariantiva delle equazioni gravitazionali dal principio di Hamilton. Rend. Circ. Mat. Palermo 43, 203-212 (1919);
93. Stephenson, G.: Variational principles & gauge theories of gravitation. J. Phys. A10, 181-184 (1977)
94. Buchdahl, H.A.: Quadratic Lagrangians and Palatini's device. J. Phys. A12, 1229-1234 (1979)
95. Shahid-Saless, B.: Palatini variation of curvature squared action and gravitational collapse. J. Math. Phys. 32, 694-697 (1991)
96. 2 corrections to the cosmological dynamics of inflation in the Palatini formulation. Class. Quantum Grav. 21, 2029-2036 (2004);
97. -1 modified gravity with an additionally squared scalar curvature term. Class. Quantum Grav. ibid. 22, 23-32 (2005);
98. Sotiriou, T.P.: Unification of inflation and cosmic acceleration in the Palatini formalism. Phys. Rev. D 73, 063515 (2006) gr-qc/0509029;
99. Constraining f (R) gravity in the Palatini formalism. Class. Quantum Grav. 23, 1253-1267 (2006), gr-qc/0512017
100. Vollick, D.N.: 1/R curvature corrections as the source of the cosmological acceleration. Phys. Rev. D 68, 063510 (2003);
101. -1-modifled gravity. Class. Quantum Grav. 20, 4949-4962 (2003);
102. Cosmological evolution in 1/R gravity theory, Class. Quantum Grav. ibid. 21, 951-960 (2004);
103. Capozziello, S., Cardone, V.F., Francaviglia, M.:f(R) theories of gravity in Palatini matched with observations, astro-ph/0410135
104. Olmo, G.J., Komp, W.; Non-linear gravity theories in the metric and Palatini formalisms. gr-qc/0403092
105. Flanagan, E.E.: Palatini form of 1/R gravity. Phys. Rev. Lett. 92, 071101 (2004);
106. Higher order gravity theories and scalar tensor theories. Class. Quantum Grav. 21, 417-426 (2004);
107. Meng, X.-H., Wang, P.: Palatini formulation of modified gravity wih squared scalar curvature, astroph/0308284;
108. Palatini formulation of modified gravity with InR terms. Phys. Lett. B584, 1-7 (2004)
109. Vollick, D.N.: On the viability of the Palatini form of 1/R gravity. Class. Quantum Grav. 21, 3813-3816 (2004)
110. Kerner, R.: Cosmology without singularity and nonlinear gravitational Lagrangians. Gen. Rel. Grav. 14, 453-469 (1982);
111. Madore, J.: On the nature of the initial singularity in a Lanczos cosmological model. Phys. Lett. 111A, 283-284 (1985);
112. Horowitz, G.T., Steif, A.R.: Spacetime singularities in string theory. Phys. Rev. Lett. 64, 260-263 (1990)
113. Biswas, T., Mazumdar, A., Siegel, W.; Bouncing universes in string-inspired gravity. JCAP 0603, 009 (2006), hep-th/05081.94;
114. Carloni, S., Dunsby, P. K.S., Solomons, D.: Bounce conditions in f(R) cosmologies. Class. Quantum Grav. 23, 1913-1922 (2006), gr-qc/0510130
115. Barrow, J.D., Ottewill, A.C.: The stability of general relativistic cosmological theory. J. Phys. A 16, 2757-2776 (1.983);
116. Müller, V., Schmidt, H.-J., Starobinsky, A.A.: The stability of the de Sitter space-time in fourth order gravity. Phys. Lett. B 202, 198-200 (1988)
117. Faraoni, V: Modified gravity and the stability of de Sitter space. Phys. Rev. D 72, 061501 (2005)
118. 2 gravity: a new gauge and new solutions. Class. Quantum Grav. 6, 219-229 (1989)
119. Quant, I., Schmidt, H.-J.: The Newtonian limit of fourth and higher order gravity. Astron. Nachr. 312, 97-102 (1991)
120. Dick, R.: On the Newtonian limit in gravity models with inverse power of R. Gen. Rel. Grav. 36, 217-224 (2004);
121. Meng, X.-H., Wang, P.: Gravitational potential in Palatini formulation of modified gravity. Gen. Rel. Grav. 36, 1947-1954 (2004);
122. Domínguez, A.E., Barraco, D.E.: Newtonian limit of the singular f (R) gravity in the Palatini formalism. Phys. Rev. D 70, 043505 (2004);
123. Capozziello, S.: Newtonian limit of extended theories of gravity, gr-qc/0412088;
124. Olmo, G.J.: The gravity Lagrangian according to solar system experiments. Phys. Rev. Lett. 95, 261102 (2005), gr-qc/0505101;
125. Post-Newtonian constraints on f(R) cosmologies in metric formalism. gr-qc/0505135, plus Post-Newtonian constraints on f(R) cosmologies in Palatini formalism. gr-qc/0505136, both in Phys. Rev. D 72, 083505 (2005);
126. Allemandi, G., Francaviglia, M., Ruggiero, M.L., Tartaglia, A.: Post-Newtonian parameters from alternative theories of gravity. Gen. Rel. Grav. 37, 1891-1904 (2005), gr-qc/0506123;
127. Sotiriou, T.P.: The nearly Newtonian regime in non-linear theories of gravity, gr-qc/0507027
128. Cembranos, J.A.R.: The Newtonian limit at intermediate energies. Phys. Rev. D 73, 064029 (2006), gr-qc/0507039
129. Capozziello, S., Troisi, A.: PPN-limit of fourth order gravity inspired by scalar-tensor gravity. Phys. Rev. D 72, 044022 (2005), astro-ph/0507545
130. 2 theories of gravity without torsion. J. Math. Phys. 24, 2793-2799 (1983)
131. 2 gravity. Phys. Rev. D 30, 2257-2259 (1984);
132. Maluf, W.: Energy spectrum of quadratic theories of gravitation. Class. Quantum Grav. 6, 1189-1195 (1989);
133. 2 theories of gravitation, Class. Quantum Grav. ibid. L151-L154
134. Magnano, G., Sokolowski, L.M.: On physical equivalence between non-linear gravity theories and a general relativistic self-gravitating scalar field. Phys. Rev. D 50, 5039-5059 (1994)
135. Magnano, G., Ferraris, M., Francaviglia, M.: Non-linear gravitational Lagrangians. Gen. Rel. Grav. 19, 465-479 (1987);
136. Legendre transformation and dynamical structure of higher derivative gravity. Class. Quantum Grav. 7, 557-570 (1990);
137. Sirousse Zia, H.: Singularity theorems and the [general relativity + additional matter fields] formulation of metric theories of gravitation. Gen. Rel. Grav. 26, 587-597 (1994)
138. Brans, C.H.: Non-linear Lagrangians and the significance of the metric. Class. Quantum Grav. 5, L197-L199 (1988)
139. Ferraris, M., Francaviglia, M., Magnano, G: Do non-linear metric theories of gravitation really exist? Class. Quantum Grav. 5, L95-L99 (1988);
140. Remarks on the physical metric in non-linear theories of gravitation, Class. Quantum Grav. ibid. 7, 261-263 (1990);
141. Sokolowski, L.M.: Physical versions of non-linear gravity theories and positivity of energy. Class. Quantum. Grav. 6, 2045-2050 (1989)
142. Pascual-Sánchez, J.-F.: Variational principles and quantum gravity. In: Verdaguer, E., Garriga, J., Céspedes, J. (eds.) Recent developments in gravitation, Proceedings Relativity Meeting, Barcelona, Spain, Sept. 1989, pp. 397-404. World Scientific, Singapore (1990)
143. Barrow, J.D., Cotsakis, S.: Inflation and the conformal structure of higher order gravity theories. Phys. Lett. B 214, 515-518 (1988);
144. Maeda, K.: Towards the Einstein-Hilbert action via conformal transformation. Phys. Rev. D 39, 3159-3162 (1989);
145. Wands, D.; Extended gravity theories and the Einstein-Fulbert action. Class. Quantum Grav. 11, 269-280 (1994);
146. Hindawi, A., Ovrut, B. A., Waldram, D.: Non-trivial vacua in higher derivative gravitation. Phys. Rev. D 53, 5597-5608 (1996)
147. Gottlöber, S., Schmidt, H-J., Starobinsky, A.A.: Sixth-order gravity and conformal transformations. Class. Quantum Grav. 7, 893-900 (1990)
148. Boulware, D.G., Deser, S.: String-generated gravity models. Phys. Rev. Lett. 55, 2656 (1985);
149. Cai, R.G., Soh, K.S.: Topological black holes in the dimensionally continued gravity. Phys. Rev. D 59, 044013 (1999);
150. Nojiri, S., Odintsov, S.D., Ogushi, S.: Cosmological and black hole brane-world universe in higher derivative gravity. Phys. Rev. D 65, 023521 (2002);
151. Cvetic, M., Nojiri, S., Odintsov, S.D.: Black hole thermodynamics and negative entropy in de Sitter and anti-de Sitter Einstein-Gauss-Bonnet gravity. Nucl. Phys. B 628, 295-330 (2002);
152. Cai, R.G.: Gauss-Bonnet black holes in AdS spaces. Phys. Rev. D 65, 084014 (2002);
153. Cho, Y.M., Neupane, I.P.: Anti-de Sitter black holes, thermal phase transition and holography in higher curvature gravity. Phys. Rev. D 66, 024044 (2002)
154. Maartens, R., Taylor, DR.: Fluid dynamics in higher order gravity. Gen. Rel. Grav. 26, 599-613 (1994);
155. Rippl, S., van Elst, H., Tavakol, R., Taylor, D.: Kinematics and dynamics of f (R) theories of gravity. Gen. Rel. Grav. 28, 193-205 (1996);
156. Brevik, I., Nojiri, S., Odintsov, S.D., Vanzo. L.: Entropy and universality of Cardy-Verlinde formula in dark energy universe. Phys. Rev. D 70, 043520 (2004)
157. Buchdahl, H.A.: Über die Variationsableitung von fundamental-invarianten beliebig hoher Ordnung. Acta Math. 85, 63-72 (1951)
158. Amendola, L., Mayer, A.B., Capozziello, S., Gottlöber, S., Müller, V., Occhionero, F., Schmidt, H.-J.: Generalized sixth order gravity and inflation. Class. Quantum Grav. 10, L43-L47 (1993)
159. Stephenson, G.: Variational principles for the gravitational field. Lett. Nuovo Cim. 1, 97-99 (1969)
160. Roxburgh, I.W.: Non-linear Lagrangian theories of gravity. Gen. Rel. Grav. 8, 219-225 (1977);
161. Coley, A.A.: Homothetic vectors and higher order Lagrangian theories of gravity. Class. Quantum. Grav. 6, 1213-1218 (1989)
162. Farhoudi, M.: Lovelock tensor as generalized Einstein tensor, gr-qc/9510060
163. Farhoudi, M.: Classical trace anomaly. Int. J. Mod. Phys. D 14, 1233-1250 (2005)
164. Duff, M. J.: Twenty years of the Weyl anomaly. Class. Quantum Grav. 11, 1387-1403 (1994)
165. Asorey, M., Gorbar, E.V., Shapiro, I.L.: Universality and ambiguities of the conformal anomaly. Class. Quantum Grav. 21, 163-178 (2003)
166. Duff, M.J.: Observations on conformal anomalies. Nucl. Phys. B 125, 334-348 (1977)
167. Bonora, L., Cotta-Ramusino, P., Reina, C.: Conformal anomaly and cohomology. Phys. Lett. 126B, 305-308 (1983)
168. Bonora, L., Pasti, P., Bregola, M.: Weyl cocycles. Class. Quantum Grav. 3, 635-649 (1986)
169. 8 correspondence. Phys. Lett. B 500, 199-208 (2001)
170. Quiros, I.: The Weyl anomaly and the nature of the background geometry, gr-qc/0011056
171. Deser, S., Duff, M.J., Isham, C.J.: Non-local conformal anomalies. Nucl. Phys. B 111, 4555 (1976);
172. Christensen, S.M.: Regularization, renormalization, and covariant geodesic point separation. Phys. Rev. D 17, 946-963 (1978)
173. Avramidi, I.G.: New algebraic methods for calculating the heat kernel and effective action in quantum gravity and gauge theories. In: Fulling, S.A. (ed.) Heat Kernel Techniques and Quantum Gravity, Discourses in Mathematics and its Applications, pp. 115-140, Department of Mathematics, Texas A&M University (1995), gr-qc/9408028
174. Fulton, T., Rohrlich, F., Witten, L.: Conformal invariance in physics. Rev. Mod. Phys. 34, 442-457 (1962)
175. Müller-Hoissen, F.: Spontaneous compactification with quadratic and cubic curvature term. Phys. Lett. 163B, 106-110 (1985)
176. Farhoudi, M.: Non-linear Lagrangian theories of gravitation, Ph.D. Thesis, Queen Mary & Westfield College, University of London (1995)
177. Wheeler, J.T.: Symmetric solutions to the Gauss-Bonnet extended Einstein equations. Nucl. Phys. B 268, 737-746 (1986)
178. Farhoudi, M.: New derivation of Weyl invariants in six dimensions, work in progress
179. Deruelle, N., Fariña-Busto, L.: The Lovelock gravitational field equations in cosmology. Phys. Rev. D 41, 3696-3708 (1990)
180. Deser, S., Schwimmer, A.: Geometric classification of conformal anomalies in arbitrary dimensions. Phys. Lett. B 309, 279-284 (1993)
181. Hamber, H.W., Williams, R.M.: Two dimensional simplical quantum gravity. Nucl. Phys. B 267, 482-496 (1986);
182. Katanayev, M.O., Volovich, I.V.: Two dimensional gravity with dynamical torsion and string. Ann. Phys. 197, 1-32 (1990);
183. Yoneya, T.: Higher derivative quantum gravity in two dimensions. Phys. Lett. 149B, 111-116 (1984)
184. Brown, J.D.: Lower Dimensional Gravity. World Scientific, Singapore (1988)
185. Lichtenegger, H., Mashhoon, B.: Mach's principle. In: Iorio, L. (ed.) The Measurment of Gravitomagnetism: A Challenging Enterprise, pp. 13-27. NOVA Science, Hauppage, New York (2005), physics/0407078
186. Stachel, J.: Einstein's struggle with general covariance, 1912-1915, presented at General Relativity and Gravitation 9th, 1980 at Jena, Germany;
187. reprinted as Einstein's search for general covariance, 1912-1915 In: Howard, D., Stachel, J. (eds.) Proceedings Einstein and the History of General Relativity, Osgood Hill Conference, Massachusetts, May 1986, pp. 63-100. The Center for Einstein Studies, Boston Univ. (1989)
188. Einstein, A.: Wrote to: P Ehrenfest, on 26th December, 1915, EA 9-363; Wrote to: Besso, M. on 3rd January, 1916 in Albert Einstein, Michele Besso, Correspondence, 1903-1955, Speziali, P. (ed.) pp. 63-64. Hermann, Paris (1972)
189. Einstein, A.: Relativity and the problem of space (1952), Appendix 5 In: Relativity, the Special and the General Theory: A Popular Exposition, translated by: Lawson, R.W. (Methuen, London, 15th edition 1954), pp 135-157.
190. Adler, I.: A New Look at Geometry. John Day Com., New York (1966)
191. Mashhoon, B., Liu, H., Wesson, P.S.: Space-time-matter. In: Proceedings 7th Marcel Grossmann Meeting, pp. 333-335, Stanford, (1994)
192. Graves, J.C.: The Conceptual Foundation of Contemporary Relativity Theory. MIT Press, Cambridge (1971)
193. Ryan Jr. M.P., Shepley, L.C.: Homogeneous Relativistic Cosmologies. Princeton Univ. Press, New Jersy (1975)
194. Schwarzchild, k.: Über das gravitationsfeld eines massenpunktes nach der Einsteinschen theorie. Sitzber. Preuss. Akad. Wiss. Berlin 189-196 (1916);
195. Taub, A.M.: Empty space-times admitting a three parameter group of motions. Ann. Math. 53, 472-490 (1951);
196. Newman, E.T., Tamburino, L., Unti, T. J.: Empty-space generalization of the Schwarzchild metric. J. Math. Phys. 4, 915-923 (1963)
197. Abbassi, A.M.: Revisiting the Mach's and correspondence principle in general relativity and concept of inertia. Ph.D. Thesis, Tarbiat Modarres University, Tehran, Iran (2001)
198. Salam, A.: Gauge unification of fundamental forces. Rev. Mod. Phys. 52, 525-538 (1980)
199. Romero, C., Tavakol, R., Zalaletdinov, R.: The embedding of general relativity in five dimensions. Gen. Rel. Grav. 28, 365-376 (1996)
200. Wesson, P.S.: Space-Time-Matter, Modern Kaluza-Klein Theory. World Scientific, Singapore (1999);
201. Wesson, P.S.: In defence of Campbell's theorem as a frame for new physics. gr-qc/0507107
202. Farhoudi, M. (work in progress)