20 research outputs found
Global existence and future asymptotic behaviour for solutions of the Einstein-Vlasov-scalar field system with surface symmetry
We prove in the cases of plane and hyperbolic symmetries a global in time
existence result in the future for comological solutions of the
Einstein-Vlasov-scalar field system, with the sources generated by a
distribution function and a scalar field, subject to the Vlasov and wave
equations respectively. The spacetime is future geodesically complete in the
special case of plane symmetry with only a scalar field. Causal geodesics are
also shown to be future complete for homogeneous solutions of the
Einstein-Vlasov-scalar field system with plane and hyperbolic symmetry.Comment: 14 page
M2-Branes and Fano 3-folds
A class of supersymmetric gauge theories arising from M2-branes probing
Calabi-Yau 4-folds which are cones over smooth toric Fano 3-folds is
investigated. For each model, the toric data of the mesonic moduli space is
derived using the forward algorithm. The generators of the mesonic moduli space
are determined using Hilbert series. The spectrum of scaling dimensions for
chiral operators is computed.Comment: 128 pages, 39 figures, 42 table
F-theory uplifts and GUTs
We study the F-theory uplift of Type IIB orientifold models on compact
Calabi-Yau threefolds containing divisors which are del Pezzo surfaces. We
consider two examples defined via del Pezzo transitions of the quintic. The
first model has an orientifold projection leading to two disjoint O7-planes and
the second involution acts via an exchange of two del Pezzo surfaces. The two
uplifted fourfolds are generically singular with minimal gauge enhancements
over a divisor and, respectively, a curve in the non-Fano base. We study
possible further degenerations of the elliptic fiber leading to F-theory GUT
models based on subgroups of E8.Comment: 28 pages, 5 tables; v2: typos removed, minor correction
Theorems on existence and global dynamics for the Einstein equations
This article is a guide to theorems on existence and global dynamics of
solutions of the Einstein equations. It draws attention to open questions in
the field. The local-in-time Cauchy problem, which is relatively well
understood, is surveyed. Global results for solutions with various types of
symmetry are discussed. A selection of results from Newtonian theory and
special relativity that offer useful comparisons is presented. Treatments of
global results in the case of small data and results on constructing spacetimes
with prescribed singularity structure or late-time asymptotics are given. A
conjectural picture of the asymptotic behaviour of general cosmological
solutions of the Einstein equations is built up. Some miscellaneous topics
connected with the main theme are collected in a separate section.Comment: Submitted to Living Reviews in Relativity, major update of Living
Rev. Rel. 5 (2002)