scholarly journals COLLAPSING AND EXPANDING CYLINDRICALLY SYMMETRIC FIELDS WITH LIGHTLIKE WAVE-FRONTS IN GENERAL RELATIVITY

2002 ◽  
Vol 11 (04) ◽  
pp. 561-579 ◽  
Author(s):  
PAULO R. C. T. PEREIRA ◽  
A. Z. WANG
Keyword(s):  
General Relativity ◽  
Spacetime Singularities ◽  
Matter Field ◽  
Wave Fronts ◽  
Flat Spacetime ◽  
Cylindrically Symmetric ◽  
General Part ◽  
The Waves ◽  
Spacelike Infinity ◽  
Matter Fields

The dynamics of collapsing and expanding cylindrically symmetric gravitational and matter fields with lightlike wave-fronts is studied in General Relativity, using the Barrabés–Israel method. As an application of the general formulae developed, the collapse of a matter field that satisfies the condition RABgAB =0, (A,B = z, φ), in an otherwise flat spacetime background is studied. In particular, it is found that the gravitational collapse of a purely gravitational wave or a null dust fluid cannot be realized in a flat spacetime background. The studies are further specified to the collapse of purely gravitational waves and the general conditions for such collapse are found. It is shown that after the waves arrive at the axis, in general, part of them is reflected to spacelike infinity along the future light cone, and part of it is focused to form spacetime singularities on the symmetry axis. The cases where the collapse does not result in the formation of spacetime singularities are also identified.

scholarly journals CANONICAL AND GRAVITATIONAL STRESS-ENERGY TENSORS

2006 ◽  
Vol 15 (07) ◽  
pp. 959-989 ◽  
Author(s):  
M. LECLERC
Keyword(s):  
General Relativity ◽  
Matter Field ◽  
Field Energy ◽  
Energy Tensor ◽  
Maxwell System ◽  
Stress Energy Tensor ◽  
Spinor Fields ◽  
Gravitational Stress ◽  
Stress Energy ◽  
Matter Fields

We deal with the question, under which circumstances the canonical Noether stress-energy tensor is equivalent to the gravitational (Hilbert) tensor for general matter fields under the influence of gravity. In the framework of general relativity, the full equivalence is established for matter fields that do not couple to the metric derivatives. Spinor fields are included into our analysis by reformulating general relativity in terms of tetrad fields, and the case of Poincaré gauge theory, with an additional, independent Lorentz connection, is also investigated. Special attention is given to the flat limit, focusing on the expressions for the matter field energy (Hamiltonian). The Dirac–Maxwell system is investigated in detail, with special care given to the separation of free (kinetic) and interaction (or potential) energy. Moreover, the stress-energy tensor of the gravitational field itself is briefly discussed.

scholarly journals Hierarchical structure of physical Yukawa couplings from matter field Kähler metric

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Keiya Ishiguro ◽  
Tatsuo Kobayashi ◽  
Hajime Otsuka
Keyword(s):  
String Theory ◽  
Hierarchical Structure ◽  
Matter Field ◽  
Heterotic String ◽  
Heterotic String Theory ◽  
Kähler Metric ◽  
Yukawa Couplings ◽  
String Compactifications ◽  
Kahler Metric ◽  
Matter Fields

Abstract We study the impacts of matter field Kähler metric on physical Yukawa couplings in string compactifications. Since the Kähler metric is non-trivial in general, the kinetic mixing of matter fields opens a new avenue for realizing a hierarchical structure of physical Yukawa couplings, even when holomorphic Yukawa couplings have the trivial structure. The hierarchical Yukawa couplings are demonstrated by couplings of pure untwisted modes on toroidal orbifolds and their resolutions in the context of heterotic string theory with standard embedding. Also, we study the hierarchical couplings among untwisted and twisted modes on resolved orbifolds.

scholarly journals A type of Levi–Civita solution in modified Gauss–Bonnet gravity

2014 ◽  
Vol 92 (2) ◽  
pp. 173-176 ◽  
Author(s):  
M.E. Rodrigues ◽  
M.J.S. Houndjo ◽  
D. Momeni ◽  
R. Myrzakulov
Keyword(s):  
Exact Solution ◽  
General Relativity ◽  
Perfect Fluid ◽  
Cosmic String ◽  
Coupling Parameter ◽  
Vacuum Solution ◽  
Einstein Gravity ◽  
Parameter Family ◽  
Bonnet Gravity ◽  
Cylindrically Symmetric

Herein we obtain an exact solution for cylindrically symmetric modified Gauss–Bonnet gravity. This metric is a generalization of the vacuum solution of Levi–Civita in general relativity. It describes an isotropic perfect fluid one-parameter family of the gravitational configurations, which can be interpreted as the exterior metric of a cosmic string. By setting the Gauss–Bonnet coupling parameter to zero, we recover the vacuum solution in the Einstein gravity as well.

Do electromagnetic waves harbour gravitational waves?

2006 ◽  
Vol 462 (2071) ◽  
pp. 1987-2000 ◽  
Author(s):  
Brian Bramson
Keyword(s):  
General Relativity ◽  
Gravitational Waves ◽  
Electric Dipole ◽  
Electromagnetic Waves ◽  
Maxwell Theory ◽  
Flat Spacetime

In linearized, Einstein–Maxwell theory on flat spacetime, an oscillating electric dipole is the source of a spin-2 field. Within this approximation to general relativity, it is shown that electromagnetic waves harbour gravitational waves.

Gravitational waves

2019 ◽  
pp. 51-72
Author(s):  
Nils Andersson
Keyword(s):  
Gravitational Waves ◽  
Curved Spacetime ◽  
Flat Spacetime ◽  
The Waves

This chapter introduces the notion of gravitational waves, starting with a discussion of weak fluctuations on a flat spacetime background and later extending the notion to a general curved spacetime. The effect the waves have on matter is described and the derivation of the quadrupole formula, which allows estimates of the strength of relevant sources, is outlined. The vexing issue of the energy carried by gravitational waves is also discussed.

scholarly journals Rotating Melvin-like Universes and Wormholes in General Relativity

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1306
Author(s):  
Kirill Bronnikov ◽  
Vladimir Krechet ◽  
Vadim Oshurko
Keyword(s):  
Magnetic Field ◽  
General Relativity ◽  
Equation Of State ◽  
Symmetry Axis ◽  
Energy Condition ◽  
Flat Space ◽  
Stiff Matter ◽  
Cylindrically Symmetric ◽  
The One ◽  
The Magnetic Field

We find a family of exact solutions to the Einstein–Maxwell equations for rotating cylindrically symmetric distributions of a perfect fluid with the equation of state p=wρ (|w|<1), carrying a circular electric current in the angular direction. This current creates a magnetic field along the z axis. Some of the solutions describe geometries resembling that of Melvin’s static magnetic universe and contain a regular symmetry axis, while some others (in the case w>0) describe traversable wormhole geometries which do not contain a symmetry axis. Unlike Melvin’s solution, those with rotation and a magnetic field cannot be vacuum and require a current. The wormhole solutions admit matching with flat-space regions on both sides of the throat, thus forming a cylindrical wormhole configuration potentially visible for distant observers residing in flat or weakly curved parts of space. The thin shells, located at junctions between the inner (wormhole) and outer (flat) regions, consist of matter satisfying the Weak Energy Condition under a proper choice of the free parameters of the model, which thus forms new examples of phantom-free wormhole models in general relativity. In the limit w→1, the magnetic field tends to zero, and the wormhole model tends to the one obtained previously, where the source of gravity is stiff matter with the equation of state p=ρ.

Role of gravity in particle physics: A unified approach

2020 ◽  
Vol 29 (11) ◽  
pp. 2041012
Author(s):  
Pedro D. Alvarez ◽  
Mauricio Valenzuela ◽  
Jorge Zanelli
Keyword(s):  
General Relativity ◽  
Standard Model ◽  
Particle Physics ◽  
Laws Of Nature ◽  
Lorentz Transformations ◽  
Unified Approach ◽  
The Standard Model ◽  
Matter Fields

General Relativity (GR) and the Standard Model (SM) of particle physics are two enormously successful frameworks for our understanding the fundamental laws of nature. However, these theoretical schemes are widely disconnected, logically independent and unrelated in scope. Yet, GR and SM at some point must intersect, producing claims about phenomena that should be reconciled. Be it as it may, both schemes share a common basic ground: symmetry under local Lorentz transformations. Here, we will focus on the consequences of assuming this feature from the beginning to combine geometry, matter fields and gauge interactions. We give a rough description of how this could be instrumental for the construction of a unified scheme of gravitation and particle physics.

Transport of momentum by gravitational waves: the linear approximation

1961 ◽  
Vol 265 (1320) ◽  
pp. 109-116 ◽  
Keyword(s):  
General Relativity ◽  
Gravitational Waves ◽  
Linear Approximation ◽  
Energy Transport ◽  
The Waves ◽  
Relative Motions

Although energy transport by gravitational waves has been extensively studied, the question whether the waves transport momentum seems not to have been previously considered. In this paper, the latter problem is investigated, within general relativity, by studying waves emitted from a source consisting of a pair of oscillating particles. It is found that, for certain relative motions of the particles, momentum is permanently removed by the waves. This must presumably cause the source to move like a rocket.

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