scholarly journals Asymptotic symmetries in Carrollian theories of gravity

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Alfredo Pérez
Keyword(s):  
General Relativity ◽  
Symmetry Algebra ◽  
Einstein Gravity ◽  
Point Of View ◽  
Asymptotic Symmetry ◽  
Gravitational Theories ◽  
Theories Of Gravity ◽  
Spatial Rotations ◽  
Lapse Function ◽  
Asymptotic Symmetries

Abstract Asymptotic symmetries in Carrollian gravitational theories in 3+1 space and time dimensions obtained from “magnetic” and “electric” ultrarelativistic contractions of General Relativity are analyzed. In both cases, parity conditions are needed to guarantee a finite symplectic term, in analogy with Einstein gravity. For the magnetic contraction, when Regge-Teitelboim parity conditions are imposed, the asymptotic symmetries are described by the Carroll group. With Henneaux-Troessaert parity conditions, the asymptotic symmetry algebra corresponds to a BMS-like extension of the Carroll algebra. For the electric contraction, because the lapse function does not appear in the boundary term needed to ensure a well-defined action principle, the asymptotic symmetry algebra is truncated, for Regge-Teitelboim parity conditions, to the semidirect sum of spatial rotations and spatial translations. Similarly, with Henneaux-Troessaert parity conditions, the asymptotic symmetries are given by the semidirect sum of spatial rotations and an infinite number of parity odd supertranslations. Thus, from the point of view of the asymptotic symmetries, the magnetic contraction can be seen as a smooth limit of General Relativity, in contrast to its electric counterpart.

Kleinian characterization of asymptotic symmetries of real general relativity

1993 ◽  
Vol 441 (1913) ◽  
pp. 465-471 ◽  
Keyword(s):  
General Relativity ◽  
Automorphism Group ◽  
Group Action ◽  
Radon Transform ◽  
Symmetry Groups ◽  
Asymptotic Symmetry ◽  
The Real ◽  
The Given ◽  
Asymptotic Symmetries

According to Klein’s Erlanger programme, one may (indirectly) specify a geometry by giving a group action. Conversely, given a group action, one may ask for the corresponding geometry. Recently, I showed that the real asymptotic symmetry groups of general relativity (in any signature) have natural ‘projective’ classical actions on suitable ‘Radon transform’ spaces of affine 3-planes in flat 4-space. In this paper, I give concrete models for these groups and actions. Also, for the ‘atomic’ cases, I give geometric structures for the spaces of affine 3-planes for which the given actions are the automorphism group.

scholarly journals The theory of spherically symmetric thin shells in conformal gravity

2018 ◽  
Vol 27 (06) ◽  
pp. 1841012 ◽  
Author(s):  
Victor Berezin ◽  
Vyacheslav Dokuchaev ◽  
Yury Eroshenko
Keyword(s):  
General Relativity ◽  
Weyl Tensor ◽  
Delta Function ◽  
Einstein Gravity ◽  
Riemann Tensor ◽  
Momentum Tensor ◽  
Thin Shells ◽  
Spherically Symmetric ◽  
Gravitational Fields ◽  
Gravitational Theories

The spherically symmetric thin shells are the nearest generalizations of the point-like particles. Moreover, they serve as the simple sources of the gravitational fields both in General Relativity and much more complex quadratic gravity theories. We are interested in the special and physically important case when all the quadratic in curvature tensor (Riemann tensor) and its contractions (Ricci tensor and scalar curvature) terms are present in the form of the square of Weyl tensor. By definition, the energy–momentum tensor of the thin shell is proportional to Diracs delta-function. We constructed the theory of the spherically symmetric thin shells for three types of gravitational theories with the shell: (1) General Relativity; (2) Pure conformal (Weyl) gravity where the gravitational part of the total Lagrangian is just the square of the Weyl tensor; (3) Weyl–Einstein gravity. The results are compared with these in General Relativity (Israel equations). We considered in detail the shells immersed in the vacuum. Some peculiar properties of such shells are found. In particular, for the traceless ([Formula: see text] massless) shell, it is shown that their dynamics cannot be derived from the matching conditions and, thus, is completely arbitrary. On the contrary, in the case of the Weyl–Einstein gravity, the trajectory of the same type of shell is completely restored even without knowledge of the outside solution.

scholarly journals Lie theory for asymptotic symmetries in general relativity: The BMS Group

2022 ◽  
Author(s):  
David Nicolas Prinz ◽  
Alexander Schmeding
Keyword(s):  
General Relativity ◽  
Lie Group ◽  
Group Structure ◽  
Symmetry Groups ◽  
Asymptotic Symmetry ◽  
Infinite Dimensional ◽  
Real Analytic ◽  
Definition Of ◽  
Future Work ◽  
Asymptotic Symmetries

Abstract We study the Lie group structure of asymptotic symmetry groups in General Relativity from the viewpoint of infinite-dimensional geometry. To this end, we review the geometric definition of asymptotic simplicity and emptiness due to Penrose and the coordinate-wise definition of asymptotic flatness due to Bondi et al. Then we construct the Lie group structure of the Bondi--Metzner--Sachs (BMS) group and discuss its Lie theoretic properties. We find that the BMS group is regular in the sense of Milnor, but not real analytic. This motivates us to conjecture that it is not locally exponential. Finally, we verify the Trotter property as well as the commutator property. As an outlook, we comment on the situation of related asymptotic symmetry groups. In particular, the much more involved situation of the Newman--Unti group is highlighted, which will be studied in future work.

scholarly journals TOWERS OF GRAVITATIONAL THEORIES

2006 ◽  
Vol 15 (12) ◽  
pp. 2293-2302 ◽  
Author(s):  
WALTER D. GOLDBERGER ◽  
IRA Z. ROTHSTEIN
Keyword(s):  
Black Hole ◽  
Bound States ◽  
Degrees Of Freedom ◽  
Mechanical Energy ◽  
Point Of View ◽  
Dissipative Effects ◽  
Physical Measurements ◽  
Gravitational Theories ◽  
Theories Of Gravity ◽  
Dynamical Degrees

In this essay, we introduce a theoretical framework designed to describe black hole dynamics. The difficulties in understanding such dynamics stems from the proliferation of scales involved when one attempts to simultaneously describe all of the relevant dynamical degrees of freedom. These range from the modes that describe the black hole horizon, which are responsible for dissipative effects, to the long wavelength gravitational radiation that drains mechanical energy from macroscopic black hole bound states. We approach the problem from a Wilsonian point of view, by building a tower of theories of gravity each of which is valid at different scales. The methodology leads to multiple new results in diverse topics including phase transitions of Kaluza–Klein black holes and the interactions of spinning black hole in non-relativistic orbits. Moreover, our methods tie together speculative ideas regarding dualities for black hole horizons to real physical measurements in gravitational wave detectors.

scholarly journals A new golden age: testing general relativity with cosmology

2011 ◽  
Vol 369 (1957) ◽  
pp. 4941-4946
Author(s):  
Rachel Bean ◽  
Pedro G. Ferreira ◽  
Andy Taylor
Keyword(s):  
General Relativity ◽  
Large Scale ◽  
Large Scale Structure ◽  
Einstein Gravity ◽  
Field Equations ◽  
The Past ◽  
Cosmological Observations ◽  
Wide Range ◽  
Theories Of Gravity ◽  
The Universe

Gravity drives the evolution of the Universe and is at the heart of its complexity. Einstein's field equations can be used to work out the detailed dynamics of space and time and to calculate the emergence of large-scale structure in the distribution of galaxies and radiation. Over the past few years, it has become clear that cosmological observations can be used not only to constrain different world models within the context of Einstein gravity but also to constrain the theory of gravity itself. In this article, we look at different aspects of this new field in which cosmology is used to test theories of gravity with a wide range of observations.

scholarly journals Extensions of the asymptotic symmetry algebra of general relativity

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Éanna É. Flanagan ◽  
Kartik Prabhu ◽  
Ibrahim Shehzad
Keyword(s):  
General Relativity ◽  
Symmetry Algebra ◽  
Asymptotic Symmetry

Scalar fields in generalized theories of gravity: Limit to general relativity

2020 ◽  
Vol 35 (02n03) ◽  
pp. 2040006
Author(s):  
Piret Kuusk
Keyword(s):  
General Relativity ◽  
Scalar Fields ◽  
Einstein Gravity ◽  
Scalar Tensor Theory ◽  
Action Functional ◽  
Tensor Theory ◽  
General Action ◽  
Theories Of Gravity ◽  
Theory Of Gravitation ◽  
Special Case

The general action functional for a scalar-tensor theory of gravitation without derivative couplings is considered together with its special case of the Brans–Dicke theory. The aim of the paper is to clarify the problem of anomalous limit of the Brans–Dicke to the Einstein gravity.

scholarly journals Asymptotic symmetries and celestial CFT

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Laura Donnay ◽  
Sabrina Pasterski ◽  
Andrea Puhm
Keyword(s):  
Principal Series ◽  
Finite Energy ◽  
Continuous Series ◽  
Asymptotic Symmetry ◽  
Null Infinity ◽  
Conformal Dimension ◽  
Contour Integrals ◽  
Celestial Sphere ◽  
Goldstone Modes ◽  
Asymptotic Symmetries

Abstract We provide a unified treatment of conformally soft Goldstone modes which arise when spin-one or spin-two conformal primary wavefunctions become pure gauge for certain integer values of the conformal dimension ∆. This effort lands us at the crossroads of two ongoing debates about what the appropriate conformal basis for celestial CFT is and what the asymptotic symmetry group of Einstein gravity at null infinity should be. Finite energy wavefunctions are captured by the principal continuous series ∆ ∈ 1 + iℝ and form a complete basis. We show that conformal primaries with analytically continued conformal dimension can be understood as certain contour integrals on the principal series. This clarifies how conformally soft Goldstone modes fit in but do not augment this basis. Conformally soft gravitons of dimension two and zero which are related by a shadow transform are shown to generate superrotations and non-meromorphic diffeomorphisms of the celestial sphere which we refer to as shadow superrotations. This dovetails the Virasoro and Diff(S2) asymptotic symmetry proposals and puts on equal footing the discussion of their associated soft charges, which correspond to the stress tensor and its shadow in the two-dimensional celestial CFT.

scholarly journals Breaking the cosmological background degeneracy by two-fluid perturbations in f(R) gravity

2015 ◽  
Vol 24 (07) ◽  
pp. 1550053 ◽  
Author(s):  
Amare Abebe
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Structure Formation ◽  
Background Level ◽  
Cosmological Perturbations ◽  
Gauge Invariant ◽  
First Order ◽  
Cosmological Background ◽  
Theories Of Gravity ◽  
Two Fluid

One of the exact solutions of f(R) theories of gravity in the presence of different forms of matter exactly mimics the ΛCDM solution of general relativity (GR) at the background level. In this work we study the evolution of scalar cosmological perturbations in the covariant and gauge-invariant formalism and show that although the background in such a model is indistinguishable from the standard ΛCDM cosmology, this degeneracy is broken at the level of first-order perturbations. This is done by predicting different rates of structure formation in ΛCDM and the f(R) model both in the complete and quasi-static regimes.

scholarly journals Astronomical tests of relativity: beyond parameterized post-Newtonian formalism (PPN), to testing fundamental principles

2009 ◽  
Vol 5 (S261) ◽  
pp. 56-61 ◽  
Author(s):  
Vladik Kreinovich
Keyword(s):  
General Relativity ◽  
Quantum Physics ◽  
Final Theory ◽  
Gravitational Theories ◽  
Cosmological Observations ◽  
Partial Analysis ◽  
Theory Of Gravitation ◽  
Improved Accuracy ◽  
Fundamental Physical ◽  
Relativistic Gravitation

AbstractBy the early 1970s, the improved accuracy of astrometric and time measurements enabled researchers not only to experimentally compare relativistic gravity with the Newtonian predictions, but also to compare different relativistic gravitational theories (e.g., the Brans-Dicke Scalar-Tensor Theory of Gravitation). For this comparison, Kip Thorne and others developed the Parameterized Post-Newtonian Formalism (PPN), and derived the dependence of different astronomically observable effects on the values of the corresponding parameters.Since then, all the observations have confirmed General Relativity. In other words, the question of which relativistic gravitation theory is in the best accordance with the experiments has been largely settled. This does not mean that General Relativity is the final theory of gravitation: it needs to be reconciled with quantum physics (into quantum gravity), it may also need to be reconciled with numerous surprising cosmological observations, etc. It is, therefore, reasonable to prepare an extended version of the PPN formalism, that will enable us to test possible quantum-related modifications of General Relativity.In particular, we need to include the possibility of violating fundamental principles that underlie the PPN formalism but that may be violated in quantum physics, such as scale-invariance, T-invariance, P-invariance, energy conservation, spatial isotropy violations, etc. In this paper, we present the first attempt to design the corresponding extended PPN formalism, with the (partial) analysis of the relation between the corresponding fundamental physical principles.

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