Extended defects in curved spacetimes

This Thesis is concerned with three particular aspects of extended cosmic strings and domain walls in cosmology: their dynamics, gravitation and interaction with a black hole. In Chapter 3, we study the dynamics of an abelian-Higgs cosmic string. We find its equations of motion from an effective action and compare, for three test trajectories, the resulting motion with that observed in the Nambu-Gotō approximation. We also present a general argument showing that the corrected motion of any string is generically antirigid. We pursue the investigation of the dynamics of topological defects in Chapter 5, where we find (from integrability conditions rather than an effective action) the effective equations governing the motion of a gravitating curved domain wall. In Chapter 4 we investigate the spacetime of a gravitating domain wall in a theory with a general potential V(ɸ). We show that, depending on the gravitational coupling e of the scalar ɸ, all nontrivial solutions fall into two categories interpretable as describing respectively domain wall and false vacuum-de Sitter solutions. Wall solutions cannot exist beyond a value (^4)(_3)ɛmax, and vacuum-de Sitter solutions are unstable to decaying into wall solutions below ɛmax at ɛmax we observe a phase transition between the two types of solution. We finally specialize for the Goldstone and sine-Gordon potentials. In Chapter 6 we consider a Nielsen-Olesen vortex whose axis passes through the centre of an extremal Reissner-Nordstr0m black hole. We examine in particular the existence of piercing and expelled solutions (where the string respectively does and does not penetrate the black hole's horizon) and determine that while thin strings penetrate the horizon — and therefore can be genuinely called hair — thick strings are expelled; the two kinds of solution are separated by a phase transition

Comment on ``Absence of abelian Higgs hair for extremal black holes''

We examine the claim of Chamblin et. al. that extreme black holes cannot support abelian Higgs hair. We provide evidence that contradicts this claim and discuss reasons for this discrepancy.Comment: 1 page 2 figures, revised titl

Thick domain wall universes

We investigate the spacetime of a thick gravitating domain wall for a general potential $V(\Phi)$. Using general analytical arguments we show that all nontrivial solutions fall into two categories: those interpretable as an isolated domain wall with a cosmological event horizon, and those which are pure false vacuum de Sitter solutions. Although this latter solution is always unstable to the field rolling coherently to its true vacuum, we show that there is an additional instability to wall formation if the scalar field does not couple too strongly to gravity. Using the $\lambda \Phi^4$ and sine-Gordon models as illustrative examples, we investigate the phase space of the gravitating domain wall in detail numerically, following the solutions from weak to strong gravity. We find excellent agreement with the analytic work. Then, we analyse the domain wall in the presence of a cosmological constant finding again the two kinds of solutions, wall and de Sitter, even in the presence of a negative cosmological constant.Comment: 20 pages revtex, epsfig, references added, some conclusions altere

Vortices and extreme black holes: the question of flux expulsion

It has been claimed that extreme black holes exhibit a phenomenon of flux expulsion for abelian Higgs vortices, irrespective of the relative width of the vortex to the black hole. Recent work by two of the authors showed a subtlety in the treatment of the event horizon, which cast doubt on this claim. We analyse in detail the vortex/extreme black hole system, showing that while flux expulsion can occur, it does not do so in all cases. We give analytic proofs for both expulsion and penetration of flux, in each case deriving a bound for that behaviour. We also present extensive numerical work backing up, and refining, these claims, and showing in detail how a vortex can end on a black hole in all situations. We also calculate the backreaction of the vortex on the geometry, and comment on the more general vortex-black hole system.Comment: 28 pages revtex, 10 figures, minor changes, reference adde

The dynamics of curved gravitating walls

We examine the dynamics of a self-gravitating domain wall using the $\lambda \Phi^4$ model as a specific example. We find that the Nambu motion of the wall is quite generic and dominates the wall motion even in the presence of gravity. We calculate the corrections to this leading order motion, and estimate the effect of the inclusion of gravity on the dynamics of the wall. We then treat the case of a spherical gravitating thick wall as a particular example, solving the field equations and calculating the corrections to the Nambu motion analytically for this specific case. We find that the presence of gravity retards collapse in this case.Comment: 19 pages revtex, 3 figures, references added, equations correcte

Effective action and motion of a cosmic string

We examine the leading order corrections to the Nambu effective action for the motion of a cosmic string, which appear at fourth order in the ratio of the width to radius of curvature of the string. We determine the numerical coefficients of these extrinsic curvature corrections, and derive the equations of motion of the worldsheet. Using these equations, we calculate the corrections to the motion of a collapsing loop, a travelling wave, and a helical breather. From the numerical coefficients we have calculated, we discuss whether the string motion can be labelled as `rigid' or `antirigid,' and hence whether cusp or kink formation might be suppressed or enhanced.Comment: 24 pages revtex, 12 figure