Zum Übergang von der Wellenoptik zur geometrischen Optik in der allgemeinen Relativitätstheorie

1967 ◽  
Vol 22 (9) ◽  
pp. 1328-1332 ◽  
Author(s):  
Jürgen Ehlers
Keyword(s):  
General Relativity ◽  
Maxwell Equations ◽  
Expansion Method ◽  
Flat Space ◽  
Space Time ◽  
Moving Medium ◽  
Formal Similarity ◽  
Curved Space ◽  
Optical Metric ◽  
Series Expansion Method

The transition from the (covariantly generalized) MAXWELL equations to the geometrical optics limit is discussed in the context of general relativity, by adapting the classical series expansion method to the case of curved space time. An arbitrarily moving ideal medium is also taken into account, and a close formal similarity between wave propagation in a moving medium in flat space time and in an empty, gravitationally curved space-time is established by means of a normal hyperbolic optical metric.

scholarly journals A Teleparallel Type Theory for Massless Spin 2 Fields

2020 ◽  
Author(s):  
José Wadih Maluf ◽  
Sérgio Costa Ulhoa
Keyword(s):  
General Relativity ◽  
Electromagnetic Field ◽  
Type Theory ◽  
Degrees Of Freedom ◽  
Symmetric Tensor ◽  
Flat Space ◽  
Space Time ◽  
Two Degrees Of Freedom ◽  
Curved Space ◽  
Massless Spin

We present the Lagrangian and Hamiltonian formulations of a theory for spin 2 fields. The construction is developed in flat space-time. The construction in curved space-time is conceptually straightforward, although it is not unique. The theory is based on a symmetric tensor $S_{\mu\nu}$, contains two degrees of freedom of radiation, is motivated by the teleparallel formulation of general relativity, and displays a certain resemblance with Maxwell's theory for the electromagnetic field.

Time, Topology, and the Twin Paradox

2011 ◽  
Author(s):  
Jean‐Pierre Luminet
Keyword(s):  
High Speed ◽  
Reference Frames ◽  
Thought Experiment ◽  
Flat Space ◽  
Space Time ◽  
Twin Paradox ◽  
Theory Of Relativity ◽  
Apparent Paradox ◽  
Curved Space ◽  
Gravitational Fields

This chapter notes that the twin paradox is the best-known thought experiment associated with Einstein's theory of relativity. An astronaut who makes a journey into space in a high-speed rocket will return home to find he has aged less than his twin who stayed on Earth. This result appears puzzling, as the homebody twin can be considered to have done the travelling with respect to the traveller. Hence, it is called a “paradox”. In fact, there is no contradiction, and the apparent paradox has a simple resolution in special relativity with infinite flat space. In general relativity (dealing with gravitational fields and curved space-time), or in a compact space such as the hypersphere or a multiply connected finite space, the paradox is more complicated, but its resolution provides new insights about the structure of space–time and the limitations of the equivalence between inertial reference frames.

THE ASYMPTOTICALLY FREE AND ASYMPTOTICALLY CONFORMALLY INVARIANT GRAND UNIFICATION THEORIES IN CURVED SPACE-TIME

1990 ◽  
Vol 05 (20) ◽  
pp. 1599-1604 ◽  
Author(s):  
I.L. BUCHBINDER ◽  
I.L. SHAPIRO ◽  
E.G. YAGUNOV
Keyword(s):  
Renormalization Group ◽  
Gravitational Field ◽  
Gauge Group ◽  
Flat Space ◽  
Space Time ◽  
Grand Unification ◽  
Curved Space ◽  
Conformally Invariant ◽  
Renormalization Group Equations ◽  
The One

GUT’s in curved space-time is considered. The set of asymptotically free and asymptotically conformally invariant models based on the SU (N) gauge group is constructed. The general solutions of renormalization group equations are considered as the special ones. Several SU (2N) models, which are finite in flat space-time (on the one-loop level) and asymptotically conformally invariant in external gravitational field are also presented.

A Class of Energetically Rigid Gravitational Fields

1974 ◽  
Vol 29 (11) ◽  
pp. 1527-1530 ◽  
Author(s):  
H. Goenner
Keyword(s):  
Flat Space ◽  
Second Fundamental Form ◽  
Momentum Tensor ◽  
Space Time ◽  
Curved Space ◽  
Geometrical Properties ◽  
Gravitational Fields ◽  
The Second Fundamental Form ◽  
Perfect Fluids ◽  
Higher Dimensional

In Einstein's theory, the physics of gravitational fields is reflected by the geometry of the curved space-time manifold. One of the methods for a study of the geometrical properties of space-time consists in regarding it, locally, as embedded in a higher-dimensional flat space. In this paper, metrics admitting a 3-parameter group of motion are considered which form a generalization of spherically symmetric gravitational fields. A subclass of such metrics can be embedded into a five- dimensional flat space. It is shown that the second fundamental form governing the embedding can be expressed entirely by the energy-momentum tensor of matter and the cosmological constant. Such gravitational fields are called energetically rigid. As an application gravitating perfect fluids are discussed.

Sine-Gordon model in (1 + 1)-dimensional curved space: Schrödinger picture approach

1996 ◽  
Vol 74 (9-10) ◽  
pp. 626-633
Author(s):  
Anjana Sinha ◽  
Rajkumar Roychoudhury
Keyword(s):  
Effective Potential ◽  
Flat Space ◽  
Space Time ◽  
Curved Space ◽  
Curvature Term ◽  
Sine Gordon Model ◽  
Schrödinger Picture

The effective potential for the sine-Gordon model in a curved space-time, given by [Formula: see text], has been calculated using the Schrödinger picture formalism. It has been shown that when α(x) → 1 our method reproduces the flat-space results. To show the effect of the curvature term, the effective potential Veff has been calculated numerically for several values of the parameter M, where α(x) has been taken to be of the form [Formula: see text].

scholarly journals Four interactions in the sedenion curved spaces

2019 ◽  
Vol 16 (02) ◽  
pp. 1950019 ◽  
Author(s):  
Zi-Hua Weng
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Classical Mechanics ◽  
Flat Space ◽  
Field Equations ◽  
Curved Space ◽  
Gravitational Fields ◽  
Curved Spaces ◽  
Spatial Parameters ◽  
Physical Quantities

The paper aims to apply the complex-sedenions to explore the field equations of four fundamental interactions, which are relevant to the classical mechanics and quantum mechanics, in the curved spaces. Maxwell was the first to utilize the quaternions to describe the property of electromagnetic fields. Nowadays, the scholars introduce the complex-octonions to depict the electromagnetic and gravitational fields. And the complex-sedenions can be applied to study the field equations of the four interactions in the classical mechanics and quantum mechanics. Further, it is able to extend the field equations from the flat space into the curved space described with the complex-sedenions, by means of the tangent-frames and tensors. The research states that a few physical quantities will make a contribution to certain spatial parameters of the curved spaces. These spatial parameters may exert an influence on some operators (such as, divergence, gradient, and curl), impacting the field equations in the curved spaces, especially, the field equations of the four quantum-fields in the quantum mechanics. Apparently, the paper and General Relativity both confirm and succeed to the Cartesian academic thought of ‘the space is the extension of substance’.

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