We investigate the evolution of small perturbations around black strings and branes which are low energy solutions of string theory. For simplicity we focus attention on the zero charge case and show that there are unstable modes for a range of time frequency and wavelength in the extra 10 − D dimensions. These perturbations can be stabililized if the extra dimensions are compactified to a scale smaller than the minimum wavelength for which instability occurs and thus will not affect large astrophysical black holes in four dimensions. We comment on the implications of this result for the Cosmic Censorship Hypothesis.

We investigate the evolution of small perturbations around charged black strings and branes which are solutions of low energy string theory. We give the details of the analysis for the uncharged case which was summarized in a previous paper. We extend the analysis to the small charge case and give also an analysis for the generic case, following the behavior of unstable modes as the charge is modified. We study specifically a magnetically charged black 6-brane, but show how the instability is generic, and that charge does not in general stabilise black strings and p-branes.

The standard picture of viable higher-dimensional theories is that direct manifestations of extra dimensions occur at short distances only, whereas long-distance physics is described by effective four-dimensional theories. We show that this is not necessarily true in models with infinite extra dimensions.As an example, we consider a five-dimensional scenario with three 3-branes in which gravity is five-dimensional both at short and very long distance scales, with conventional four-dimensional gravity operating at intermediate length scales. A phenomenologically acceptable range of validity of four-dimensional gravity extending from microscopic to cosmological scales is obtained without strong fine-tuning of parameters.

We study (3+1)-dimensional holographic superconductors in Einstein-Gauss-Bonnet gravity both numerically and analytically. It is found that higher curvature corrections make condensation harder. We give an analytic proof of this result, and directly demonstrate an analytic approximation method that explains the qualitative features of superconductors as well as giving quantitatively good numerical results. We also calculate conductivity and ωg/Tc, for ωg and Tc the gap in the frequency dependent conductivity and the critical temperature respectively. It turns out that the 'universal' behaviour of conductivity, ωg/Tc ≃ 8, is not stable to the higher curvature corrections. In the appendix, for completeness, we show our analytic method can also explain (2+1)-dimensional superconductors.

Starting from a completely general standpoint, we find the most general brane-Universe solutions for a three-brane in a five dimensional spacetime. The brane can border regions of spacetime with or without a cosmological constant. Making no assumptions other than the usual cosmological symmetries of the metric, we prove that the equations of motion form an integrable system, and find the exact solution. The cosmology is indeed a boundary of a (class II) Schwarzschild-AdS spacetime, or a Minkowski (class I) spacetime. We analyse the various cosmological trajectories focusing particularly on those bordering vacuum spacetimes. We find, not surprisingly, that not all cosmologies are compatible with an asymptotically flat spacetime branch. We comment on the role of the radion in this picture.

We calculate the linearized metric perturbation corresponding to a massless four-dimensional scalar field, the radion, in a five-dimensional two-brane model of Randall and Sundrum. In this way we obtain relative strengths of the radion couplings to matter residing on each of the branes. The results are in agreement with the analysis of Garriga and Tanaka of gravitational and Brans-Dicke forces between matter on the branes. We also introduce a model with infinite fifth dimension and "almost" confined graviton, and calculate the radion properties in that model. PACS numbers: 04.50.+h, 11.25.Mj hep-th/9912160 Recently, considerable interest has been raised by a five-dimensional model with an S 1 /Z 2 orbifold extra dimension with two 3-branes residing at its boundaries. 1This model and its non-compact analogues 2-5 (see Ref. 6for an account of earlier works) provide a novel setting for discussing various conceptual and phenomenological issues related to compactification of extra dimensions in models motivated by M-theory. In the two-brane Randall-Sundrum model, 1 the branes have tensions +σ and −σ, and the bulk cosmological constant is chosen in such a way that the classical solution describes fivedimensional space-time whose four-dimensional slices are flat,Here a(z) = e −k|z| , the fifth coordinate z runs from z + = 0 to z − = r c and k = (4π/3)G 5 σ where G 5 is Newton's constant in five dimensions. The orbifold symmetry, a local reflection symmetry at each brane, is assumed to hold for all fields in this space-time.The excitations above the background metric (1) contain a massless four-dimensional graviton (whose wave function is peaked at the positive tension brane) and the corresponding Kaluza-Klein tower.3 This is not the whole story, however. In general when one has a wall in spacetime, one might expect a translational zero mode giving rise to free motion of the wall. In the case of antide Sitter spacetime, ∂ z is not a translational Killing vector but a conformal Killing vector, nonetheless we can identify solutions to the perturbation equations which correspond to proper motion of the wall (although these will be singular on the AdS horizon). In the conventional application of the Israel equations, one identifies the extrinsic curvature, K µν , on each side of the wall, and then applies a Z 2 symmetry across the wall leading toK µν = (K + µν + K − µν )/2 = 0; geometrically this means that the wall is locally 'flat' i.e. totally geodesic. To describe proper dynamical motion of the wall, we require a nonzeroK µν , which is possible if the Z 2 -symmetry is not imposed. The appropriate solution for such a motion then turns out to bewhereK µ µ = 0, which is recognised as the 'Nambu' equation for a brane. Since this solution blows up at large z, it does not correspond to a small perturbation of the spacetime, and is indicative that in the presence of such free motion, the asymptotic structure of the spacetime is altered, similar to the difference between the metrics of a straight cosmic string and a crinkly...

We systematically explore the spectrum of gravitational perturbations in codimension-1 DGP braneworlds, and find a 4D ghost on the self-accelerating branch of solutions. The ghost appears for any value of the brane tension, although depending on the sign of the tension it is either the helicity-0 component of the lightest localized massive tensor of mass 0 < m 2 < 2H 2 for positive tension, the scalar 'radion' for negative tension, or their admixture for vanishing tension. Because the ghost is gravitationally coupled to the brane-localized matter, the self-accelerating solutions are not a reliable benchmark for cosmic acceleration driven by gravity modified in the IR. In contrast, the normal branch of solutions is ghost-free, and so these solutions are perturbatively safe at large distance scales. We further find that when the Z 2 orbifold symmetry is broken, new tachyonic instabilities, which are much milder than the ghosts, appear on the self-accelerating branch. Finally, using exact gravitational shock waves we analyze what happens if we relax boundary conditions at infinity. We find that non-normalizable bulk modes, if interpreted as 4D phenomena, may open the door to new ghost-like excitations.

We consider an exotic "compactification" of spacetime in which there are two infinite extra dimensions, using a global string instead of a domain wall. By having a negative cosmological constant we prove the existence of a nonsingular static solution using a dynamical systems argument. A nonsingular solution also exists in the absence of a cosmological constant with a time-dependent metric. We compare and contrast this solution with the Randall-Sundrum universe and the Cohen-Kaplan spacetime and consider the options of using such a model as a realistic resolution of the hierarchy problem.There has been a great deal of excitement recently over exotic compactifications of spacetime, where our fourdimensional world emerges as a defect in a higher dimensional spacetime. This idea, while not new (see [1,2] for some past work on this subject), has received impetus from the unusual suggestion of Randall and Sundrum [3] that a resolution of the hierarchy problem might be forthcoming from just such a scenario. In Randall and Sundrum's original paper, spacetime was five dimensional, and our four-dimensional spacetime emerged as a domain wall at one end of the universe; a mirror wall at the other end of the universe plus a conformal factor dependent on the distance between the two was responsible for the suppression of interactions relative to gravity on our "visible sector" domain wall. In a later paper [4], Randall and Sundrum explicitly demonstrated how the gravitational interactions effectively localized on the "hidden" domain wall, by showing that a five-dimensional universe with a domain wall had low energy spin-2 excitations which were localized on that wall. A more general calculation involving a smooth wall solution has been performed in [5].A key feature of the Randall-Sundrum solution,ds 2 e 22kj yj h mn dx m dx n 2 dy 2 ,is that in order to have a static solution a negative cosmological constant is required in the bulk spacetime. The value of this cosmological constant, and the value of the wall energy density, is related in a precise manner to the five-dimensional Planck mass and k, the constant appearing in the metric (1). Without this precision balance, nonstatic solutions would have to be considered [6]; see [7] (and references therein) for a comprehensive summary of domain walls in supergravity.