Post-Newtonian expansion of an algebraically extended theory of gravity

1991 ◽  
Vol 69 (5) ◽  
pp. 641-654
Author(s):  
J. H. Palmer ◽  
R. B. Mann
Keyword(s):  
Mass Parameter ◽  
Alternative Theory ◽  
Energy Tensor ◽  
Type Solution ◽  
Antisymmetric Part ◽  
Extended Theory ◽  
Stress Energy ◽  
Theory Of Gravitation ◽  
Theory Of Gravity ◽  
Nonsymmetric Metric

The post-Newtonian expansion is analyzed for an algebraically extended theory of gravity equivalent to a theory with a real, nonsymmetric metric, previously referred to as Algebraically Extended Hilbert Gravity (AHG). The hermiticity of the algebra-valued covariant and contravariant metrics is found to constrain the form of the expansion of the antisymmetric part of the real metric to one of two possibilities. Both of these display a qualitatively new technical feature: the lowest order equations are nonlinear, depriving the post-Newtonian expansion of its greatest asset. In one case, they lead to a solution with a negative Newtonian mass parameter. In the other case, they lead to a contact-type solution in which some metric components depend directly upon the stress–energy tensor rather than the integral of this distribution. The unphysical nature of these solutions rules out AHG as a physically viable alternative theory of gravitation.

scholarly journals Einstein–Cartan–Dirac gravity with U(1) symmetry breaking

2019 ◽  
Vol 79 (12) ◽  
Author(s):  
Francisco Cabral ◽  
Francisco S. N. Lobo ◽  
Diego Rubiera-Garcia
Keyword(s):  
Spin Density ◽  
Affine Connection ◽  
New Physics ◽  
Energy Tensor ◽  
Field Equations ◽  
Antisymmetric Part ◽  
Stress Energy ◽  
Physical Effects ◽  
Cartan Theory ◽  
Spin Densities

AbstractEinstein–Cartan theory is an extension of the standard formulation of General Relativity where torsion (the antisymmetric part of the affine connection) is non-vanishing. Just as the space-time metric is sourced by the stress-energy tensor of the matter fields, torsion is sourced via the spin density tensor, whose physical effects become relevant at very high spin densities. In this work we introduce an extension of the Einstein–Cartan–Dirac theory with an electromagnetic (Maxwell) contribution minimally coupled to torsion. This contribution breaks the U(1) gauge symmetry, which is suggested by the possibility of a torsion-induced phase transition in the early Universe, yielding new physics in extreme (spin) density regimes. We obtain the generalized gravitational, electromagnetic and fermionic field equations for this theory, estimate the strength of the corrections, and discuss the corresponding phenomenology. In particular, we briefly address some astrophysical considerations regarding the relevance of the effects which might take place inside ultra-dense neutron stars with strong magnetic fields (magnetars).

scholarly journals THEORY OF GRAVITATION THEORIES: A NO-PROGRESS REPORT

2008 ◽  
Vol 17 (03n04) ◽  
pp. 399-423 ◽  
Author(s):  
THOMAS P. SOTIRIOU ◽  
STEFANO LIBERATI ◽  
VALERIO FARAONI
Keyword(s):  
Equivalence Principle ◽  
Progress Report ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Gravitational Fields ◽  
Stress Energy ◽  
Theories Of Gravity ◽  
Theory Of Gravitation ◽  
Conformal Frames ◽  
Shaky Ground

Already in the 1970s there where attempts to present a set of ground rules, sometimes referred to as a theory of gravitation theories, which theories of gravity should satisfy in order to be considered viable in principle and, therefore, interesting enough to deserve further investigation. From this perspective, an alternative title of this paper could be "Why Are We Still Unable to Write a Guide on How to Propose Viable Alternatives to General Relativity?". Attempting to answer this question, it is argued here that earlier efforts to turn qualitative statements, such as the Einstein equivalence principle, into quantitative ones, such as the metric postulates, stand on rather shaky ground — probably contrary to popular belief — as they appear to depend strongly on particular representations of the theory. This includes ambiguities in the identification of matter and gravitational fields, dependence of frequently used definitions (such as those of the stress–energy tensor or classical vacuum) on the choice of variables, etc. Various examples are discussed and possible approaches to this problem are pointed out. In the course of this study, several common misconceptions related to the various forms of the equivalence principle, the use of conformal frames and equivalence between theories are clarified.

scholarly journals Mimetic Einstein-Cartan-Sciama-Kibble (ECSK) gravity

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Fernando Izaurieta ◽  
Perla Medina ◽  
Nelson Merino ◽  
Patricio Salgado ◽  
Omar Valdivia
Keyword(s):  
Differential Forms ◽  
Spin Connection ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Total Stress ◽  
Mimetic Theory ◽  
Form Parameter ◽  
First Order ◽  
Stress Energy ◽  
Theory Of Gravity

Abstract In this paper, we formulate the Mimetic theory of gravity in first-order formalism for differential forms, i.e., the mimetic version of Einstein-Cartan-Sciama-Kibble (ECSK) gravity. We consider different possibilities on how torsion is affected by Weyl transformations and discuss how this translates into the interpolation between two different Weyl transformations of the spin connection, parameterized with a zero-form parameter λ. We prove that regardless of the type of transformation one chooses, in this setting torsion remains as a non-propagating field. We also discuss the conservation of the mimetic stress-energy tensor and show that the trace of the total stress-energy tensor is not null but depends on both, the value of λ and spacetime torsion.

scholarly journals SEMICLASSICAL GRAVITATIONAL EFFECTS AROUND GLOBAL MONOPOLE IN BRANS–DICKE THEORY

2008 ◽  
Vol 23 (32) ◽  
pp. 2763-2770 ◽  
Author(s):  
F. RAHAMAN ◽  
P. GHOSH
Keyword(s):  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Energy Tensor ◽  
Quantum Fields ◽  
Global Monopole ◽  
Stress Energy Tensor ◽  
Gravitational Effects ◽  
Expectation Value ◽  
Stress Energy ◽  
Theory Of Gravity

Recently, W. A. Hiscock4studied the semi classical gravitational effects around global monopole. He obtained the vacuum expectation value of the stress–energy tensor of an arbitrary collection of conformal mass less free quantum fields (scalar, spinor and vectors) in the spacetime of a global monopole. With this stress–energy tensor, we study the semiclassical gravitational effects of a global monopole in the context of Brans–Dicke theory of gravity.

scholarly journals Genesis of general relativity — A concise exposition

2016 ◽  
Vol 25 (14) ◽  
pp. 1630004
Author(s):  
Wei-Tou Ni
Keyword(s):  
General Relativity ◽  
Special Relativity ◽  
Equivalence Principle ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Relativistic Fluids ◽  
Schwarzschild Solution ◽  
Stress Energy ◽  
Perihelion Advance ◽  
Theory Of Gravity

This short exposition starts with a brief discussion of situation before the completion of special relativity (Le Verrier’s discovery of the Mercury perihelion advance anomaly, Michelson–Morley experiment, Eötvös experiment, Newcomb’s improved observation of Mercury perihelion advance, the proposals of various new gravity theories and the development of tensor analysis and differential geometry) and accounts for the main conceptual developments leading to the completion of the general relativity (CGR): gravity has finite velocity of propagation; energy also gravitates; Einstein proposed his equivalence principle and deduced the gravitational redshift; Minkowski formulated the special relativity in four-dimentional spacetime and derived the four-dimensional electromagnetic stress–energy tensor; Einstein derived the gravitational deflection from his equivalence principle; Laue extended Minkowski’s method of constructing electromagnetic stress-energy tensor to stressed bodies, dust and relativistic fluids; Abraham, Einstein, and Nordström proposed their versions of scalar theories of gravity in 1911–13; Einstein and Grossmann first used metric as the basic gravitational entity and proposed a “tensor” theory of gravity (the “Entwurf” theory, 1913); Einstein proposed a theory of gravity with Ricci tensor proportional to stress–energy tensor (1915); Einstein, based on 1913 Besso–Einstein collaboration, correctly derived the relativistic perihelion advance formula of his new theory which agreed with observation (1915); Hilbert discovered the Lagrangian for electromagnetic stress–energy tensor and the Lagrangian for the gravitational field (1915), and stated the Hilbert variational principle; Einstein equation of GR was proposed (1915); Einstein published his foundation paper (1916). Subsequent developments and applications in the next two years included Schwarzschild solution (1916), gravitational waves and the quadrupole formula of gravitational radiation (1916, 1918), cosmology and the proposal of cosmological constant (1917), de Sitter solution (1917), Lense–Thirring effect (1918).

scholarly journals Stress-energy tensor correlators from the world-sheet

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Hanno Bertle ◽  
Andrea Dei ◽  
Matthias R. Gaberdiel
Keyword(s):  
Vertex Operator ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
World Sheet ◽  
Stress Energy ◽  
The World

Abstract The large N limit of symmetric orbifold theories was recently argued to have an AdS/CFT dual world-sheet description in terms of an sl(2, ℝ) WZW model. In previous work the world-sheet state corresponding to the symmetric orbifold stress-energy tensor was identified. We calculate certain 2- and 3-point functions of the corresponding vertex operator on the world-sheet, and demonstrate that these amplitudes reproduce exactly what one expects from the dual symmetric orbifold perspective.

Higgs-like field from extended theory of gravitation

2014 ◽  
Vol 11 (02) ◽  
pp. 1460001
Author(s):  
L. Fatibene ◽  
M. Ferraris ◽  
G. Magnano ◽  
M. Palese ◽  
M. Capone ◽  
...  
Keyword(s):  
Scalar Field ◽  
Extended Theory ◽  
Theory Of Gravitation ◽  
Conformal Scalar Field

We shall consider possible potentials emerging in (purely metric) f(R)-theories for the conformal scalar field. We shall discuss possible approaches to determine models with specific potentials and show that some potentials qualitatively similar to the typical Higgs potentials are allowed.

ON THE ELECTROMAGNETIC PERTURBATIONS OF A MULTICONICAL SPACETIME

1996 ◽  
Vol 11 (27) ◽  
pp. 2171-2177
Author(s):  
A.N. ALIEV
Keyword(s):  
Cosmic Strings ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Stress Energy ◽  
Electromagnetic Perturbations

The electromagnetic perturbations propagating in the multiconical spacetime of N parallel cosmic strings are described. The expression for vacuum average of the stress-energy tensor is reduced to a form involving only zero-spin-weighted perturbation modes.

scholarly journals Gradient estimates for semilinear elliptic systems and other related results

2015 ◽  
Vol 145 (6) ◽  
pp. 1313-1330 ◽  
Author(s):  
Panayotis Smyrnelis
Keyword(s):  
Liouville Theorem ◽  
Elliptic Systems ◽  
Gradient Estimates ◽  
Alternative Form ◽  
Strong Monotonicity ◽  
Energy Tensor ◽  
Planar Domains ◽  
Stress Energy ◽  
General Phase ◽  
Double Well Potential

A periodic connection is constructed for a double well potential defined in the plane. This solution violates Modica's estimate as well as the corresponding Liouville theorem for general phase transition potentials. Gradient estimates are also established for several kinds of elliptic systems. They allow us to prove the Liouville theorem in some particular cases. Finally, we give an alternative form of the stress–energy tensor for solutions defined in planar domains. As an application, we deduce a (strong) monotonicity formula.

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