Exact Half-BPS Flux Solutions in M-theory III: Existence and rigidity of global solutions asymptotic to AdS4 x S7

The BPS equations in M-theory for solutions with 16 residual supersymmetries, $SO(2,2)\times SO(4)\times SO(4)$ symmetry, and $AdS_4 \times S^7$ asymptotics, were reduced in [arXiv:0806.0605] to a linear first order partial differential equation on a Riemann surface with boundary, subject to a non-trivial quadratic constraint. In the present paper, suitable regularity and boundary conditions are imposed for the existence of global solutions. We seek regular solutions with multiple distinct asymptotic $AdS_4 \times S^7$ regions, but find that, remarkably, such solutions invariably reduce to multiple covers of the M-Janus solution found by the authors in [arXiv:0904.3313], suggesting rigidity of the half-BPS M-Janus solution. In particular, we prove analytically that no other smooth deformations away from the M-Janus solution exist, as such deformations invariably violate the quadratic constraint. These rigidity results are contrasted to the existence of half-BPS solutions with non-trivial 4-form fluxes and charges asymptotic to $AdS_7 \times S^4$. The results are related to the possibility of M2-branes to end on M5-branes, but the impossibility of M5-branes to end on M2-branes, and to the non-existence of half-BPS solutions with simultaneous $AdS_4 \times S^7$ and $AdS_7 \times S^4$ asymptotic regions.Comment: 52 pages, 2 figures, pdf-latex. Minor change

On vortex/wave interactions. Part 1. Non-symmetrical input and cross-flow in boundary layers

The paper studies certain effects of non-symmetry on vortex/wave interactions, for inviscid inflexional waves interacting nonlinearly with the vortex component of the mean flow in boundary-layer transition at large Reynolds number. Two types of non-symmetry are investigated, namely for unequal input wave amplitudes and for small cross-flows. These lead to coupled integro-differential equations for spatial development of the wave amplitudes, which are examined in an essentially equivalent differential form for various degrees of the non-symmetry present. Each type of non-symmetry can have a significant influence on the nonlinear interaction properties. Special emphasis is given to bounded solutions, and numerous interesting new flow responses are found analytically and computationally. The theory provides a basis for tackling enhanced non-symmetry in the input or stronger cross-flows

Spherically Symmetric Solutions in Higher-Derivative Gravity

Extensions of Einstein gravity with quadratic curvature terms in the action arise in most effective theories of quantised gravity, including string theory. This article explores the set of static, spherically symmetric and asymptotically flat solutions of this class of theories. An important element in the analysis is the careful treatment of a Lichnerowicz-type `no-hair' theorem. From a Frobenius analysis of the asymptotic small-radius behaviour, the solution space is found to split into three asymptotic families, one of which contains the classic Schwarzschild solution. These three families are carefully analysed to determine the corresponding numbers of free parameters in each. One solution family is capable of arising from coupling to a distributional shell of matter near the origin; this family can then match on to an asymptotically flat solution at spatial infinity without encountering a horizon. Another family, with horizons, contains the Schwarzschild solution but includes also non-Schwarzschild black holes. The third family of solutions obtained from the Frobenius analysis is nonsingular and corresponds to `vacuum' solutions. In addition to the three families identified from near-origin behaviour, there are solutions that may be identified as `wormholes', which can match symmetrically on to another sheet of spacetime at finite radius.Comment: 57 pages, 6 figures; version appearing in journal; minor corrections and clarifications to v

Covariant theory of asymptotic symmetries, conservation laws and central charges

Under suitable assumptions on the boundary conditions, it is shown that there is a bijective correspondence between equivalence classes of asymptotic reducibility parameters and asymptotically conserved n-2 forms in the context of Lagrangian gauge theories. The asymptotic reducibility parameters can be interpreted as asymptotic Killing vector fields of the background, with asymptotic behaviour determined by a new dynamical condition. A universal formula for asymptotically conserved n-2 forms in terms of the reducibility parameters is derived. Sufficient conditions for finiteness of the charges built out of the asymptotically conserved n-2 forms and for the existence of a Lie algebra g among equivalence classes of asymptotic reducibility parameters are given. The representation of g in terms of the charges may be centrally extended. An explicit and covariant formula for the central charges is constructed. They are shown to be 2-cocycles on the Lie algebra g. The general considerations and formulas are applied to electrodynamics, Yang-Mills theory and Einstein gravity.Comment: 86 pages Latex file; minor correction