235 research outputs found
Asymptotic Symmetries in the Gauge Fixing Approach and the BMS Group
These notes are an introduction to asymptotic symmetries in gauge theories,
with a focus on general relativity in four dimensions. We explain how to impose
consistent sets of boundary conditions in the gauge fixing approach and how to
derive the asymptotic symmetry parameters. The different procedures to obtain
the associated charges are presented. As an illustration of these general
concepts, the examples of four-dimensional general relativity in asymptotically
(locally) (A)dS and asymptotically flat spacetimes are covered. This
enables us to discuss the different extensions of the Bondi-Metzner-Sachs-van
der Burg (BMS) group and their relevance for holography, soft gravitons
theorems, memory effects, and black hole information paradox. These notes are
based on lectures given at the XV Modave Summer School in Mathematical Physics.Comment: 56 pages, 2 figures, published versio
The -BMS group of dS and new boundary conditions for AdS
Using the dictionary between Bondi and Fefferman-Graham gauges, we identify
the analogues of the Bondi news, Bondi mass and Bondi angular momentum aspects
at the boundary of generic asymptotically locally (A)dS spacetimes. We
introduce the -BMS group as the residual symmetry group of the
metric in Bondi gauge after boundary gauge fixing. This group consists of
infinite-dimensional non-abelian supertranslations and superrotations and it
reduces in the asymptotically flat limit to the extended BMS group.
Furthermore, we present new boundary conditions for asymptotically locally
AdS spacetimes which admit times the group of area-preserving
diffeomorphisms as the asymptotic symmetry group. The boundary conditions
amount to fix 2 components of the holographic stress-tensor while allowing 2
components of the boundary metric to fluctuate. They correspond to a
deformation of a holographic CFT which is coupled to a fluctuating spatial
metric of fixed area.Comment: 42 pages, 1 figure, attached Mathematica notebook, published versio
Conserved currents in the Cartan formulation of general relativity
We derive the expressions for the local, on-shell closed co-dimension 2 forms
in the Cartan formulation of general relativity and explicitly show their
equivalence to those of the metric formulation.Comment: 14 pages, Proceedings of the workshop "About various kinds of
interactions" in honour of Philippe Spindel, 4 & 5 June 2015, Mons, Belgiu
On the Various Extensions of the BMS Group
The Bondi-Metzner-Sachs-van der Burg (BMS) group is the asymptotic symmetry
group of radiating asymptotically flat spacetimes. It has recently received
renewed interest in the context of the flat holography and the infrared
structure of gravity. In this thesis, we investigate the consequences of
considering extensions of the BMS group in four dimensions with superrotations.
In particular, we apply the covariant phase space methods on a class of first
order gauge theories that includes the Cartan formulation of general relativity
and specify this analysis to gravity in asymptotically flat spacetime.
Furthermore, we renormalize the symplectic structure at null infinity to obtain
the generalized BMS charge algebra associated with smooth superrotations. We
then study the vacuum structure of the gravitational field, which allows us to
relate the so-called superboost transformations to the velocity kick/refraction
memory effect. Afterward, we propose a new set of boundary conditions in
asymptotically locally (A)dS spacetime that leads to a version of the BMS group
in the presence of a non-vanishing cosmological constant, called the
-BMS asymptotic symmetry group. Using the holographic renormalization
procedure and a diffeomorphism between Bondi and Fefferman-Graham gauges, we
construct the phase space of -BMS and show that it reduces to the one
of the generalized BMS group in the flat limit.Comment: PhD Thesis, 204 pages, 2 figure
Charge Algebra in Al(A)dS Spacetimes
The gravitational charge algebra of generic asymptotically locally (A)dS
spacetimes is derived in dimensions. The analysis is performed in the
Starobinsky/Fefferman-Graham gauge, without assuming any further boundary
condition than the minimal falloffs for conformal compactification. In
particular, the boundary structure is allowed to fluctuate and plays the role
of source yielding some symplectic flux at the boundary. Using the holographic
renormalization procedure, the divergences are removed from the symplectic
structure, which leads to finite expressions. The charges associated with
boundary diffeomorphisms are generically non-vanishing, non-integrable and not
conserved, while those associated with boundary Weyl rescalings are
non-vanishing only in odd dimensions due to the presence of Weyl anomalies in
the dual theory. The charge algebra exhibits a field-dependent -cocycle in
odd dimensions. When the general framework is restricted to three-dimensional
asymptotically AdS spacetimes with Dirichlet boundary conditions, the
-cocycle reduces to the Brown-Henneaux central extension. The analysis is
also specified to leaky boundary conditions in asymptotically locally (A)dS
spacetimes that lead to the -BMS asymptotic symmetry group. In the
flat limit, the latter contracts into the BMS group in dimensions.Comment: 48 pages, 1 figure, published versio
Nonlinear oscillations, transition to chaos and escape in the Duffing system with non-classical damping
We investigate the power of a ripping head in the process of concrete cutting. Using nonlinear embedding methods we study the corresponding time series obtained during the cutting process. The calculated maximal Lyapunov exponent indicates the exponential divergence typical for chaotic or stochastic systems. The recurrence plots technique has been used to get nonlinear process statistics for identification and description of nonlinear dynamics, lying behind the cutting process
Coadjoint representation of the BMS group on celestial Riemann surfaces
The coadjoint representation of the BMS group in four dimensions is
constructed in a formulation that covers both the sphere and the punctured
plane. The structure constants are worked out for different choices of bases.
The conserved current algebra of non-radiative asymptotically flat spacetimes
is explicitly interpreted in these terms.Comment: 45 pages Latex file, minimal cosmetic changes in version
Conserved currents in the Palatini formulation of general relativity
We derive the expressions for the local, on-shell closed co-dimension 2 forms
in the Palatini formulation of general relativity and explicitly show their
on-shell equivalence to those of the metric formulation. When compared to other
first order formulations, two subtleties have to be addressed during the
construction: off-shell non-metricity and the fact that the transformation of
the connection under infinitesimal diffeomorphisms involves second order
derivatives of the associated vector fields.Comment: 12 Page
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