Quadratic Poincar� gauge theory of gravity: A comparison with the general relativity theory

1989 ◽  
Vol 21 (11) ◽  
pp. 1107-1142 ◽  
Author(s):  
Yu. N. Obukhov ◽  
V. N. Ponomariev ◽  
V. V. Zhytnikov
Keyword(s):  
General Relativity ◽  
Gauge Theory ◽  
Relativity Theory ◽  
General Relativity Theory ◽  
Theory Of Gravity ◽  
Gauge Theory Of Gravity

BORN'S RECIPROCAL GENERAL RELATIVITY THEORY AND COMPLEX NON-ABELIAN GRAVITY AS GAUGE THEORY OF THE QUAPLECTIC GROUP: A NOVEL PATH TO QUANTUM GRAVITY

2008 ◽  
Vol 23 (10) ◽  
pp. 1487-1506 ◽  
Author(s):  
CARLOS CASTRO
Keyword(s):  
General Relativity ◽  
Gauge Theory ◽  
Planck Scale ◽  
Relativity Theory ◽  
Target Space ◽  
Speed Limit ◽  
General Relativity Theory ◽  
Curved Space ◽  
Maximal Speed ◽  
Proper Force

Born's reciprocal relativity in flat space–times is based on the principle of a maximal speed limit (speed of light) and a maximal proper force (which is also compatible with a maximal and minimal length duality) and where coordinates and momenta are unified on a single footing. We extend Born's theory to the case of curved space–times and construct a reciprocal general relativity theory (in curved space–times) as a local gauge theory of the quaplectic group and given by the semidirect product [Formula: see text], where the non-Abelian Weyl–Heisenberg group is H(1, 3). The gauge theory has the same structure as that of complex non-Abelian gravity. Actions are presented and it is argued why such actions based on Born's reciprocal relativity principle, involving a maximal speed limit and a maximal proper force, is a very promising avenue to quantize gravity that does not rely in breaking the Lorentz symmetry at the Planck scale, in contrast to other approaches based on deformations of the Poincaré algebra, quantum groups. It is discussed how one could embed the quaplectic gauge theory into one based on the U(1, 4), U(2, 3) groups where the observed cosmological constant emerges in a natural way. We conclude with a brief discussion of complex coordinates and Finsler spaces with symmetric and nonsymmetric metrics studied by Eisenhart as relevant closed-string target space backgrounds where Born's principle may be operating.

A gauge theory of gravity in curved phase-spaces

2016 ◽  
Vol 13 (07) ◽  
pp. 1650097
Author(s):  
Carlos Castro
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Cotangent Bundle ◽  
Finsler Geometry ◽  
Relativity Theory ◽  
Field Equations ◽  
Double Field Theory ◽  
Theory Of Gravity ◽  
Curvature And Torsion ◽  
Gauge Theory Of Gravity

After a cursory introduction of the basic ideas behind Born’s Reciprocal Relativity theory, the geometry of the cotangent bundle of spacetime is studied via the introduction of nonlinear connections associated with certain nonholonomic modifications of Riemann–Cartan gravity within the context of Finsler geometry. A novel gauge theory of gravity in the [Formula: see text] cotangent bundle [Formula: see text] of spacetime is explicitly constructed and based on the gauge group [Formula: see text] which acts on the tangent space to the cotangent bundle [Formula: see text] at each point [Formula: see text]. Several gravitational actions involving curvature and torsion tensors and associated with the geometry of curved phase-spaces are presented. We conclude with a brief discussion of the field equations, the geometrization of matter, quantum field theory (QFT) in accelerated frames, T-duality, double field theory, and generalized geometry.

T4 gauge theory of gravity and new general relativity

1990 ◽  
Vol 22 (5) ◽  
pp. 511-524
Author(s):  
Qian Si-ming ◽  
Wu You-lin
Keyword(s):  
General Relativity ◽  
Gauge Theory ◽  
Theory Of Gravity ◽  
Gauge Theory Of Gravity

ON TIME DISLOCATION SOLUTION OF EINSTEIN FIELD EQUATIONS

1999 ◽  
Vol 14 (02) ◽  
pp. 93-97 ◽  
Author(s):  
L. C. GARCIA DE ANDRADE
Keyword(s):  
General Relativity ◽  
Gauge Theory ◽  
External Solution ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Birkhoff Theorem ◽  
The Core ◽  
Theory Of Gravity ◽  
Gauge Theory Of Gravity

The theory considered here is not Einstein general relativity, but is a Poincaré type gauge theory of gravity, therefore the Birkhoff theorem is not applied and the external solution is not vacuum spherically symmetric and tachyons may exist outside the core defect.

scholarly journals Vaidya solutions in general covariant Hořava–Lifshitz gravity without projectability: Infrared limit

2014 ◽  
Vol 23 (08) ◽  
pp. 1450068 ◽  
Author(s):  
O. Goldoni ◽  
M. F. A. da Silva ◽  
G. Pinheiro ◽  
R. Chan
Keyword(s):  
General Relativity ◽  
Gauge Field ◽  
Radiation Field ◽  
Relativity Theory ◽  
Covariant Theory ◽  
Spherically Symmetric ◽  
Theory U ◽  
General Relativity Theory ◽  
Infrared Limit ◽  
Symmetric Spacetime

In this paper, we have studied nonstationary radiative spherically symmetric spacetime, in general covariant theory (U(1) extension) of Hořava–Lifshitz (HL) gravity without the projectability condition and in the infrared (IR) limit. The Newtonian prepotential φ was assumed null. We have shown that there is not the analogue of the Vaidya's solution in the Hořava–Lifshitz Theory (HLT), as we know in the General Relativity Theory (GRT). Therefore, we conclude that the gauge field A should interact with the null radiation field of the Vaidya's spacetime in the HLT.

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