Cartan's soldered spaces and conservation laws in physics

2015 ◽  
Vol 12 (09) ◽  
pp. 1550089 ◽  
Author(s):  
Joseph Kouneiher ◽  
Cécile Barbachoux
Keyword(s):  
Conservation Laws ◽  
Local Cohomology ◽  
Differential Forms ◽  
Einstein Equations ◽  
Vacuum Field ◽  
Order System ◽  
Mathematical Framework ◽  
Field Equations ◽  
Yang Mills ◽  
Integrability Conditions

In this paper, we will introduce a generalized soldering p-forms geometry, which can be the right framework to describe many new approaches and concepts in modern physics. Here we will treat some aspects of the theory of local cohomology in fields theory or more precisely the theory of soldering-form conservation laws in physics. We provide some illustrative applications, primarily taken from the Einstein equations of general theory of relativity and Yang–Mills theory. This theory can be considered to be a generalization of Noether's theory of conserved current to differential forms of any degree. An essential result of this, is that the conservation of the energy–momentum in general relativity, is linked to the fact that the vacuum field equations are equivalent to the integrability conditions of a first-order system of differential equations. We also apply the idea of the soldered space and the integrability conditions to the case of Yang–Mills theory. The mathematical framework, where these intuitive considerations would fit naturally, can be used to describe also the dynamics of changing manifolds.

scholarly journals THE SEIBERG–WITTEN MAP FOR NON-COMMUTATIVE PURE GRAVITY AND VACUUM MAXWELL THEORY

2013 ◽  
Vol 10 (06) ◽  
pp. 1350023 ◽  
Author(s):  
ELISABETTA DI GREZIA ◽  
GIAMPIERO ESPOSITO ◽  
MARCO FIGLIOLIA ◽  
PATRIZIA VITALE
Keyword(s):  
Explicit Construction ◽  
Einstein Equations ◽  
Electromagnetic Potential ◽  
Field Equations ◽  
Maxwell Theory ◽  
Commutative Field ◽  
Yang Mills ◽  
First Order ◽  
Pure Gravity ◽  
Vacuum Solutions

In this paper the Seiberg–Witten map is first analyzed for non-commutative Yang–Mills theories with the related methods, developed in the literature, for its explicit construction, that hold for any gauge group. These are exploited to write down the second-order Seiberg–Witten map for pure gravity with a constant non-commutativity tensor. In the analysis of pure gravity when the classical space–time solves the vacuum Einstein equations, we find for three distinct vacuum solutions that the corresponding non-commutative field equations do not have solution to first order in non-commutativity, when the Seiberg–Witten map is eventually inserted. In the attempt of understanding whether or not this is a peculiar property of gravity, in the second part of the paper, the Seiberg–Witten map is considered in the simpler case of Maxwell theory in vacuum in the absence of charges and currents. Once more, no obvious solution of the non-commutative field equations is found, unless the electromagnetic potential depends in a very special way on the wave vector.

Symmetries and conservation laws of some asymptotically symmetric spacetimes of interest in gravitational waves

2019 ◽  
Vol 16 (10) ◽  
pp. 1950152 ◽  
Author(s):  
Ashfaque H. Bokhari ◽  
A. H. Kara ◽  
B. B. I. Gadjagboui ◽  
Ghulam Shabbir
Keyword(s):  
Conservation Laws ◽  
Gravitational Waves ◽  
Flat Space ◽  
Einstein Equations ◽  
Necessary Condition ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Asymptotically Flat ◽  
Symmetric Spacetimes ◽  
Flat Spacetimes

In this paper, we discuss symmetries and the corresponding conservation laws of certain exact solutions of the Einstein field equations (EFEs) representing a Schwarzschild black hole and gravitational waves in asymptotically flat space times. Of particular interest are symmetries of asymptotically flat spacetimes because they admit a property that identifies them for the existence of gravitational waves there. In the light of this fact, we discuss symmetry algebras of a few recently published solutions of Einstein equations in asymptotically flat metrics. Given the fact that gravitational waves are of great interest in relativity, we focus in this paper on finding the type of symmetries they admit and their corresponding conservation laws. We also show how these symmetries are radically different from the other well-known symmetries and present necessary condition that distinguishes them.

scholarly journals NON-ABELIAN GAUGE SYMMETRIES INDUCED BY THE UNOBSERVABILITY OF EXTRA DIMENSIONS IN A KALUZA–KLEIN APPROACH

2006 ◽  
Vol 21 (03) ◽  
pp. 265-274 ◽  
Author(s):  
FRANCESCO CIANFRANI ◽  
GIOVANNI MONTANI
Keyword(s):  
Extra Dimensions ◽  
Gauge Coupling ◽  
Einstein Equations ◽  
Field Equations ◽  
Abelian Gauge ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Gauge Symmetries ◽  
The Right ◽  
Kaluza Klein

In this work we deal with the extension of the Kaluza–Klein approach to a non-Abelian gauge theory; we show how we need to consider the link between the n-dimensional model and a four-dimensional observer physics, in order to reproduce field equations and gauge transformations in the four-dimensional picture. More precisely, in field equations any dependence on extra coordinates is canceled out by an integration, as consequence of the unobservability of extra dimensions. Thus, by virtue of this extra dimension unobservability, we are able to recast the multidimensional Einstein equations into the four-dimensional Einstein–Yang–Mills ones, as well as all the right gauge transformations of fields are induced. The same analysis is performed for the Dirac equation describing the dynamics of the matter fields and, again, the gauge coupling with Yang–Mills fields are inferred from the multidimensional free fields theory, together with the proper spinors transformations.

scholarly journals f(R) GRAVITY WITH TORSION: A GEOMETRIC APPROACH WITHIN THE $\mathcal{J}$-BUNDLES FRAMEWORK

2008 ◽  
Vol 05 (05) ◽  
pp. 765-788 ◽  
Author(s):  
S. CAPOZZIELLO ◽  
R. CIANCI ◽  
C. STORNAIOLO ◽  
S. VIGNOLO
Keyword(s):  
Conservation Laws ◽  
Perfect Fluid ◽  
Geometric Approach ◽  
Empty Space ◽  
Field Equations ◽  
Jet Bundles ◽  
Yang Mills ◽  
Dirac Fields ◽  
Theories Of Gravity ◽  
Curvature Tensors

We discuss the f(R)-theories of gravity with torsion in the framework of [Formula: see text]-bundles. Such an approach is particularly useful since the components of the torsion and curvature tensors can be chosen as fiber [Formula: see text]-coordinates on the bundles and then the symmetries and the conservation laws of the theory can be easily achieved. Field equations of f(R)-gravity are studied in empty space and in presence of various forms of matter as Dirac fields, Yang–Mills fields and spin perfect fluid. Such fields enlarge the jet bundles framework and characterize the dynamics. Finally we give some cosmological applications and discuss the relations between f(R)-gravity and scalar-tensor theories.

TIME-DEPENDENT SOLUTIONS OF 5D VACUUM EINSTEIN EQUATIONS WITH COSMOLOGICAL CONSTANT

2011 ◽  
Vol 26 (22) ◽  
pp. 1673-1679 ◽  
Author(s):  
TAE HOON LEE
Keyword(s):  
Cosmological Constant ◽  
Time Dependence ◽  
Scale Factor ◽  
Einstein Equations ◽  
Time Dependent ◽  
Vacuum Field ◽  
Field Equations ◽  
Vacuum Einstein Equations ◽  
Dimensional Gravity

We solve vacuum field equations in five-dimensional gravity with cosmological constant to determine the time-dependence of the Robertson–Walker scale factor. We discuss its cosmological implications.

scholarly journals New Solutions of Einstein Equations Representing Spinning Masses

1974 ◽  
Vol 64 ◽  
pp. 191-191
Author(s):  
Humitaka Sato ◽  
Akira Tomimatsu
Keyword(s):  
Exact Solutions ◽  
Event Horizon ◽  
Equatorial Plane ◽  
Space Time ◽  
Einstein Equations ◽  
Vacuum Field ◽  
Kerr Metric ◽  
Field Equations ◽  
Asymptotically Flat

We found new, stationary axisymmetric, asymptotically flat exact solutions to Einstein's vacuum field equations, which are classified by an integer δ and Kerr metric is the solution of δ = 1. The number of ring singularity on the equatorial plane is δ. The odd δ metrices contain the surfaces of event horizon but the even δ metrices do not. Except the Kerr metric, however, the space-time becomes singular at the poles on these surfaces.

Can quantum black holes be (q, p)-fermions?

2017 ◽  
Vol 32 (15) ◽  
pp. 1750080 ◽  
Author(s):  
Emre Dil
Keyword(s):  
Black Holes ◽  
Gravitational Field ◽  
Fermi Gas ◽  
Einstein Equations ◽  
Quantum Corrections ◽  
Field Equations ◽  
Gravitational Field Equations ◽  
Entropic Gravity ◽  
Two Parameter

In this study, to investigate the very nature of quantum black holes, we try to relate three independent studies: (q, p)-deformed Fermi gas model, Verlinde’s entropic gravity proposal and Strominger’s quantum black holes obeying the deformed statistics. After summarizing Strominger’s extremal quantum black holes, we represent the thermostatistics of (q, p)-fermions to reach the deformed entropy of the (q, p)-deformed Fermi gas model. Since Strominger’s proposal claims that the quantum black holes obey deformed statistics, this motivates us to describe the statistics of quantum black holes with the (q, p)-deformed fermions. We then apply the Verlinde’s entropic gravity proposal to the entropy of the (q, p)-deformed Fermi gas model which gives the two-parameter deformed Einstein equations describing the gravitational field equations of the extremal quantum black holes obeying the deformed statistics. We finally relate the obtained results with the recent study on other modification of Einstein equations obtained from entropic quantum corrections in the literature.

scholarly journals A MAXWELL-LIKE FORMULATION OF GRAVITATIONAL THEORY IN MINKOWSKI SPACE–TIME

2007 ◽  
Vol 16 (06) ◽  
pp. 1027-1041 ◽  
Author(s):  
EDUARDO A. NOTTE-CUELLO ◽  
WALDYR A. RODRIGUES
Keyword(s):  
Gravitational Field ◽  
Minkowski Space ◽  
Gravitational Theory ◽  
Space Time ◽  
Lorentzian Geometry ◽  
Field Equations ◽  
Yang Mills ◽  
Minkowski Space Time ◽  
Clifford Bundle ◽  
Gauge Fixing

Using the Clifford bundle formalism, a Lagrangian theory of the Yang–Mills type (with a gauge fixing term and an auto interacting term) for the gravitational field in Minkowski space–time is presented. It is shown how two simple hypotheses permit the interpretation of the formalism in terms of effective Lorentzian or teleparallel geometries. In the case of a Lorentzian geometry interpretation of the theory, the field equations are shown to be equivalent to Einstein's equations.

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