ASYMPTOTICALLY FLAT SPACETIMES AT SPATIAL INFINITY: THE FIELD APPROACH AND THE LAGRANGIAN DESCRIPTION

1995 ◽  
Vol 04 (04) ◽  
pp. 451-478 ◽  
Author(s):  
A.N. PETROV
Keyword(s):  
Lagrangian Description ◽  
Energy Tensor ◽  
Integrals Of Motion ◽  
Spatial Infinity ◽  
Suggested Approach ◽  
Asymptotically Flat ◽  
Gauge Transformations ◽  
Stress Energy ◽  
Flat Spacetimes ◽  
Definition Of

An asymptotically flat spacetime (AFST) at spatial infinity is studied. The technique of the field formulation of general relativity developed earlier is used. The properties of the latter are similar to those of an ordinary gauge field theory in a fixed background spacetime. We give a definition of an AFST. The role of a background is played by Minkowski space. Integrals of motion are defined with the use of a stress-energy tensor of the gravitational field together with its sources and Killing vectors of the background spacetime. For each of the following AFST characteristics, namely the definition and the values of the integrals of motion and the action integral, we have found the weakest asymptotics for gauge transformations such that this characteristic does not change under the gauge transformations. These three kinds of falloff conditions are compared. The suggested approach is discussed and compared with some known results and methods.

Asymptotically Flat Spacetimes at Spatial Infinity: II. Gauge Invariance of the Integrals of Motion in the Field Approach

1997 ◽  
Vol 06 (02) ◽  
pp. 239-261 ◽  
Author(s):  
A. N. Petrov
Keyword(s):  
Gauge Invariance ◽  
Point Of View ◽  
Lagrangian Description ◽  
Integrals Of Motion ◽  
Spatial Infinity ◽  
Hamiltonian Description ◽  
Asymptotically Flat ◽  
Gauge Transformations ◽  
Field Approach ◽  
Flat Spacetimes

In this paper we complete the work which was started in an earlier paper where asymptotically flat spacetimes at spatial infinity were examined in the framework in the field approach to general relativity (GR) in the Lagrangian description. In the field formulation of GR, the Hamiltonian description of a real isolated system for which all the physical fields are concentrated in a confined domain of space is developed. The integrals of motion are constructed and examined under the weakest fall-off conditions for gravitational potentials found earlier. It is shown that these integrals of motion are exactly the Arnowitt–Deser–Misner (ADM) integrals. The gauge invariance of the integrals of motion in both the Lagrangian and the Hamiltonian descriptions in studied from the point of view of the field approach to GR. It is found that the invariance of the ADM integrals of motion, which follows from the Stokes theorem, is explained as a gauge invariance of the linear field of the spin 2. The ambiguities in the ADM angular momentum can be explained as a violation of the weakest fall-off conditions for the gauge transformations found earlier.

scholarly journals BMS flux algebra in celestial holography

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Laura Donnay ◽  
Romain Ruzziconi
Keyword(s):  
Solution Space ◽  
Coadjoint Representation ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Asymptotically Flat ◽  
Flat Spacetime ◽  
Stress Energy ◽  
Momentum Fluxes ◽  
Non Local ◽  
Asymptotic Symmetries

Abstract Starting from gravity in asymptotically flat spacetime, the BMS momentum fluxes are constructed. These are non-local expressions of the solution space living on the celestial Riemann surface. They transform in the coadjoint representation of the extended BMS group and correspond to Virasoro primaries under the action of bulk superrotations. The relation between the BMS momentum fluxes and celestial CFT operators is then established: the supermomentum flux is related to the supertranslation operator and the super angular momentum flux is linked to the stress-energy tensor of the celestial CFT. The transformation under the action of asymptotic symmetries and the OPEs of the celestial CFT currents are deduced from the BMS flux algebra.

Singular gauge transformations in geometrodynamics

2021 ◽  
pp. 2150150
Author(s):  
Alcides Garat
Keyword(s):  
Electromagnetic Fields ◽  
Local Group ◽  
Energy Tensor ◽  
Direct Connection ◽  
Maxwell Stress ◽  
Direct Link ◽  
Stress Energy Tensor ◽  
Gauge Transformations ◽  
Local Gauge ◽  
Stress Energy

The new tetrads introduced previously for non-null electromagnetic fields in Einstein–Maxwell spacetimes enable a direct link to the local electromagnetic gauge group of transformations. Due to the peculiar elements in the construction of these new tetrads, a direct connection can be established between the local group of electromagnetic gauge transformations and local groups of tetrad transformations on two different local and orthogonal planes of eigenvectors of the Einstein–Maxwell stress–energy tensor. These tetrad vectors are gauge dependent. It is an interesting and relevant problem to study if there are local gauge transformations that can map on the timelike-spacelike plane, the timelike and the spacelike vectors into the intersection of the local light cone and the plane itself. How many of these local gauge transformations exist and how the mathematics and the geometry of these particular transformations play out. These local gauge transformations would be singular and it is important to identify them.

scholarly journals ANALYSIS OF UNBALANCED BLACK RING SOLUTIONS WITHIN THE QUASILOCAL FORMALISM

2011 ◽  
Vol 20 (04) ◽  
pp. 581-591 ◽  
Author(s):  
ZHENXING LIU ◽  
ZEQIAN CHEN
Keyword(s):  
Black Ring ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Asymptotically Flat ◽  
Black Rings ◽  
Balance Condition ◽  
Extra Term ◽  
Stress Energy ◽  
Boundary Stress ◽  
Kaluza Klein

We investigate the properties of rotating asymptotically flat black ring solutions in five-dimensional Einstein–Maxwell-dilaton gravity with the Kaluza–Klein coupling. Within the quasilocal formalism, the balance condition for these solutions is derived by using the conservation of the renormalized boundary stress–energy tensor, which is a new method proposed by Astefanesei and his collaborators. We also study the thermodynamics of unbalanced black rings. The conserved charges and the thermodynamical quantities are computed. Due to the existence of a conical singularity in the boundary, these quantities differ from the original regular ones. It is shown that the Smarr relation and the quantum statistical relation are still satisfied. However, we get an extra term in the first law of thermodynamics. As the balance condition is imposed this extra term vanishes.

scholarly journals New Tetrads in Riemannian Geometry and New Ensuing Results in Group Theory, Gauge Theory and Fundamental Physics in Particle Physics, General Relativity and Astrophysics

2017 ◽  
Vol 45 ◽  
pp. 1760004 ◽  
Author(s):  
Alcides Garat
Keyword(s):  
Particle Physics ◽  
Maxwell Equations ◽  
Local Group ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Fundamental Physics ◽  
Gauge Transformations ◽  
Stress Energy ◽  
The Sixties ◽  
Evolution Algorithms

A new tetrad is introduced within the framework of geometrodynamics for non-null electromagnetic fields. This tetrad diagonalizes the electromagnetic stress-energy tensor and allows for maximum simplification of the expression of the electromagnetic field. The Einstein-Maxwell equations will also be simplified. New group isomorphisms are proved. The local group of electromagnetic gauge transformations is isomorphic to the new group LB1. LB1 is the group of local tetrad transformations comprised by SO(1,1) plus two different kinds of discrete transformations. The local group of electromagnetic gauge transformations is also isomorphic to the local group of tetrad transformations LB2, which is SO(2), as well. Therefore, we proved that LB1 is isomorphic to LB2. These group results amount to proving that the no-go theorems of the sixties like the S. Coleman- J. Mandula, the S. Weinberg or L. ORaifeartagh versions are incorrect. Not because of their internal logic, but because of the assumptions made at the outset of all these versions. These new tetrads are useful in astrophysics spacetime evolution algorithms since they introduce maximum simplification in all relevant objects, specially in stress-energy tensors.

Signature-causality reflection generated by Abelian gauge transformations

2020 ◽  
Vol 35 (15) ◽  
pp. 2050119
Author(s):  
Alcides Garat
Keyword(s):  
Lorentz Transformation ◽  
Local Group ◽  
The Other ◽  
Energy Tensor ◽  
Abelian Gauge ◽  
Discrete Transformation ◽  
Gauge Transformations ◽  
Stress Energy ◽  
Local Plane ◽  
Electromagnetic Tensor

In this paper, we want to better understand the causality reflection that arises under a subset of Abelian local gauge transformations in geometrodynamics. We proved in previous papers that in Einstein–Maxwell spacetimes, there exist two local orthogonal planes of gauge symmetry at every spacetime point for non-null electromagnetic fields. Every vector in these planes is an eigenvector of the Einstein–Maxwell stress–energy tensor. The vectors that span these local orthogonal planes are dependent on electromagnetic gauge. The local group of Abelian electromagnetic gauge transformations has been proved isomorphic to the local groups of tetrad transformations in these planes. We called LB1 the local group of tetrad transformations made up of SO(1, 1) plus two different kinds of discrete transformations. One of the discrete transformations is the full inversion two by two which is a Lorentz transformation. The other discrete transformation is given by a matrix with zeroes on the diagonal and ones off-diagonal two by two, a reflection. The group LB1 is realized on this plane, we call this plane one, and is spanned by the time-like and one space-like vectors. The other local orthogonal plane is plane two and the local group of tetrad transformations, we call this LB2, which is just SO(2). The local group of Abelian electromagnetic gauge transformations is isomorphic to both LB1 and LB2, independently. It has already been proved that a subset of local electromagnetic gauge transformations that leave the electromagnetic tensor invariant induces a change in sign in the norm of the tetrad vectors that span the local plane one. The reason is that one of the discrete transformations on the local plane one that belongs to the group LB1 is not a Lorentz transformation, it is a flip or reflection. It is precisely on this kind of discrete transformation that we have an interest since it has the effect of changing the signature and the causality. This effect has never been noticed before.

scholarly journals Tetrads in SU(3) × SU(2) × U(1) Yang–Mills geometrodynamics

2018 ◽  
Vol 15 (03) ◽  
pp. 1850045 ◽  
Author(s):  
Alcides Garat
Keyword(s):  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Noncompact Group ◽  
Gauge Invariant ◽  
Gauge Groups ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Local Gauge ◽  
Stress Energy ◽  
Local Plane

The relationship between gauge and gravity amounts to understanding the underlying new geometrical local structures. These structures are new tetrads specially devised for Yang–Mills theories, Abelian and non-Abelian in four-dimensional Lorentzian curved spacetimes. In the present paper, a new tetrad is introduced for the Yang–Mills [Formula: see text] formulation. These new tetrads establish a link between local groups of gauge transformations and local groups of spacetime transformations that we previously called LB1 and LB2. New theorems are proved regarding isomorphisms between local internal [Formula: see text] groups and local tensor products of spacetime LB1 and LB2 groups of transformations. These new tetrads define at every point in spacetime two orthogonal planes that we called blades or planes one and two. These are the local planes of covariant diagonalization of the stress–energy tensor. These tetrads are gauge dependent. Tetrad local gauge transformations leave the tetrads inside the local original planes without leaving them. These local tetrad gauge transformations enable the possibility to connect local gauge groups Abelian or non-Abelian with local groups of tetrad transformations. On the local plane one, the Abelian group [Formula: see text] of gauge transformations was already proved to be isomorphic to the tetrad local group of transformations LB1, for example. LB1 is [Formula: see text] plus two different kinds of discrete transformations. On the local orthogonal plane two [Formula: see text] is isomorphic to LB2 which is just [Formula: see text]. That is, we proved that LB1 is isomorphic to [Formula: see text] which is a remarkable result since a noncompact group plus two discrete transformations is isomorphic to a compact group. These new tetrads have displayed manifestly and nontrivially the coupling between Yang–Mills fields and gravity. The new tetrads and the stress–energy tensor allow for the introduction of three new local gauge invariant objects. Using these new gauge invariant objects and in addition a new general local duality transformation, a new algorithm for the gauge invariant diagonalization of the Yang–Mills stress–energy tensor is developed as an application. This is a paper about grand Standard Model gauge theories — General Relativity gravity unification and grand group unification in four-dimensional curved Lorentzian spacetimes.

scholarly journals Implications of a frame dependent gravitational effective action for perturbations on the Robertson–Walker metric

2017 ◽  
Vol 26 (14) ◽  
pp. 1750159 ◽  
Author(s):  
Stephen L. Adler
Keyword(s):  
Effective Action ◽  
Scalar Perturbation ◽  
Energy Tensor ◽  
Scaling Invariance ◽  
Gauge Transformations ◽  
Stress Energy ◽  
Walker Metric ◽  
Three Space ◽  
Coordinate Invariance ◽  
Metric Perturbation

In earlier work we showed that a frame dependent effective action motivated by the postulates of three-space general coordinate invariance and Weyl scaling invariance exactly mimics a cosmological constant in Robertson–Walker (RW) spacetimes. Here we study the implications of this effective action for small fluctuations around a spatially flat RW background geometry. The equations for the conserving extension of the modified stress-energy tensor can be integrated in closed form, and involve only the metric perturbation [Formula: see text]. Hence the equations for tensor and vector perturbations are unmodified, but there are Hubble scale additions to the scalar perturbation equations, which nonetheless admit no propagating wave solutions. Consequently, there are no modifications to standard gravitational wave propagation theory, but there may be observable implications for cosmology. We give a self-contained discussion, including an analysis of the restricted class of gauge transformations that act when a frame dependent effective action is present.

scholarly journals Wormhole geometries in Eddington-Inspired Born–Infeld gravity

2015 ◽  
Vol 30 (35) ◽  
pp. 1550190 ◽  
Author(s):  
Tiberiu Harko ◽  
Francisco S. N. Lobo ◽  
M. K. Mak ◽  
Sergey V. Sushkov
Keyword(s):  
Exact Solution ◽  
Nonlinear Electrodynamics ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Field Equations ◽  
Asymptotically Flat ◽  
Gravitational Field Equations ◽  
Stress Energy ◽  
Modified Theory Of Gravity ◽  
Modified Theory

Eddington-inspired Born–Infeld (EiBI) gravity is a recently proposed modified theory of gravity, based on the classic work of Eddington and Born–Infeld nonlinear electrodynamics. In this paper, we consider the possibility that wormhole geometries are sustained in EiBI gravity. We present the gravitational field equations for an anisotropic stress–energy tensor and consider the generic conditions, for the auxiliary metric, at the wormhole throat. In addition to this, we obtain an exact solution for an asymptotically flat wormhole.

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