New conservation laws for zero rest-mass fields in asymptotically flat space-time

1968 ◽  
Vol 305 (1481) ◽  
pp. 175-204 ◽  
Keyword(s):  
Conservation Laws ◽  
Rest Mass ◽  
Power Series Expansion ◽  
Flat Space ◽  
Arbitrary Spin ◽  
Space Time ◽  
Maxwell Theory ◽  
Asymptotically Flat ◽  
Gravitational Fields ◽  
Higher Spin

Some recently discovered exact conservation laws for asymptotically flat gravitational fields are discussed in detail. The analogous conservation laws for zero rest-mass fields of arbitrary spin s = 0,½,1,...) in flat or asymptotically flat space-time are also considered and their connexion with a generalization of Kirchoff’s integral is pointed out. In flat space-time, an infinite hierarchy of such conservation laws exists for each spin value, but these have a somewhat trivial interpretation, describing the asymptotic incoming field (in fact giving the coefficients of a power series expansion of the incoming field). The Maxwell and linearized Einstein theories are analysed here particularly. In asymptotically flat space-time, only the first set of quantities of the hierarchy remain absolutely conserved. These are 4 s + 2 real quantities, for spin s , giving a D ( s , 0) representation of the Bondi-Metzner-Sachs group. But even for these quantities the simple interpretation in terms of incoming waves no longer holds good: it emerges from a study of the stationary gravitational fields that a contribution to the quantities involving the gravitational multipole structure of the field must also be present. Only the vacuum Einstein theory is analysed in this connexion here, the corresponding discussions of the Einstein-Maxwell theory (by Exton and the authors) and the Einstein-Maxwell-neutrino theory (by Exton) being given elsewhere. (A discussion of fields of higher spin in curved space-time along these lines would encounter the familiar difficulties first pointed out by Buchdahl.) One consequence of the discussion given here is that a stationary asymptotically flat gravitational field cannot become radiative and then stationary again after a finite time, except possibly if a certain (origin independent) quadratic combination of multipole moments returns to its original value. This indicates the existence of ‘tails’ to the outgoing waves (or back-scattered field),which destroys the stationary nature of the final field.

Peeling and conservation laws in the Born-Infeld theory of electromagnetism

1972 ◽  
Vol 72 (2) ◽  
pp. 319-324 ◽  
Author(s):  
John R. Porter
Keyword(s):  
General Relativity ◽  
Conservation Laws ◽  
Iterative Methods ◽  
Linear Theory ◽  
Point Charge ◽  
Flat Space ◽  
The Self ◽  
Conserved Quantities ◽  
Maxwell Theory ◽  
Asymptotically Flat

1. Introduction Born and Infeld originally proposed their non-linear theory of electromagnetism (1) as one derivable from a Lorentz invariant Lagrangian and, in contradistinction to the usual Maxwell theory, possessing solutions of the ‘point charge’ type without singularities at the position of the charge. Subsequently, examination of the theory by means of iterative methods (2) has demonstrated the self-scattering of outgoing radiation and the existence of wave tails. In the present paper it is shown that the theory, under suitable asymptotic conditions, gives rise to peeling of the type exhibited by Maxwell's theory as well as by the asymptotically flat space-times of general relativity (3, 4, 5). It is also shown that certain conserved quantities exist paralleling those exhibited in the above theories. The Maxwell theory exhibits a sequence of such conserved quantities, the truncation of which is examined in detail for the Born-Infeld theory.

scholarly journals The Thermodynamic Relationship between the RN-AdS Black Holes and the RN Black Hole in Canonical Ensemble

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Yu-Bo Ma ◽  
Li-Chun Zhang ◽  
Jian Liu ◽  
Ren Zhao ◽  
Shuo Cao
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Flat Space ◽  
Space Time ◽  
Asymptotically Flat ◽  
Time Space ◽  
Ads Black Holes ◽  
Different Types ◽  
Thermodynamic Relationship ◽  
The Relationship

In this paper, by analyzing the thermodynamic properties of charged AdS black hole and asymptotically flat space-time charged black hole in the vicinity of the critical point, we establish the correspondence between the thermodynamic parameters of asymptotically flat space-time and nonasymptotically flat space-time, based on the equality of black hole horizon area in the two different types of space-time. The relationship between the cavity radius (which is introduced in the study of asymptotically flat space-time charged black holes) and the cosmological constant (which is introduced in the study of nonasymptotically flat space-time) is determined. The establishment of the correspondence between the thermodynamics parameters in two different types of space-time is beneficial to the mutual promotion of different time-space black hole research, which is helpful to understand the thermodynamics and quantum properties of black hole in space-time.

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.

ON THE PHYSICAL INTERPRETATION OF ASYMPTOTICALLY FLAT GRAVITATIONAL FIELDS

2008 ◽  
Vol 17 (13n14) ◽  
pp. 2599-2606
Author(s):  
CARLOS KOZAMEH ◽  
EZRA T. NEWMAN ◽  
GILBERTO SILVA-ORTIGOZA
Keyword(s):  
Vector Fields ◽  
Center Of Mass ◽  
Flat Space ◽  
Einstein Equations ◽  
Position Vector ◽  
Approximate Symmetry ◽  
Asymptotically Flat ◽  
Gravitational Fields ◽  
Maxwell Fields ◽  
Physical Information

A problem in general relativity is how to extract physical information from solutions to the Einstein equations. Most often information is found from special conditions, e.g., special vector fields, symmetries or approximate symmetries. Our concern is with asymptotically flat space–times with approximate symmetry: the BMS group. For these spaces the Bondi four-momentum vector and its evolution, found at infinity, describes the total energy–momentum and the energy–momentum radiated. By generalizing the simple idea of the transformation of (electromagnetic) dipoles under a translation, we define (analogous to center of charge) the center of mass for asymptotically flat Einstein–Maxwell fields. This gives kinematical meaning to the Bondi four-momentum, i.e., the four-momentum and its evolution is described in terms of a center of mass position vector, its velocity and spin-vector. From dynamical arguments, a unique (for our approximation) total angular momentum and evolution equation in the form of a conservation law is found.

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.

Higher spin theories in flat space–time

2018 ◽  
Vol 33 (34) ◽  
pp. 1845007
Author(s):  
Loriano Bonora
Keyword(s):  
Equations Of Motion ◽  
Flat Space ◽  
Space Time ◽  
Local Fields ◽  
Field Theories ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Higher Spin ◽  
Chern Simons

It is shown that, contrary to a widespread prejudice, massless higher spin (HS) field theories can be defined in flat space–time. Examples of Yang–Mills-like theories with infinite many local fields of any spin are constructed explicitly in any dimension, along with Chern–Simons-like models in any odd dimension. These theories are defined via actions invariant under HS gauge transformations and their equations of motion are derived. It is also briefly explained why these theories circumvent well-known no-go theorems.

Flat space-times with gravitational fields

1959 ◽  
Vol 252 (1268) ◽  
pp. 45-50 ◽  
Keyword(s):  
Gravitational Field ◽  
Curvature Tensor ◽  
Flat Space ◽  
Space Time ◽  
Gravitational Fields ◽  
Extended Region

The geometry of an extended region of space-time is not fully determined by the vanishing of the Hiemann curvature tensor. This suggests the possible existence of a non-trivial gravitational field where space-time is flat. Two examples of such fields are considered with reference to their sources.

scholarly journals Mass in de Sitter and Anti-de-Sitter Universes with Regard to Dark Matter

2020 ◽  
Author(s):  
Jean-Pierre Gazeau
Keyword(s):  
Dark Matter ◽  
Irreducible Representation ◽  
Rest Mass ◽  
Flat Space ◽  
Space Time ◽  
Energy Scale ◽  
Unitary Irreducible Representation ◽  
De Sitter ◽  
Rest Energy ◽  
Point Energy

An explanation of the origin of dark matter is suggested in this work. The argument is based on symmetry considerations about the concept of mass. In the Wigner's view, the rest mass and the spin of a free elementary particle in flat space-time are the two invariants that characterize the associated unitary irreducible representation of the Poincar\'e group. The Poincar\'e group has two and only two deformations with maximal symmetry. They describe respectively the de Sitter (dS) and Anti de Sitter (AdS) kinematic symmetries. Analogously to their shared flat space-time limit, two invariants, spin and energy scale for de Sitter and rest energy for Anti de Sitter, characterize the unitary irreducible representation associated with dS and AdS elementary systems. While the dS energy scale is a simple deformation of the Poincaré rest energy and so has a purely mass nature, AdS rest energy is the sum of a purely mass component and a kind of zero-point energy derived from the curvature. An analysis based on recent estimates on the chemical freeze-out temperature marking in Early Universe the phase transition quark-gluon plasma epoch to the hadron epoch supports the guess that dark matter energy might originate from an effective AdS curvature energy.

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