Gravitational memory effects and Bondi-Metzner-Sachs symmetries in scalar-tensor theories

Abstract The relation between gravitational memory effects and Bondi-Metzner-Sachs symmetries of the asymptotically flat spacetimes is studied in the scalar-tensor theory. For this purpose, the solutions to the equations of motion near the future null infinity are obtained in the generalized Bondi-Sachs coordinates with a suitable determinant condition. It turns out that the Bondi-Metzner-Sachs group is also a semi-direct product of an infinite dimensional supertranslation group and the Lorentz group as in general relativity. There are also degenerate vacua in both the tensor and the scalar sectors in the scalar-tensor theory. The supertranslation relates the vacua in the tensor sector, while in the scalar sector, it is the Lorentz transformation that transforms the vacua to each other. So there are the tensor memory effects similar to the ones in general relativity, and the scalar memory effect, which is new. The evolution equations for the Bondi mass and angular momentum aspects suggest that the null energy fluxes and the angular momentum fluxes across the null infinity induce the transition among the vacua in the tensor and the scalar sectors, respectively.

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Plane Symmetric Solutions of a Scalar-Tensor Theory of Gravitation

Australian Journal of Physics ◽

10.1071/ph770109 ◽

1977 ◽

Vol 30 (1) ◽

pp. 109 ◽

Cited By ~ 6

Author(s):

DRK Reddy

Keyword(s):

General Relativity ◽

Empty Space ◽

Scalar Fields ◽

Scalar Tensor Theory ◽

Field Equations ◽

Plane Symmetric ◽

Zero Mass ◽

Tensor Theory ◽

Special Cases ◽

Theory Of Gravitation

Plane symmetric solutions of a scalar-tensor theory proposed by Dunn have been obtained. These solutions are observed to be similar to the plane symmetric solutions of the field equations corresponding to zero mass scalar fields obtained by Patel. It is found that the empty space-times of general relativity discussed by Taub and by Bera are obtained as special cases.

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Brans–Dicke type teleparallel scalar–tensor theory

Modern Physics Letters A ◽

10.1142/s0217732317501838 ◽

2017 ◽

Vol 32 (34) ◽

pp. 1750183 ◽

Cited By ~ 5

Author(s):

Mustafa Salti ◽

Oktay Aydogdu ◽

Hilmi Yanar ◽

Figen Binbay

Keyword(s):

General Relativity ◽

Dark Energy ◽

Scalar Field ◽

Noether Symmetry ◽

Scalar Tensor Theory ◽

Minimal Coupling ◽

Energy Effect ◽

New Model ◽

Symmetry Approach ◽

Tensor Theory

The teleparallel alternative of general relativity which is based on torsion instead of curvature is considered as the gravitational sector to explore the dark universe. Inspired from the well-known Brans–Dicke gravity, here, we introduce a new proposal for the galactic dark energy effect. The new model includes a scalar field with self-interacting potential and a non-minimal coupling between the gravity and scalar field. Additionally, we analyze the idea via the Noether symmetry approach and thermodynamics.

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Is Spacetime Non-metric?

Expert Opinion on Astronomy and Astrophysics ◽

10.18063/eoaa.v2i1.384 ◽

2018 ◽

Vol 2 (1) ◽

Cited By ~ 2

Author(s):

Mark D. Roberts

Keyword(s):

General Relativity ◽

Higher Dimensions ◽

Christoffel Symbol ◽

Einstein Frame ◽

Jordan Frame ◽

Scalar Tensor Theory ◽

Field Equations ◽

Extra Information ◽

Tensor Theory ◽

Palatini Variation

If one assumes higher dimensions and that dimensional reduction from higher dimensions produces scalar-tensor theory and also that Palatini variation is the correct method of varying scalar-tensor theory then spacetime is nonmetric. Palatini variation of Jordan frame lagrangians gives an equation relating the dilaton to the object of non-metricity and hence the existence of the dilaton implies that the spacetime connection is more general than that given soley by the Christoffel symbol of general relativity. Transferring from Jordan to Einstein frame, which connection, lagrangian, field equations and stress conservation equations occur are discussed: it is found that the Jordan frame has more information, this can be expressed in several ways, the simplest is that the extra information corresponds to the function multiplying the Ricci scalar in the action. The Einstein frame has the advantages that stress conservation implies no currents and that the field equations are easier to work with. This is illustrated by application to Robertson-Walker spacetime.

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Schiff's Proposed Gyroscope Experiment as a Test of the Scalar-Tensor Theory of General Relativity

Physical Review Letters ◽

10.1103/physrevlett.20.69 ◽

1968 ◽

Vol 20 (2) ◽

pp. 69-71 ◽

Cited By ~ 21

Author(s):

R. F. O'Connell

Keyword(s):

General Relativity ◽

Scalar Tensor Theory ◽

Tensor Theory

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A NOETHER SYMMETRY STUDY IN SCALAR-TENSOR THEORY

International Journal of Modern Physics A ◽

10.1142/s0217751x98001967 ◽

1998 ◽

Vol 13 (24) ◽

pp. 4163-4171 ◽

Cited By ~ 1

Author(s):

B. MODAK ◽

S. KAMILYA ◽

S. BISWAS

Keyword(s):

General Relativity ◽

Functional Form ◽

Noether Symmetry ◽

Scalar Tensor Theory ◽

Field Equations ◽

Tensor Theory ◽

Exponential Expansion ◽

General Scalar ◽

Spatially Homogeneous ◽

The Universe

In this work we study a general scalar-tensor theory in which the coupling and potential functions are determined from Noether symmetry arguments. We also obtain exact solutions of the field equations and found that the universe asymptotically follows an exponential expansion having no graceful exit. The study of the functional form of ω(φ) reveals that the theory asymptotically becomes an attractor of general relativity. We restrict ourselves to spatially homogeneous, isotropic flat universe.

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Symplectic geometry of radiative modes and conserved quantities at null infinity

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1981.0109 ◽

1981 ◽

Vol 376 (1767) ◽

pp. 585-607 ◽

Cited By ~ 117

Keyword(s):

Angular Momentum ◽

Gravitational Field ◽

Phase Space ◽

Degrees Of Freedom ◽

Symplectic Geometry ◽

Conserved Quantities ◽

Null Infinity ◽

Hamiltonian Description ◽

Infinite Dimensional ◽

Massless Spin

The Hamiltonian description of massless spin zero- and one-fields in Minkowski space is first recast in a way that refers only to null infinity and fields thereon representing radiative modes. With this framework as a guide, the phase space of the radiative degrees of freedom of the gravitational field (in exact general relativity) is introduced. It has the structure of an infinite-dimensional affine manifold (modelled on a Fréchet space) and is equipped with a continuous, weakly non-degenerate symplectic tensor field. The action of the Bondi-Metzner-Sachs group on null infinity is shown to induce canonical transformations on this phase space. The corresponding Hamiltonians – i. e. generating functions – are computed and interpreted as fluxes of supermomentum and angular momentum carried away by gravitational waves. The discussion serves three purposes: it brings out, via symplectic methods, the universality of the interplay between symmetries and conserved quantities; it sheds new light on the issue of angular momentum of gravitational radiation; and, it suggests a new approach to the quantization of the ‘true’ degrees of freedom of the gravitational field.

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Quasi-local mass and angular momentum in general relativity

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1982.0058 ◽

1982 ◽

Vol 381 (1780) ◽

pp. 53-63 ◽

Cited By ~ 239

Keyword(s):

General Relativity ◽

Angular Momentum ◽

Twistor Space ◽

New Approach ◽

Local Mass ◽

Bondi Mass ◽

Definition Of

A new approach to defining energy-momentum and angular momentum in general relativity is presented which avoids some of the difficulties of previous definitions and which can be applied quasi-locally. It depends on the construction of a twistor space T α ( S ) associated with any spacelike topological 2-sphere S . Though several problems of interpretation remain to be solved, the new definition works well at I + , reproducing the Bondi-mass-momentum as four of the ten precisely determined quantities at each cut of I + . The remaining six quantities provide a definition of angular momentum which appears to be new.

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