scholarly journals Asymptotically Flat Boundary Conditions for the U(1)3 Model for Euclidean Quantum Gravity

Universe ◽  
2021 ◽  
Vol 7 (3) ◽  
pp. 68
Author(s):  
Sepideh Bakhoda ◽  
Hossein Shojaie ◽  
Thomas Thiemann
Keyword(s):  
General Relativity ◽  
Gauge Theory ◽  
Quantum Gravity ◽  
Boundary Conditions ◽  
Crucial Role ◽  
Test Laboratory ◽  
Asymptotically Flat ◽  
Generally Covariant ◽  
Asymptotic Symmetries

A generally covariant U(1)3 gauge theory describing the GN→0 limit of Euclidean general relativity is an interesting test laboratory for general relativity, specially because the algebra of the Hamiltonian and diffeomorphism constraints of this limit is isomorphic to the algebra of the corresponding constraints in general relativity. In the present work, we the study boundary conditions and asymptotic symmetries of the U(1)3 model and show that while asymptotic spacetime translations admit well-defined generators, boosts and rotations do not. Comparing with Euclidean general relativity, one finds that the non-Abelian part of the SU(2) Gauss constraint, which is absent in the U(1)3 model, plays a crucial role in obtaining boost and rotation generators.

Real and complex asymptotic symmetries in quantum gravity, irreducible representations, polygons, polyhedra, and the A, D, E series

1992 ◽  
Vol 338 (1650) ◽  
pp. 271-299 ◽  
Keyword(s):  
General Relativity ◽  
Quantum Gravity ◽  
Irreducible Representations ◽  
Symmetry Groups ◽  
Regular Polygons ◽  
Lorentzian Space ◽  
Asymptotically Flat ◽  
Irreducible Unitary Representations ◽  
The Common ◽  
Asymptotic Symmetries

The Bondi-Metzner-Sachs group B is the common asymptotic group of all asymptotically flat (lorentzian) space-times, and is the best candidate for the universal symmetry group of general relativity. However, in quantum gravity, complexified or euclidean versions of general relativity are frequently considered, and the question arises: Are there similar symmetry groups for these versions of the theory? In this paper it is shown that there are such analogues of B and a variety of further ones, either real in any signature, or complex. The relationships between these various groups are described. Irreducible unitary representations (IRS) of the complexification CB of B itself are analysed. It is proved that all induced IRS of CB arise from IRS of compact 'little groups’. It follows that some IRS of CB are controlled by the IRS of the ‘ A,D,E ' series of finite symmetry groups of regular polygons and polyhedra in ordinary euclidean 3-space. Possible applications to quantum gravity are indicated.

scholarly journals Einstein’s quadrupole formula from the kinetic-conformal Hořava theory

2017 ◽  
Vol 27 (01) ◽  
pp. 1750174 ◽  
Author(s):  
Jorge Bellorín ◽  
Alvaro Restuccia
Keyword(s):  
General Relativity ◽  
Degrees Of Freedom ◽  
Coupling Constants ◽  
Asymptotically Flat ◽  
Weak Source ◽  
The Family ◽  
Linearized Theory ◽  
Leading Mode ◽  
The One ◽  
Generally Covariant

We analyze the radiative and nonradiative linearized variables in a gravity theory within the family of the nonprojectable Hořava theories, the Hořava theory at the kinetic-conformal point. There is no extra mode in this formulation, the theory shares the same number of degrees of freedom with general relativity. The large-distance effective action, which is the one we consider, can be given in a generally-covariant form under asymptotically flat boundary conditions, the Einstein-aether theory under the condition of hypersurface orthogonality on the aether vector. In the linearized theory, we find that only the transverse-traceless tensorial modes obey a sourced wave equation, as in general relativity. The rest of variables are nonradiative. The result is gauge-independent at the level of the linearized theory. For the case of a weak source, we find that the leading mode in the far zone is exactly Einstein’s quadrupole formula of general relativity, if some coupling constants are properly identified. There are no monopoles nor dipoles in this formulation, in distinction to the nonprojectable Horava theory outside the kinetic-conformal point. We also discuss some constraints on the theory arising from the observational bounds on Lorentz-violating theories.

scholarly journals ABELIAN DECOMPOSITION OF GENERAL RELATIVITY

2009 ◽  
Vol 24 (18n19) ◽  
pp. 3327-3341 ◽  
Author(s):  
Y. M. CHO
Keyword(s):  
General Relativity ◽  
Gauge Theory ◽  
Quantum Gravity ◽  
Lorentz Group ◽  
Lorentz Invariance ◽  
Gauge Potential ◽  
Abelian Decomposition ◽  
Gravitational Source ◽  
Einstein’S General Relativity ◽  
Local Lorentz Invariance

We present an Abelian decomposition of Einstein's general relativity, viewing Einstein's theory as a gauge theory of Lorentz group and identifying the gravitational connection as the gauge potential of Lorentz group. The decomposition confirms the existence of the restricted gravity which is much simpler than Einstein's theory but which has the full local Lorentz invariance (and thus the full general invariance). Moreover, it tells that Einstein's theory can be viewed as the restricted gravity which has the Lorentz covariant valence connection as the gravitational source. With the Abelian decomposition we show how to construct all possible vacuum gravitational connections, which can be classified by the knot topology π3(S3) = π3(S2). We discuss the physical implications of our result in quantum gravity.

scholarly journals A note on boundary conditions in Euclidean gravity

2021 ◽  
pp. 2140004
Author(s):  
Edward Witten
Keyword(s):  
Boundary Condition ◽  
General Relativity ◽  
Perturbation Theory ◽  
Quantum Gravity ◽  
Boundary Conditions ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Conformal Geometry ◽  
Extrinsic Curvature ◽  
Euclidean Signature

We review what is known about boundary conditions in General Relativity on a spacetime of Euclidean signature. The obvious Dirichlet boundary condition, in which one specifies the boundary geometry, is actually not elliptic and in general does not lead to a well-defined perturbation theory. It is better-behaved if the extrinsic curvature of the boundary is suitably constrained, for instance if it is positive- or negative-definite. A different boundary condition, in which one specifies the conformal geometry of the boundary and the trace of the extrinsic curvature, is elliptic and always leads formally to a satisfactory perturbation theory. These facts might have interesting implications for semiclassical approaches to quantum gravity. April, 2018

scholarly journals Gravitational breathing memory and dual symmetries

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Ali Seraj
Keyword(s):  
General Relativity ◽  
Gauge Theory ◽  
Scalar Field ◽  
Memory Effects ◽  
Balance Equations ◽  
Symmetry Principle ◽  
Dual Formulation ◽  
Physical Role ◽  
Asymptotic Symmetries

Abstract Brans-Dicke theory contains an additional propagating mode which causes homogeneous expansion and contraction of test bodies in transverse directions. This “breathing” mode is associated with novel memory effects in addition to those of general relativity. Standard tensor mode memories are related to a symmetry principle: they are determined by the balance equations corresponding to the BMS symmetries. In this paper, we show that the leading and subleading breathing memory effects are determined by the balance equations associated with the leading and “overleading” asymptotic symmetries of a dual formulation of the scalar field in terms of a two-form gauge field. The memory effect causes a transition in the vacuum of the dual gauge theory. These results highlight the significance of dual charges and the physical role of overleading asymptotic symmetries.

scholarly journals Aspects of gravitational wave/particle duality: Bulk torsion ↔boundary gravity correspondence

2020 ◽  
Vol 29 (02) ◽  
pp. 2050019
Author(s):  
Rohit K. Gupta ◽  
Supriya Kar ◽  
R. Nitish
Keyword(s):  
General Relativity ◽  
Gauge Theory ◽  
Quantum Gravity ◽  
Qualitative Analysis ◽  
Gravitational Wave ◽  
Detailed Analysis ◽  
Newtonian Potential ◽  
Local Degree ◽  
Wave Particle Duality ◽  
Killing Symmetries

A geometric torsion (GT) underlying a [Formula: see text]-form in a [Formula: see text]-dimensional [Formula: see text] gauge theory is revisited with a renewed perspective for a nonperturbation (NP) gravity in [Formula: see text]. In this context, we provide evidences to a holographic correspondence between a bulk GT and a boundary NP gravity. Interestingly the Killing symmetries in General Relativity (GR) are shown to provide a subtle clue to the quantum gravity. The NP gravity is shown to incorporate a [Formula: see text] coupling, sourced by a non-Newtonian potential, to an exact geometry in GR. Remarkably the NP correction is identified as a mass dipole and is shown to be sourced by a propagating GT. A detailed analysis is performed in a bulk GT to show a modification to the precession of perihelion in a boundary NP gravity. The perspective of an electromagnetic (EM) wave in the bulk is investigated to reveal a spin [Formula: see text] (mass-less) quantum sourced by an apparent 2-form. A Goldstone scalar is absorbed by the apparent 2-form to describe a massive [Formula: see text]-form in the coulomb gauge. Alternately a Goldstone scalar together with a local degree of GT and 2-form is argued to govern a composite (mass-less) spin [Formula: see text] particle in Lorentz gauge. Both the scenarios, further ensure a graviton in a boundary NP gravity. A qualitative analysis reveals a (noninteracting) graviton underlying a plausible gravitational wave/particle duality in NP gravity.

scholarly journals Brans-Dicke theory in Bondi-Sachs form: Asymptotically flat solutions, asymptotic symmetries, and gravitational-wave memory effects

2021 ◽  
Vol 103 (10) ◽  
Author(s):  
Shammi Tahura ◽  
David A. Nichols ◽  
Alexander Saffer ◽  
Leo C. Stein ◽  
Kent Yagi
Keyword(s):  
Gravitational Wave ◽  
Memory Effects ◽  
Asymptotically Flat ◽  
Asymptotic Symmetries

scholarly journals The Kerr-Schild double copy in Lifshitz spacetime

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Gökhan Alkaç ◽  
Mehmet Kemal Gümüş ◽  
Mustafa Tek
Keyword(s):  
General Relativity ◽  
Gauge Theory ◽  
Charge Density ◽  
Localized Source ◽  
Curvature Term ◽  
Constant Charge Density ◽  
Arbitrary Dimensions ◽  
Double Copy ◽  
Theory Solution ◽  
Constant Charge

Abstract The Kerr-Schild double copy is a map between exact solutions of general relativity and Maxwell’s theory, where the nonlinear nature of general relativity is circumvented by considering solutions in the Kerr-Schild form. In this paper, we give a general formulation, where no simplifying assumption about the background metric is made, and show that the gauge theory source is affected by a curvature term that characterizes the deviation of the background spacetime from a constant curvature spacetime. We demonstrate this effect explicitly by studying gravitational solutions with non-zero cosmological constant. We show that, when the background is flat, the constant charge density filling all space in the gauge theory that has been observed in previous works is a consequence of this curvature term. As an example of a solution with a curved background, we study the Lifshitz black hole with two different matter couplings. The curvature of the background, i.e., the Lifshitz spacetime, again yields a constant charge density; however, unlike the previous examples, it is canceled by the contribution from the matter fields. For one of the matter couplings, there remains no additional non-localized source term, providing an example for a non-vacuum gravity solution corresponding to a vacuum gauge theory solution in arbitrary dimensions.

scholarly journals Clock-dependent spacetime

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Sung-Sik Lee
Keyword(s):  
Hilbert Space ◽  
General Relativity ◽  
Quantum Gravity ◽  
Hilbert Spaces ◽  
Coordinate Systems ◽  
Physical Laws

Abstract Einstein’s theory of general relativity is based on the premise that the physical laws take the same form in all coordinate systems. However, it still presumes a preferred decomposition of the total kinematic Hilbert space into local kinematic Hilbert spaces. In this paper, we consider a theory of quantum gravity that does not come with a preferred partitioning of the kinematic Hilbert space. It is pointed out that, in such a theory, dimension, signature, topology and geometry of spacetime depend on how a collection of local clocks is chosen within the kinematic Hilbert space.

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