Report on GRG18, Session A3, Mathematical Studies of the Field Equations

Abstract

In this report I will give a summary of some of the main topics covered in Session A3, mathematical studies of the field equations, at GRG18, Sydney. Unfortunately, due to length constraints, some of the topics covered at the session will be very briefly mentioned or left out altogether. The summary is mainly based on extended abstracts submitted by the speakers and some of those who presented posters at the session. I would like to thank all participants for their contributions and help with this summary.

arXiv comment12 pages

References in corpus (68)

• The Black Hole in Three Dimensional Space Time
• The Dynamics of General Relativity
• Quasilocal Energy and Conserved Charges Derived from the Gravitational Action
• Accurate Evolutions of Orbiting Black-Hole Binaries Without Excision
• Gravitational wave extraction from an inspiraling configuration of merging black holes
• On the Numerical Integration of Einstein's Field Equations
• The AdS/CFT Correspondence and a New Positive Energy Conjecture for General Relativity
• Calibration of Moving Puncture Simulations
• A Higher Dimensional Stationary Rotating Black Hole Must be Axisymmetric
• Quiescent cosmological singularities
• Super-energy tensors
• Sharp bounds on $2m/r$ of general spherically symmetric static objects
• General relativistic gravitational field of a rigidly rotating disk of dust: Solution in terms of ultraelliptic functions
• The Bianchi IX attractor
• Geometry and Regularity of Moving Punctures
• Existence of non-trivial, vacuum, asymptotically simple space-times
• The past attractor in inhomogeneous cosmology
• Spin-Two Glueballs, Positive Energy Theorems and the AdS/CFT Correspondence
• Gravitational collapse in 2+1 dimensional AdS spacetime
• Curvature blow up in Bianchi VIII and IX vacuum spacetimes
• First-order symmetric-hyperbolic Einstein equations with arbitrary fixed gauge
• Towards the classification of static vacuum spacetimes with negative cosmological constant
• A rigorous solution concept for geodesic and geodesic deviation equations in impulsive gravitational waves
• Asymptotically Flat Initial Data with Prescribed Regularity at Infinity
• Hyperbolicity of the BSSN system of Einstein evolution equations
• Problems which are well-posed in a generalized sense with applications to the Einstein equations
• Asymptotic silence of generic cosmological singularities
• Critical collapse of collisionless matter - a numerical investigation
• A note on the Penrose junction conditions
• On the structure of the post-Newtonian expansion in general relativity
• A dynamical systems approach to geodesics in Bianchi cosmologies
• An exact solution for 2+1 dimensional critical collapse
• A new class of obstructions to the smoothness of null infinity
• Initial data for stationary space-times near space-like infinity
• A uniqueness theorem for the adS soliton
• Critical phenomena at the threshold of black hole formation for collisionless matter in spherical symmetry
• Bounds on 2m/R for static spherical objects
• Well-posed forms of the 3+1 conformally-decomposed Einstein equations
• Generalised hyperbolicity in conical space-times
• Exact Relativistic Gravitational Field of a Stationary Counterrotating Dust Disk
• Well-posed initial-boundary value problem for the harmonic Einstein equations using energy estimates
• Exact relativistic treatment of stationary counter-rotating dust disks III. Physical Properties
• Fluid observers and tilting cosmology
• Critical collapse in 2+1 dimensional AdS spacetime: quasi-CSS solutions and linear perturbations
• Rest Frame System for Asymptotically Flat Spacetimes
• The formation of black holes in spherically symmetric gravitational collapse
• The future asymptotics of Bianchi VIII vacuum solutions
• Self-Renormalization of the Classical Quasilocal Energy
• Initial data sets for the Schwarzschild spacetime
• The Newtonian limit for perfect fluids
• Asymptotic singular behavior of Gowdy spacetimes in string theory
• Time asymmetric spacetimes near null and spatial infinity. I. Expansions of developments of conformally flat data
• Time asymmetric spacetimes near null and spatial infinity. II. Expansions of developments of initial data sets with non-smooth conformal metrics
• Post-Newtonian expansions for perfect fluids
• Conformal regularization of Einstein's field equations
• Kinematic and Weyl singularities
• On a class of 2-surface observables in general relativity
• Sectors of spherical homothetic collapse
• Odd-parity perturbations of self-similar Vaidya spacetime
• The cosmological billiard attractor
• Field Theories from the Relativistic Law of Motion
• Generalised hyperbolicity: hypersurface singularities
• Thurston's Geometrization Conjecture and cosmological models
• On the well posedness of Robinson Trautman Maxwell solutions
• Notes on Isolated Horizons
• Bounds for scalar waves on self-similar naked-singularity backgrounds
• A global theory of algebras of generalized functions
• Collapsing shells of radiation in higher dimensional space-time and the cosmic censorship conjecture