Projective and amplified symmetries in metric-affine theories. (English) Zbl 1481.83012


83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83C40 Gravitational energy and conservation laws; groups of motions
51E15 Finite affine and projective planes (geometric aspects)
83B05 Observational and experimental questions in relativity and gravitational theory
81V22 Unified quantum theories
58A15 Exterior differential systems (Cartan theory)


Full Text: DOI arXiv


[1] Aldrovandi, R.; Pereira, J. G., Teleparallel Gravity (2013), Berlin: Springer, Berlin
[2] Bejarano, C.; Delhom, A.; Jiménez-Cano, A.; Olmo, G. J.; Rubiera-Garcia, D., Geometric inequivalence of metric and Palatini formulations of general relativity (2019)
[3] Bernal, A. N.; Janssen, B.; Jiménez-Cano, A.; Orejuela, J. A.; Sánchez, M.; Sánchez-Moreno, P., On the (non-)uniqueness of the Levi-Civita solution in the Einstein-Hilbert-Palatini formalism, Phys. Lett. B, 768, 280-287 (2017) · Zbl 1370.53062
[4] Burton, H.; Mann, R. B., Palatini variational principle for an extended Einstein-Hilbert action, Phys. Rev. D, 57, 4754-4759 (1998)
[5] Cartan, E., On Manifolds with Affine Connection and the Theory of General Relativity (1986), Napoli: Bibliopolis, Napoli
[6] Cho, Y. M., Einstein Lagrangian as the translational Yang-Mills Lagrangian, Phys. Rev. D, 14, 2521-2525 (1976)
[7] Cho, Y. M., A generalisation of Cartan theory of gravitation, J. Phys. A: Math. Gen., 11, 2385-2387 (1978)
[8] Dadhich, N.; Pons, J. M., On the equivalence of the Einstein-Hilbert and the Einstein-Palatini formulations of general relativity for an arbitrary connection, Gen. Relativ. Gravit., 44, 2337-2352 (2012) · Zbl 1250.83047
[9] Einstein, A., Einheitliche Feldtheorie von Gravitation und Elektrizität [A Unified Field Theory of Gravitation and Electricity], Sitz. Pruess. Akad. Wiss., 22, 414-419 (1925) · JFM 51.0704.06
[10] Ferraris, M.; Francaviglia, M.; Reina, C., Variational formulation of general relativity from 1915 to 1925 ‘Palatini’s method’ discovered by Einstein in 1925, Gen. Relativ. Gravit., 14, 243-254 (1982) · Zbl 0541.49019
[11] García-Parrado, A.; Stein, L., xTerior: exterior calculus in Mathematica (2018)
[12] Giachetta, G.; Mangiarotti, L., Projective invariance and Einstein’s equations, Gen. Relativ. Gravit., 29, 5-18 (1997) · Zbl 0872.53065
[13] Hammond, R. T., Torsion gravity, Rep. Prog. Phys., 65, 599-649 (2002)
[14] Harada, J., Connection independent formulation of general relativity, Phys. Rev. D, 101 (2020)
[15] Hayashi, K.; Shirafuji, T., New general relativity, Phys. Rev. D, 19, 3524-3553 (1979) · Zbl 1267.83090
[16] Hehl, F. W.; Kerlick, G. D., Metric-affine variational principles in general relativity. I. Riemannian space-time, Gen. Relativ. Gravit., 9, 691-710 (1978) · Zbl 0412.53034
[17] Hehl, F. W.; Lord, E. A.; Smalley, L. L., Metric-affine variational principles in general relativity II. Relaxation of the Riemannian constraint, Gen. Relativ. Gravit., 13, 1037-1056 (1981) · Zbl 0477.53037
[18] Hehl, F. W.; McCrea, J. D.; Mielke, E. W.; Ne’eman, Y., Metric-affine gauge theory of gravity: field equations, Noether identities, world spinors, and breaking of dilation invariance, Phys. Rep., 258, 1-171 (1995)
[19] Hehl, F. W.; von der Heyde, P.; Kerlick, G. D.; Nester, J. M., General relativity with spin and torsion: foundations and prospects, Rev. Mod. Phys., 48, 393-416 (1976) · Zbl 1371.83017
[20] Järv, L.; Rünkla, M.; Saal, M.; Vilson, O., Nonmetricity formulation of general relativity and its scalar-tensor extension, Phys. Rev. D, 97 (2018)
[21] Beltrán Jiménez, J.; Heisenberg, L.; Koivisto, T., Coincident general relativity, Phys. Rev. D, 98 (2018)
[22] Jiménez, J. B.; Heisenberg, L.; Koivisto, T., The coupling of matter and spacetime geometry, Class. Quantum Grav., 37 (2020)
[23] Hehl, F. W.; Kerlick, G. D.; von der Heyde, P.; Hehl, F. W.; Kerlick, G. D.; von der Heyde, P.; Hehl, F. W.; Kerlick, G. D.; von der Heyde, P., On hypermomentum in general relativity I. The notion of hypermomentum. On hypermomentum in general relativity II. The geometry of spacetime. On hypermomentum in general relativity III. Coupling hypermomentum to geometry, Z. Naturforsch. A. Z. Naturforsch. A. Z. Naturforsch. A, 31, 823 (1976)
[24] Hehl, F. W.; Lord, E. A.; Ne’eman, Y., Hypermomentum in hadron dynamics and in gravitation, Phys. Rev. D, 17, 428-433 (1978)
[25] Hehl, F. W.; Lord, E. A.; Ne’eman, Y., Hadron dilation, shear and spin as components of the intrinsic hypermomentum current and metric-affine theory of gravitation, Phys. Lett. B, 71, 432-434 (1977)
[26] Kibble, T. W B., Lorentz invariance and the gravitational field, J. Math. Phys., 2, 212-221 (1961) · Zbl 0095.22903
[27] Kopczyński, W., Variational principles for gravity and fluids, Ann. Phys., 203, 308-338 (1990) · Zbl 0737.58018
[28] Luz, P.; Mena, F. C., Singularity theorems and the inclusion of torsion in affine theories of gravity, J. Math. Phys., 61 (2020) · Zbl 1436.83050
[29] Luz, P.; Vitagliano, V., Raychaudhuri equation in spacetimes with torsion, Phys. Rev. D, 96 (2017)
[30] Schücker, T.; Göckeler, M., Differential Geometry, Gauge Theories and Gravity (1989), Cambridge: Cambridge University Press, Cambridge · Zbl 0682.53002
[31] Mannheim, P. D.; Kazanas, D., Exact vacuum solution to conformal Weyl gravity and galactic rotation curves, Astrophys. J., 342, 635-638 (1989)
[32] Moon, T.; Lee, J.; Oh, P., Conformal invariance in Einstein-Cartan-Weyl space, Mod. Phys. Lett. A, 25, 3129-3143 (2010) · Zbl 1208.83125
[33] Ne’eman, Y.; Šijački, D., Unified affine gauge theory of gravity and strong interactions with finite and infinite \(####\) spinor fields, Ann. Phys., 120, 292-315 (1979)
[34] Nester, J. M.; Yo, H. J., Symmetric teleparallel general relativity, Chin. J. Phys., 37, 113 (1999)
[35] Palatini, A., Deduzione invariantiva delle equazioni gravitazionali dal principio di Hamilton, Rend. Circ. Matem. Palermo, 43, 203-212 (1919) · JFM 47.0698.02
[36] Popławski, N. J., On the nonsymmetric purely affine gravity, Mod. Phys. Lett. A, 22, 2701-2720 (2007) · Zbl 1158.83005
[37] Romero, C.; Fonseca-Neto, J. B.; Pucheu, M. L., General relativity and Weyl geometry, Class. Quantum Grav., 29 (2012) · Zbl 1248.83113
[38] Sandberg, V. D., Are torsion theories of gravitation equivalent to metric theories?, Phys. Rev. D, 12, 3013-3018 (1975)
[39] Sciama, D. W., The physical structure of general relativity, Rev. Mod. Phys., 36, 463-469 (1964)
[40] Trautman, A.; Trautman, A.; Trautman, A., On the Einstein-Cartan equations I. On the Einstein-Cartan equations II. On the Einstein-Cartan equations III, Bull. Acad. Pol. Sci.. Bull. Acad. Pol. Sci.. Bull. Acad. Pol. Sci., 20, 895-896 (1972)
[41] Trautman, A., On the Einstein-Cartan equations IV, Bull. Acad. Pol. Sci., 21, 346-345 (1973)
[42] Trautman, A., On the structure of Einstein-Cartan equations, Differential Geometry, 139-162 (1973), London: Academic, London
[43] Trautman, A., Recent advances in the Einstein-Cartan theory of gravity, Ann. New York Acad. Sci., 262, 241-245 (1975)
[44] Trautman, A., Einstein-Cartan theory, Encyclopedia of Mathematical Physics, vol 2, 189-195 (2006), Oxford: Elsevier, Oxford
[45] Pasmatsiou, K.; Tsagas, C. G.; Barrow, J. D., Kinematics of Einstein-Cartan universes, Phys. Rev. D, 95 (2017)
[46] Vitagliano, V., The role of nonmetricity in metric-affine theories of gravity, Class. Quantum Grav., 31 (2014) · Zbl 1286.83088
[47] Vitagliano, V.; Sotiriou, T. P.; Liberati, S., The dynamics of metric-affine gravity, Ann. Phys., 326, 1259-1273 (2011) · Zbl 1223.83044
[48] Weinberg, S., The Quantum Theory of Fields, vol 1 (1995), Cambridge: Cambridge University Press, Cambridge
[49] Wheeler, J. T., Weyl geometry, Gen. Relativ. Gravit., 50, 80 (2018) · Zbl 1398.83090
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