On a Fermat principle in general relativity. A Morse theory for light rays

1996 ◽  
Vol 28 (7) ◽  
pp. 855-897 ◽  
Author(s):  
Fabio Giannoni ◽  
Antonio Masiello
Keyword(s):  
General Relativity ◽  
Morse Theory ◽  
Fermat Principle ◽  
Light Rays

scholarly journals Fermat Metrics

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1422
Author(s):  
Antonio Masiello
Keyword(s):  
Variational Methods ◽  
Morse Theory ◽  
Sagnac Effect ◽  
Variational Theory ◽  
Global Hyperbolicity ◽  
Fermat Principle ◽  
Multiple Image ◽  
Light Rays ◽  
Stationary Spacetimes

In this paper we present a survey of Fermat metrics and their applications to stationary spacetimes. A Fermat principle for light rays is stated in this class of spacetimes and we present a variational theory for the light rays and a description of the multiple image effect. Some results on variational methods, as Ljusternik-Schnirelmann and Morse Theory are recalled, to give a description of the variational methods used. Other applications of the Fermat metrics concern the global hyperbolicity and the geodesic connectedeness and a characterization of the Sagnac effect in a stationary spacetime. Finally some possible applications to other class of spacetimes are considered.

scholarly journals The Fermat principle in general relativity and applications

2002 ◽  
Vol 43 (1) ◽  
pp. 563-596 ◽  
Author(s):  
F. Giannoni ◽  
A. Masiello ◽  
P. Piccione
Keyword(s):  
General Relativity ◽  
Fermat Principle

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 A finite dimensional approach to light rays in General Relativity

2018 ◽  
Vol 168 ◽  
pp. 198-221
Author(s):  
Roberto Giambò ◽  
Fabio Giannoni ◽  
Paolo Piccione
Keyword(s):  
General Relativity ◽  
Dimensional Approach ◽  
Finite Dimensional ◽  
Light Rays

Black hole fusion made easy

2016 ◽  
Vol 25 (12) ◽  
pp. 1644015
Author(s):  
Roberto Emparan ◽  
Marina Martínez
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Black Hole ◽  
Event Horizon ◽  
Critical Behavior ◽  
Equivalence Principle ◽  
The Other ◽  
Schwarzschild Solution ◽  
Null Geodesics ◽  
Light Rays

The fusion of two black holes — a signature phenomenon of General Relativity — is usually regarded as a process so complex that nothing short of a supercomputer simulation can accurately capture it. In this essay, we explain how the event horizon of the merger can be found in an exact analytic way in the limit where one of the black holes is much smaller than the other. Remarkably, the ideas and techniques involved are elementary: the equivalence principle, null geodesics in the Schwarzschild solution, and the notion of event horizon itself. With these, one can identify features such as the line of caustics at which light rays enter the horizon, and find indications of universal critical behavior when the two black holes touch.

Failure of Einstein's theory of relativity. II. Arguments of Einstein disproving his own theory of general relativity and absurd consequences of relativistic physics

2019 ◽  
Vol 32 (4) ◽  
pp. 451-459 ◽  
Author(s):  
Reiner Georg Ziefle
Keyword(s):  
General Relativity ◽  
Time Dilation ◽  
Theory Of Relativity ◽  
Time Dilatation ◽  
Light Rays ◽  
Light Beams

The theory of special and general relativity causes a “schizophrenic” dilemma in physics. It undeniably provides mathematically correct values, but it is undeniably epistemologically wrong in many respects. Including the relativistic explanation of the gravitational “time dilation” and the curvature of light beams at the surfaces of large masses, the author demonstrates the illogical character of relativistic physics. When one thinks the relativistic explanations of gravitational time dilatation and of the curvature of light rays by masses through to the end, they lead to absurd and contradictory logical conclusions.

scholarly journals A Morse theory for massive particles and photons in general relativity

2000 ◽  
Vol 35 (1) ◽  
pp. 1-34 ◽  
Author(s):  
Fabio Giannoni ◽  
Antonio Masiello ◽  
Paolo Piccione
Keyword(s):  
General Relativity ◽  
Morse Theory ◽  
Massive Particles

General relativity in terms of a background space

1963 ◽  
Vol 276 (1366) ◽  
pp. 413-417 ◽  
Keyword(s):  
General Relativity ◽  
Euclidean Space ◽  
Test Particle ◽  
Space Time ◽  
Red Shift ◽  
Schwarzschild Metric ◽  
Background Space ◽  
Light Rays ◽  
Theory Of Gravitation

R. d’E. Atkinson has shown that the path of a test particle, the light rays and the gravitational red shift predicted by general relativity for the case of the Schwarzschild metric may all be interpreted in terms of Euclidean space. By introducing the concept of a background space it is shown that Atkinson’s interpretation may be extended for the case of any finite static gravitating system. It is pointed out that the interpretation is applicable to any theory of gravitation in which the path of a test particle and the light rays are geodesics of the space-time metric.

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