scholarly journals Obstruction tensors in Weyl geometry and holographic Weyl anomaly

2021 ◽  
Vol 104 (12) ◽  
Author(s):  
Weizhen Jia ◽  
Manthos Karydas
Keyword(s):  
Weyl Geometry

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 Behavior of a vacuum and naked singularity under a smooth gauge function in Lyra geometry

2018 ◽  
Vol 96 (9) ◽  
pp. 969-977
Author(s):  
Haizhao Zhi
Keyword(s):  
Physical Meaning ◽  
Conformal Geometry ◽  
Naked Singularity ◽  
Lyra Geometry ◽  
Space Time ◽  
Gauge Function ◽  
Weyl Geometry ◽  
Irregular Singular Point ◽  
New Space ◽  
Symmetric Gauge

Lyra geometry is a conformal geometry that originated from Weyl geometry. In this article, we derive the exterior field equation under a spherically symmetric gauge function x0(r) and metric in Lyra geometry. When we impose a specific form of the gauge function x0(r), the radial differential equation of the metric component g00 will possess an irregular singular point (ISP) at r = 0. Moreover, we can apply the method of dominant balance to get the asymptotic behavior of the new space–time solution. The significance of this work is that we can use a series of smooth gauge functions x0(r) to modulate the degree of divergence of the singularity at r = 0, which will become a naked singularity under certain conditions. Furthermore, we investigate the physical meaning of this novel behavior of space–time in Lyra geometry and find out that no spaceship with finite integrated acceleration can arrive at this singularity at r = 0. The physical meaning of the gauge function and integrability is also discussed.

scholarly journals GENERAL RELATIVITY AND WEYL FRAMES

2011 ◽  
Vol 03 ◽  
pp. 27-35
Author(s):  
C. ROMERO ◽  
J. B. FONSECA-NETO ◽  
M. L. PUCHEU
Keyword(s):  
General Relativity ◽  
General Theory ◽  
Riemannian Geometry ◽  
Vacuum Solution ◽  
Gravitational Theory ◽  
Mathematical Formalism ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Weyl Geometry ◽  
Starting Point

We present the general theory of relativity in the language of a non-Riemannian geometry, namely, Weyl geometry. We show that the new mathematical formalism may lead to different pictures of the same gravitational phenomena, by making use of the concept of Weyl frames. We show that, in this formalism, it is possible to construct a scalar-tensor gravitational theory that is invariant with respect to the so-called Weyl tranformations and reduces to general relativity in a particular frame, the Riemann frame. In this approach the Weyl geometry plays a fundamental role since it appears as the natural geometrical setting of the theory when viewed in an arbitrary frame. Our starting point is to build an action that is manifestly invariant with respect to Weyl transformations. When this action is expressed in more familiar terms of Riemannian geometry we find that the theory has some similarities with Brans-Dicke theory of gravity. We illustrate this point with an example in which a known Brans-Dicke vacuum solution may appear when reinterpreted in a particular Weyl frame.

scholarly journals Einstein–Weyl geometry, dispersionless Hirota equation and Veronese webs

2014 ◽  
Vol 157 (1) ◽  
pp. 139-150 ◽  
Author(s):  
MACIEJ DUNAJSKI ◽  
WOJCIECH KRYŃSKI
Keyword(s):  
Heisenberg Group ◽  
Twistor Space ◽  
Three Dimensional ◽  
Poisson Structures ◽  
Weyl Geometry ◽  
Hirota Equation ◽  
Five Dimensions ◽  
Dispersionless Hirota Equation

AbstractWe exploit the correspondence between the three–dimensional Lorentzian Einstein–Weyl geometries of the hyper–CR type and the Veronese webs to show that the former structures are locally given in terms of solutions to the dispersionless Hirota equation. We also demonstrate how to construct hyper–CR Einstein–Weyl structures by Kodaira deformations of the flat twistor space$T\mathbb{CP}^1$, and how to recover the pencil of Poisson structures in five dimensions illustrating the method by an example of the Veronese web on the Heisenberg group.

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