scholarly journals Weyl geometry and gauge-invariant gravitation

2014 ◽  
Vol 23 (11) ◽  
pp. 1450091 ◽  
Author(s):  
F. P. Poulis ◽  
J. M. Salim
Keyword(s):  
General Relativity ◽  
Gauge Symmetry ◽  
Proper Time ◽  
Gauge Invariant ◽  
Weyl Geometry ◽  
Test Particles ◽  
Constant Solution ◽  
Intimate Relation ◽  
Theory Of Gravitation ◽  
Particles Trajectories

In this paper, we provide a gauge-invariant theory of gravitation in the context of Weyl Integrable Spacetimes. After making a brief review of the theory's postulates, we carefully define the observers' proper-time and point out its relation with spacetime description. As a consequence of this relation and the theory's gauge symmetry we recover all predictions of general relativity. This feature is made even clearer by a new exact solution we provide which reveals the importance of a well defined proper-time. The thermodynamical description of the source fields is given and we observe that each of the geometric fields have a certain physical significance, despite the gauge-invariance. This is shown by two examples, where one of them consists of a new cosmological constant solution. Our conclusions highlight the intimate relation among test particles trajectories, proper-time and spacetime description which can also be applied in any other situation, whether or not it recovers general relativity results and also in the absence of a gauge symmetry.

scholarly journals WEYL GEOMETRY AS CHARACTERIZATION OF SPACE-TIME

2011 ◽  
Vol 03 ◽  
pp. 87-97 ◽  
Author(s):  
F. P. POULIS ◽  
J. M. SALIM
Keyword(s):  
General Relativity ◽  
Scalar Field ◽  
Riemannian Geometry ◽  
Axiomatic Approach ◽  
Space Time ◽  
Weyl Geometry ◽  
Test Particles ◽  
Variational Formalism ◽  
Physical Fields

Motivated by an axiomatic approach to characterize space-time it is investigated a reformulation of Einstein's gravity where the pseudo-riemannian geometry is substituted by a Weyl one. It is presented the main properties of the Weyl geometry and it is shown that it gives extra contributions to the trajectories of test particles, serving as one more motivation to study general relativity in Weyl geometry. It is introduced its variational formalism and it is established the coupling with other physical fields in such a way that the theory acquires a gauge symmetry for the geometrical fields. It is shown that this symmetry is still present for the red-shift and it is concluded that for cosmological models it opens the possibility that observations can be fully described by the new geometrical scalar field. It is concluded then that this reformulation, although representing a theoretical advance, still needs a complete description of their objects.

scholarly journals A Proposed Experiment to Test Spin-Dependent Effects Beyond Einstein's Theory of Gravitation: The Pound-Rebka Experiment with Spin

2017 ◽  
Vol 3 (1) ◽  
pp. 4-15
Author(s):  
Noah Schlossberger ◽  
Tasman Payne
Keyword(s):  
General Relativity ◽  
Geometric Theory ◽  
Experimental Tests ◽  
Point Particles ◽  
Test Particles ◽  
Experimental Apparatus ◽  
Potential Sources ◽  
Theory Of Gravitation ◽  
Nonzero Spin ◽  
First Time

Einstein’s geometric theory of gravity was constructed in part to explain why test particles in a gravitational field all follow the same trajectory independent of the mass of the particle. However, it is known that point particles in quantum mechanics must all possess at least two properties: mass and angular momentum. Many have speculated that spin-dependent effects in gravity might exist which are not contained in Einstein’s theory, yet few experimental tests for such a possibility have ever been conducted. We describe an experiment which is very similar to the famous Pound-Rebka experiment, which used the Mössbauer effect to verify for the first time Einstein’s prediction for the curvature of time, but which employs Mossbauer emitters and absorbers with nonzero spin. We present a specific, realistic proposal for such an experiment. We outline the theory for the “normal” effects of general relativity a la Pound-Rebka, the proposed experimental apparatus including spinpolarized emitters and absorbers, the expected sensitivity of the experiment, and potential sources of systematic error. 

General Relativity: A Field Theory of Gravitation

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Gravitational Field ◽  
Equivalence Principle ◽  
Affine Connection ◽  
Classical Field Theory ◽  
Classical Field ◽  
Gauge Invariant ◽  
Theory Of Gravitation ◽  
Bending Of Light

General relativity. The equivalence principle and the derivation of the Einstein–Hilbert equations. The geometrical notions of curvature and affine connection are introduced. Geodesics and the bending of light by a gravitational field. General relativity as a gauge invariant classical field theory.

scholarly journals Breaking the cosmological background degeneracy by two-fluid perturbations in f(R) gravity

2015 ◽  
Vol 24 (07) ◽  
pp. 1550053 ◽  
Author(s):  
Amare Abebe
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Structure Formation ◽  
Background Level ◽  
Cosmological Perturbations ◽  
Gauge Invariant ◽  
First Order ◽  
Cosmological Background ◽  
Theories Of Gravity ◽  
Two Fluid

One of the exact solutions of f(R) theories of gravity in the presence of different forms of matter exactly mimics the ΛCDM solution of general relativity (GR) at the background level. In this work we study the evolution of scalar cosmological perturbations in the covariant and gauge-invariant formalism and show that although the background in such a model is indistinguishable from the standard ΛCDM cosmology, this degeneracy is broken at the level of first-order perturbations. This is done by predicting different rates of structure formation in ΛCDM and the f(R) model both in the complete and quasi-static regimes.

scholarly journals Astronomical tests of relativity: beyond parameterized post-Newtonian formalism (PPN), to testing fundamental principles

2009 ◽  
Vol 5 (S261) ◽  
pp. 56-61 ◽  
Author(s):  
Vladik Kreinovich
Keyword(s):  
General Relativity ◽  
Quantum Physics ◽  
Final Theory ◽  
Gravitational Theories ◽  
Cosmological Observations ◽  
Partial Analysis ◽  
Theory Of Gravitation ◽  
Improved Accuracy ◽  
Fundamental Physical ◽  
Relativistic Gravitation

AbstractBy the early 1970s, the improved accuracy of astrometric and time measurements enabled researchers not only to experimentally compare relativistic gravity with the Newtonian predictions, but also to compare different relativistic gravitational theories (e.g., the Brans-Dicke Scalar-Tensor Theory of Gravitation). For this comparison, Kip Thorne and others developed the Parameterized Post-Newtonian Formalism (PPN), and derived the dependence of different astronomically observable effects on the values of the corresponding parameters.Since then, all the observations have confirmed General Relativity. In other words, the question of which relativistic gravitation theory is in the best accordance with the experiments has been largely settled. This does not mean that General Relativity is the final theory of gravitation: it needs to be reconciled with quantum physics (into quantum gravity), it may also need to be reconciled with numerous surprising cosmological observations, etc. It is, therefore, reasonable to prepare an extended version of the PPN formalism, that will enable us to test possible quantum-related modifications of General Relativity.In particular, we need to include the possibility of violating fundamental principles that underlie the PPN formalism but that may be violated in quantum physics, such as scale-invariance, T-invariance, P-invariance, energy conservation, spatial isotropy violations, etc. In this paper, we present the first attempt to design the corresponding extended PPN formalism, with the (partial) analysis of the relation between the corresponding fundamental physical principles.

scholarly journals Effective field theory, past and future

2016 ◽  
Vol 31 (06) ◽  
pp. 1630007 ◽  
Author(s):  
Steven Weinberg
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Effective Field Theories ◽  
Standard Model ◽  
Effective Field Theory ◽  
Effective Field ◽  
Field Theories ◽  
Strong Interactions ◽  
The Standard Model ◽  
Theory Of Gravitation

I reminisce about the early development of effective field theories of the strong interactions, comment briefly on some other applications of effective field theories, and then take up the idea that the Standard Model and General Relativity are the leading terms in an effective field theory. Finally, I cite recent calculations that suggest that the effective field theory of gravitation and matter is asymptotically safe.

GEOMETRY OF SPACETIME AND FINSLER GEOMETRY

2009 ◽  
Vol 24 (08n09) ◽  
pp. 1678-1685 ◽  
Author(s):  
REZA TAVAKOL
Keyword(s):  
General Relativity ◽  
String Theory ◽  
Riemannian Geometry ◽  
Lorentz Invariance ◽  
Finsler Geometry ◽  
Spacetime Geometry ◽  
Test Particles ◽  
Light Rays ◽  
Recent Developments ◽  
Underlying Geometry

A central assumption in general relativity is that the underlying geometry of spacetime is pseudo-Riemannian. Given the recent attempts at generalizations of general relativity, motivated both by theoretical and observational considerations, an important question is whether the spacetime geometry can also be made more general and yet still remain compatible with observations? Here I briefly summarize some earlier results which demonstrate that there are special classes of Finsler geometry, which is a natural metrical generalization of the Riemannian geometry, that are strictly compatible with the observations regarding the motion of idealised test particles and light rays. I also briefly summarize some recent attempts at employing Finsler geometries motivated by more recent developments such as those in String theory, whereby Lorentz invariance is partially broken.

scholarly journals Plane Symmetric Solutions of a Scalar-Tensor Theory of Gravitation

1977 ◽  
Vol 30 (1) ◽  
pp. 109 ◽  
Author(s):  
DRK Reddy
Keyword(s):  
General Relativity ◽  
Empty Space ◽  
Scalar Fields ◽  
Scalar Tensor Theory ◽  
Field Equations ◽  
Plane Symmetric ◽  
Zero Mass ◽  
Tensor Theory ◽  
Special Cases ◽  
Theory Of Gravitation

Plane symmetric solutions of a scalar-tensor theory proposed by Dunn have been obtained. These solutions are observed to be similar to the plane symmetric solutions of the field equations corresponding to zero mass scalar fields obtained by Patel. It is found that the empty space-times of general relativity discussed by Taub and by Bera are obtained as special cases.

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