Research Group in General Relativity

1. Research Group in General Relativity Ghent University, Dept. of Mathematical Analysis, Galglaan 2, 9000 Ghent geodesic conformally flat rotating fluid Penrose flow lines diagram asymptotic flatness linearisation instability integrability conditions kinematical quantities cosmological constant expansion scalar field equations non-twisting null geodesics tidal effects Petrov CLASSI irrotational dust Type I initial value problem Swiss cheese silent universes Ricci PMpf’s Cartan equations Riemann curvature Fröbenius theorem normalized timelike four-velocity Petrov classification pp- waves gravito-magnetic monopoles Bianchi type VI0 cosmological model Killing spinors inhomogeneous stiff fluid cosmologies GRTensor gravitational waves pure radiation Gödel metric non-diverging vectorfield normal geodesic flow plane waves Bianchi identities SHEEP • NO-GO • RESULTS • FOR • Purely • Magnetic • ROTATING • DUST initial hypersurfaces Levi-Civita connection LRS canonical quantization Ricci-Bianchi equations covariant ADM formalism Tolman dust propagation algebraic classification singularities geodesic deviation equation PUTH Ricci-rotation coefficients observational homogeneity of the universe constraint equations stationary axisymmetric perfect fluid Jacobi identities embedding class- 2 vacua twistor equation vanishing Cotton tensor OSH EPS Kerr- Schild Killing-Yano • tidal effects • cannot be • absent in • a vacuum isometry group MOTS tensors CKT Penrose - Floyd tensor Hamilton- Jacobi separability Robert Debever, ketje & grote meneer KS1 commutator relations G3 on T2 Friedmann equation null congruence Jebsen – Birkhoff Kerr- Newman black hole consistency conditions dynamical variables gravito-electro-magnetism Plebanski-Demianski family a new topolgy on the space of Lorentzian metrics Goldberg-Sachs theorem Geroch-Held-Penrose formalism Einstein - Hilbert action type D Hauser - Malhiot spacetimesadmittingKilling two-spinors conformal Killing tensor Schwarzschild black hole Arianrhod-McIntosh classification C K Y OCN Bianchi VIII Szekeres locally rotationally symmetric spacetimes KS2 quadratic first integrals ADM shear-eigenframe models E = M c 2 Ist das wirklich so ? Weyl- spinor kinematically homogeneous perfect fluids PEpf Plebanski formalism Raychaudhuri-equation S C K’s bivectors spin foam modified gravity loop quantum gravity Cartan scalars Petrov type I silent universes withG3 isometry group polynomial scalar invariants spatial infinity differentially rotating charged dust W E P Segré type LRS I Killing vectors conformastationary vacua the mag-vac conjecture Brans- Dicke theory Wahlquist`s solution Hamiltonian constraint Vaidya metric cosmic topology LRS II diffeomorphism invariance Cauchy aligned Newman- Tamburino-Maxwell spacetimes Newman - Penrose equations Finsler geometry worm hole non- abelian G2 horizon diverging Einstein-Maxwell null fields shearfree perfect fluids with solenoidal magnetic curvature Rainich conditions B K L Kundt metrics Weyl tensor optical scalars Karlhede formalism twisting type N LTB Robinson-Trautman orthonormal tetrad approach light cone special conformal Killing tensors KSMH Friedman -Lemaitre - Robinson - Walker universe Mach’s Principle • relativistic shear-free • perfect fluids with an • equation of state • are non-rotating or non- • expanding : True or Not ? why study exact solutions? principal null directions non-metric gravity Ashtekar variables Einstein spaces LRS III Weyl canonical tetrad Ehlers Pirani Schild Conformally Ricci Flat Perfect Fluids non-inheriting Maxwell fields connection one-forms Petrov type D pure radiation fields Lorentzian Gromov-Hausdorff theory spatially homogeneous cosmologies Vanishing magnetic curvature Palatini variational principle isotropy group expanding perfect fluid generalizations of the C-metric anti-Newtonian universes do not exist Members: David Beke, Liselotte De Groote, Hamid Reza Karimian, Norbert Van den Bergh, Lode Wylleman Contact: Norbert Van den Bergh (norbert.vandenbergh@ugent.be)