Mysteries of R^ik = 0: A novel paradigm in Einstein’s theory of gravitation

Abstract

Despite a century-long effort, a proper energy-stress tensor of the gravitational field, could not have been discovered. Furthermore, it has been discovered recently that the standard formulation of the energy-stress tensor of matter, suffers from various inconsistencies and paradoxes, concluding that the tensor is not consistent with the geometric formulation of gravitation [Astrophys. Space Sci., 2009, 321: 151; Astrophys. Space Sci., 2012, 340: 373]. This perhaps hints that a consistent theory of gravitation should not have any bearing on the energy-stress tensor. It is shown here that the so-called “vacuum” field equations Rik= 0 do not represent an empty spacetime, and the energy, momenta and angular momenta of the gravitational and the matter fields are revealed through the geometry, without including any formulation thereof in the field equations. Though, this novel discovery appears baffling and orthogonal to the usual understanding, is consistent with the observations at all scales, without requiring the hypothetical dark matter, dark energy or inflation. Moreover, the resulting theory circumvents the long-standing problems of the standard cosmology, besides explaining some unexplained puzzles.

Graphical abstract

Keywords

general relativity and gravitation – / fundamental problems and general formalism / cosmological observations

References

[1] R. G. Vishwakarma, Gravity of Rμν = 0: A new paradigm in GR, to appear in Open Astron. J., arXiv: 1206.2795 , 2012
[2] R. G. Vishwakarma, Mysteries of the geometrization of gravitation, arXiv: 1206.5789 , 2012
[3] R. G. Vishwakarma, Einstein’s gravity under pressure, Astrophys. Space Sci. , 2009, 321: 15110.1007/s10509-009-0016-8
[4] R. G. Vishwakarma, On the relativistic formulation of matter, Astrophys. Space Sci. , 2012, 340: 37310.1007/s10509-012-1051-4
[5] S. W. Hawking and G. F. R.Ellis, The Large Scale Structure of Spacetime, Cambridge: Cambridge University Press, 197310.1017/CBO9780511524646
[6] E. Kasner, Geometrical theorems on Einstein’s cosmological equations, Am. J. Math. , 1921, 43: 21710.2307/2370192
[7] V. V. Narlikar and K. R. Karmarkar, A curious solution of Einstein’s field equations, Curr. Sci. , 1946, 3: 69
[8] J. V. Narlikar, An Introduction to Cosmology, Cambridge: Cambridge University Press, 2002
[9] S. Hawking and L. Milodinow, The Grand Design, Bantom Books, New York , 2010
[10] E. Ayon-Beato, C. Martinez, R. Tronoso, and J. Zanelli, Gravitational Cheshire effect: Nonminimally coupled scalar fields may not curve spacetime, Phys. Rev. D , 2005, 71: 10403710.1103/PhysRevD.71.104037
[11] R. G. Vishwakarma, A curious explanation of some cosmological phenomena, Phys. Scripta , 2013, 05: 05590110.1088/0031-8949/87/05/055901
[12] A. Einstein, Relativity: The Special and the General Theory, 1955
[13] S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, John Wiley & Sons , 1972
[14] J. M. M.Senovilla, New class of inhomogeneous cosmological perfect-fluid solutions without big-bang singularity, Phys. Rev. Lett. , 1990, 64: 221910.1103/PhysRevLett.64.2219
[15] N. Dadhich, L. K. Patel, and R. Tikekar, Singularity free spacetimes- I: Metric and fluid models, Pramana- J. Phys. , 1995, 44: 303
[16] R. G. Vishwakarma, A dark energy model resulting from a Ricci symmetry revisited, Nuovo Cim. B , 2007, 122: 113
[17] S. Perlmutter, ., Measurements of Ωand Λfrom 42 high-redshift supernovae, Astrophys. J. , 1999, 517: 56510.1086/307221
[18] R. G. Vishwakarma and J. V. Narlikar, A critique of supernova data analysis in cosmology, Res. Astron. Astrophys. , 2010, 10: 119510.1088/1674-4527/10/12/001
[19] A. Riess, ., New Hubble Space Telescope discoveries of Type Ia supernovae at z>1: Narrowing constraints on the early behavior of dark energy, Astrophys. J. , 2007, 659: 9810.1086/510378
[20] D. O. Jones, , The discovery of the most distant known Type Ia supernova at redshift 1.914, Astrophys. J. , 2013, 768:16610.1088/0004-637X/768/2/166
[21] J. C. Jackson and M. Dodgson, Deceleration without dark matter, Mon. Not. R. Astron. Soc. , 1997, 285: 80610.1093/mnras/285.4.806
[22] L. I. Gurvits, Apparent milliarcsecond sizes of active galactic nuclei and the geometry of the Universe, Astrophys. J. , 1994, 425: 44210.1086/173999
[23] S. K. Banerjee and J. V. Narlikar, The quasi-steady state cosmology: A study of angular size against redshift, Mon. Not. R. Astron. Soc. , 1999, 307:7310.1046/j.1365-8711.1999.02610.x
[24] R. G. Vishwakarma, A study of angular size-redshift relation for models in which Λdecays as the energy density, Class. Quantum Grav. , 2000, 17:383310.1088/0264-9381/17/18/317
[25] R. G. Vishwakarma and P. Singh, Can brane cosmology with a vanishing Λ explain the observations? Class. Quantum Grav. , 2003, 20: 203310.1088/0264-9381/20/11/306
[26] L. I. Gurvits, K. I. Kellermann, and S. Frey, The “angular size- redshift” relation for compact radio structures in quasars and radio galaxies, Astron. Astrophys. , 1999, 342: 378
[27] R. G. Vishwakarma, Consequences on variable lambda models from distant type Ia supernovae and compact radio sources, Class. Quantum Grav. , 2001, 18: 115910.1088/0264-9381/18/7/301
[28] J. R. Mould, , The HST key project on the extragalactic distance scale XXVIII: Combining the constraints on the Hubble constant, Astrophys. J ., 2000, 529: 78610.1086/308304
[29] O. Y. Gnedin, O. Lahav, M. J. Rees, Do globular clusters time the Universe? arXiv: astro-ph/0108034 , 2001
[30] R. Cayrel, , Measurement of stellar age from uranium decay, Nature , 2001, 409: 69110.1038/35055507
[31] D. Larson, , Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Power spectra and WMAP-derived parameters, Astrophys. J. Suppl. , 2011, 192: 1610.1088/0067-0049/192/2/16
[32] D. Mania and B. Ratra, Constraints on dark energy from H II starburst galaxy apparent magnitude versus redshift data, Phys. Lett. B , 2012, 715: 910.1016/j.physletb.2012.07.011
[33] R. R. Siegel, , Towards a precision cosmology from starburst galaxies at z>2, Mon. Not. R. Astron. Soc. , 2005, 356: 111710.1111/j.1365-2966.2004.08539.x
[34] L. P. Grishchuk, Duration of inflation and possible remnants of the preinflationary Universe, Phys. Rev. D , 1992, 45: 471710.1103/PhysRevD.45.4717
[35] L. P. Grishchuk, Some uncomfortable thoughts on the nature of gravity, cosmology, and the early Universe, Space Sci. Rev. , 2009, 148: 31510.1007/s11214-009-9509-6
[36] C. Corda, Interferometric detection of gravitational waves: the definitive test for General Relativity, Int. J. Mod. Phys. D , 2009, 18: 227510.1142/S0218271809015904
[37] R. G. Vishwakarma, Is the present expansion of the Universe really accelerating? Mon. Not. R. Astron. Soc . 2003, 345: 54510.1046/j.1365-8711.2003.06960.x