We consider four-dimensional de Sitter, flat and anti de Sitter branes embedded in a six-dimensional bulk spacetime whose dynamics is dictated by Lovelock theory. We find, applying a generalised version of Birkhoff's theorem, that all possible maximally symmetric braneworld solutions are embedded in Wick-rotated black hole spacetimes of Lovelock theory. These are warped solitonic spaces, where the horizons of the black hole geometries correspond to the possible positions of codimension-2 branes. The horizon temperature is related via conical singularities to the tension or vacuum energy of the branes. We classify the braneworld solutions for certain combinations of bulk parameters, according to their induced curvature, their vacuum energy and their effective compactness in the extra dimensions. The bulk Lovelock theory gives an induced gravity term on the brane, which, we argue, generates four-dimensional gravity up to some distance scale.
As a result, some simple solutions, such as the Lovelock corrected Schwarzschild black hole in six dimensions, are shown to give rise to self-accelerating braneworlds. We also find that several other solutions have self-tuning properties. Finally, we present regular gravitational instantons of Lovelock gravity and comment on their significance.
We derive the Lichnerowicz equation in the presence of the Gauss-Bonnet term. Using the modified Lichnerowicz equation we study the metric perturbations of Gauss-Bonnet black strings in Codimension-2 Braneworlds.
We consider five-dimensional gravity with a Gauss-Bonnet term in the bulk and an induced gravity term on a 2-brane of codimension-2. We show that this system admits BTZ-like black holes on the 2-brane which are extended into the bulk with regular horizons.
We study a codimension 2 braneworld in the Einstein Gauss-Bonnet gravity. We carefully examine the structure of possible singularities in the system which characterize the braneworld through matching conditions. Consequently, we find that the thickness of the brane can be incorporated as the distributional source, which we dub quasi-thickness. On the basis of our formalism, we analyze the linearized gravity and show the conventional Einstein gravity can be recovered on the brane. In the nonlinear regime, however, we find corrections due to the thickness and the bulk geometry. We also point out…
The quantum creation probability and entropy of a 2-codimensional braneworld are calculated in the framework of no-boundary universe. The entropy can take an arbitrarily large value as the brane tensions increase, in violation of the conjectured "N-bound" in quantum gravity, even for a 4-dimensional ordinary universe.
We study the matching conditions of intersecting brane worlds in Lovelock gravity in arbitrary dimension. We show that intersecting various codimension 1 and/or codimension 2 branes one can find solutions that represent energy-momentum densities localized in the intersection, providing thus the first examples of infinitesimally thin higher codimension braneworlds that are free of singularities and where the backreaction of the brane in the background is fully taken into account.
In this work, we compute the corrections in the Newton's law of gravitation due to Kaluza-Klein gravitons in codimension-1 warped thick braneworld scenarios. We focus in some models recently proposed in the literature, the so-called asymmetric hybrid brane and compact brane. Such models are deformations of the $ϕ^4$ and sine-Gordon topological defects, respectively. Therefore we consider the branes engendered by such defects and we also compute the corrections in their cases. We use suitable numerical techniques to attain the mass spectrum and its corresponding eigenfunctions which are the ess…
We consider five-dimensional gravity with a Gauss-Bonnet term in the bulk and an induced gravity term on a 2-brane of codimension-2. We show that this system admits BTZ black holes on the 2-brane which are extended into the bulk with regular horizons.
We consider the propagation of gravitational waves in six dimensions induced by sources living on 3-branes in the context of a recent exact solution hep-th/0506050. The brane geometries are de Sitter and the bulk is a warped geometry supported by a positive cosmological constant as well as a 2-form flux. We show that at low energies ordinary gravity is reproduced, and explicitly compute the leading corrections from six dimensional effects. After regulating the brane we find a logarithmic dependence on the cutoff scale of brane physics even for modes whose frequency is much less than this energ…
We study axially symmetric codimension-2 cosmology for a distributional braneworld fueled by a localised 4D perfect fluid, in a 6D Lovelock theory. We argue that only the matching conditions (dubbed topological) where the extrinsic curvature on the brane has no jump describe a pure codimension-2 brane. If there is discontinuity in the extrinsic curvature on the brane, this induces inevitably codimension-1 distributional terms. We study these topological matching conditions, together with constraints from the bulk equations evaluated at the brane position, for two cases of regularisation of the…
It has recently been argued that codimension-two braneworlds offer a promising line of attack on the cosmological constant problem, since in such models the Hubble rate is not directly related to the brane tension. We point out challenges to building more general models where the brane content is not restricted to pure tension. In order to address these challenges, we construct a thick brane model which we linearize around a well known static solution. We show that the model's cosmology does reduce to standard FRW behaviour, but find no hint of a self-tuning mechanism which might help solve th…
We discuss black hole solutions with a Gauss-Bonnet term in the bulk and an induced gravity term on a thin brane of codimension-2. We show that these black holes can be localized on the brane, and they can be extended further into the bulk by a warp function. These solutions have regular horizons and no other curvature singularities appear apart from the string-like ones. The projection of the Gauss-Bonnet term on the brane imposes a constraint relation which dictates the form of matter on the brane and in the bulk.
Building on earlier work on football shaped extra dimensions, we construct a compact codimension two braneworld with precisely one brane. The two extra dimensions topologically represent a 2-torus which is stabilized by a bulk cosmological constant and magnetic flux. The torus has positive constant curvature almost everywhere, except for a single conical singularity at the location of the brane. In contradistinction to the football shaped case, there is no fine-tuning required for the brane tension. We also present some plausibility arguments why the model should not suffer from serious stabil…
We consider maximally symmetric 3-branes embedded in a six-dimensional bulk spacetime with Lovelock dynamics. We study the properties of the solutions with respect to their induced curvature, their vacuum energy and their effective compactness in the extra dimensions. Some simple solutions are shown to give rise to self-accelerating braneworlds, whereas several others solutions have self-tuning properties. For the case of geometric self-acceleration we argue that the cross-over scale in between four-dimensional and higher-dimensional gravity and the scale of late-time geometric acceleration, f…
In the context of six-dimensional conical braneworlds we consider a simple and explicit model that incorporates long distance modification of gravity and regularization of codimension-2 singularities. To resolve the conical singularities we replace the codimension-2 branes with ring-like codimension-1 branes, filling in the interiors with regular caps. The six-dimensional Planck scale in the cap is assumed to be much greater than the bulk Planck scale, which gives rise to the effect analogous to brane-induced gravity. Weak gravity on the regularized brane is studied in the case of a sharp coni…
We consider a thick p-brane embedded in an n-dimensional spacetime possessing radial symmetry in the directions orthogonal to the brane. We first consider a static brane, and find a general fine tuning relationship between the brane and bulk parameters required for the brane to be flat. We then consider the cosmology of a time dependent brane in a static bulk, and find the Friedmann equation for the brane scale factor a(t). The singularities that would ordinarily arise when considering arbitrary codimensions are avoided by regularizing the brane, giving it a finite profile in the transverse di…
Recently, in (Eur.Phys.J.C 80 (2020) 5, 432), the present authors obtained general stringent conditions on the localization of fields in braneworlds by imposing that its zero-mode must satisfy Einstein's equations (EE). Here, we continue this study by considering free $p$-form. These fields present an on-shell equivalency relation between a $p$-form and a $(D-p-2)$-form, provided by Hodge duality (HD). This symmetry will impose a new consistency condition, namely, confinement of a $p$-form must imply the localization of its dual. We apply the above conditions to $6$D braneworlds. With this, we…
We look at general braneworlds in six-dimensional Einstein-Gauss-Bonnet gravity. We find the general matching conditions for the Einstein-Gauss-Bonnet braneworld, which remarkably turn out to give precisely the four-dimensional Einstein equations for the induced metric and matter on the brane, even when the extra dimensions are non-compact and have infinite volume. We also show that relaxing regularity of the curvature in the vicinity of the brane, or alternatively having a finite width brane, gives rise to an additional possible correction to the Einstein equations, which contains information…
Lagrangian description of lightlike p-branes is presented in two equivalent forms - a Polyakov-type formulation and a dual to it Nambu-Goto-type formulation. Next, the properties of lightlike brane dynamics in generic gravitational backgrounds of spherically symmetric and axially symmetric type are discussed in some detail: "horizon straddling" and "mass inflation" effects for codimension-one lightlike branes and ground state behavior of codimension-two lightlike "braneworlds".
We continue the investigation of a recent proposal on alternative matching conditions for self-gravitating defects which generalize the standard matching conditions. The reasoning for this study is the need for consistency of the various codimension defects and the existence of a meaningful equation of motion at the probe limit, things that seem to lack from the standard approach. These matching conditions arise by varying the brane-bulk action with respect to the brane embedding fields (and not with respect to the bulk metric at the brane position) in a way that takes into account the gravita…
It has been suggested that codimension-two braneworlds might naturally explain the vanishing of the 4D effective cosmological constant, due to the automatic relation between the deficit angle and the brane tension. To investigate whether this cancellation happens dynamically, and within the context of a realistic cosmology, we study a codimension-two braneworld with spherical extra dimensions compactified by magnetic flux. Assuming Einstein gravity, we show that when the brane contains matter with an arbitrary equation of state, the 4D metric components are not regular at the brane, unless the…
We present a comprehensive study of the cosmological solutions of 6D braneworld models with azimuthal symmetry in the extra dimensions, moduli stabilization by flux or a bulk scalar field, and which contain at least one 3-brane that could be identified with our world. We emphasize an unusual property of these models: their expansion rate depends on the 3-brane tension either not at all, or in a nonstandard way, at odds with the naive expected dimensional reduction of these systems to 4D general relativity at low energies. Unlike other braneworld attempts to find a self-tuning solution to the c…
Braneworld models are interesting theoretical and phenomenological frameworks to search for new physics beyond the standard model of particles and cosmology. In this work, we discuss braneworld models whose gravitational dynamics are governed by teleparallel $f(T)$ gravities. Here, we emphasize a codimension two axisymmetric model, also known as a string-like brane. Likewise, in the 5D domain-walls models, the $f(T)$ gravitational modification leads to a phase transition on the perfect fluid source providing a brane-splitting mechanism. Furthermore, the torsion changes the gravitational pertur…
We study the Friedmann equation for the warped codimension-two braneworld background which most closely resembles the Randall-Sundrum model. Extra matter on the (Planck) 4-brane, with equation of state p_θ=(α-1)ρfor the azimuthal pressure, is required to satisfy the junction conditions. For 1 < α< 5, we show that there are two static solutions to the Einstein equations for given values of the brane stress-energies. Close to the static solutions, the relation between Hubble expansion rate H and brane tension reproduces the standard 4D result for small H, but exhibits unusual deviations when H i…
We show that quantum mechanical supersymmetries are emerged in Kaluza-Klein spectrum of linearized gravity in several warped backgrounds as a consequence of higher-dimensional general coordinate invariance. These emergent supersymmetries play an essential role for the spectral structure of braneworld gravity. We show that for the case of braneworld models with two codimension-1 branes the spectral pattern is completely determined only through the supersymmetries.
We construct a familly of exact solutions of Lovelock equations describing codimension four branes with discrete symmetry in the transverse space. Unlike what is known from pure Einstein gravity, where such brane solutions of higher codimension are singular, the solutions we find, for the complete Lovelock theory, only present removable singularities. The latter account for a localised tension-like energy-momentum tensor on the brane, in analogy with the case of a codimension two self-gravitating cosmic string in pure Einstein gravity. However, the solutions we discuss present two main distinc…
We give a short review of the recent development in the investigation of the vacuum expectation values of the bulk and surface energy-momentum tensors generated by quantum fluctuations of a massive scalar field with general curvature coupling parameter subject to Robin boundary conditions on two codimension one parallel branes located on $(D+1)$-dimensional anti-de Sitter (AdS) bulk. An application to the Randall-Sundrum braneworld with arbitrary mass terms on the branes is discussed.
We describe a concise general scheme for constructing solutions of Einstein-Maxwell-Kalb-Ramond gravity-matter system in bulk space-time interacting self-consistently with one or more (widely separated) codimension-one electrically charged lightlike branes. The lightlike brane dynamics is explicitly given by manifestly reparametrization invariant world-volume actions. We present several explicit classes of solutions with different physical interpretation as wormhole-like space-times with one, two or more "throats", singularity-free black holes, brane worlds and space-times undergoing a sequenc…
We study linearized gravity in a six-dimensional Einstein-Maxwell model of warped braneworlds, where the extra dimensions are compactified by a magnetic flux. It is difficult to construct a strict codimension two braneworld with matter sources other than pure tension. To overcome this problem we replace the codimension two defect by an extended brane, with one spatial dimension compactified on a Kaluza-Klein circle. Our background is composed of a warped, axisymmetric bulk and one or two branes. We find that weak gravity sourced by arbitrary matter on the brane(s) is described by a four-dimens…
We discuss a particular higher order gravity theory, Lovelock theory, that generalises in higher dimensions, general relativity. After briefly motivating modifications of gravity, we will introduce the theory in question and we will argue that it is a unique, mathematically sensible, and physically interesting extension of general relativity. We will see, by using the formalism of differential forms, the relation of Lovelock gravity to differential geometry and topology of even dimensional manifolds. We will then discuss a generic staticity theorem, which will give us the charged static black …
The self-accelerating branch of the Dvali-Gabadadze-Porrati (DGP) five-dimensional braneworld has provided a compelling model for the current cosmic acceleration. Recent observations, however, have not favored it so much. We discuss the solutions which contain a de Sitter 3-brane in the cascading DGP braneworld model, which is a kind of higher-dimensional generalizations of the DGP model,where a $p$-dimensional brane is placed on a $(p+1)$-dimensional one and the $p$-brane action contains the $(p+1)$-dimensional induced scalar curvature term. In the simplest six-dimensional model, we derive th…
We construct exact solutions with the bubble of nothing in the Dvali-Gabadadze-Porrati braneworld model. The configuration with a single brane can be constructed, unlike in the Randall-Sundrum braneworld model. The geometry on the single brane looks like the Einstein-Rosen bridge. We also discuss the junction of multibranes. Surprisingly, even without any artificial matter fields on the branes such as three-dimensional tension of the codimension-two objects, two branes can be connected in certain configurations. We investigate solutions of multibranes too. The presence of solutions may indicat…
We study the effective gravitational theory on a brane in a six-dimensional Einstein-Maxwell model of flux compactification, regularizing a conical defect as a codimension-one brane. We employ the gradient expansion technique valid at low energies. A lowest order analysis showed that standard four-dimensional Einstein gravity is reproduced on the brane. We extend this study to include second order corrections in the effective equations, and show that the correction term is given by a quadratic energy-momentum tensor. Taking the thin-brane limit where the regularized brane shrinks to the pole, …
A unified model is developed within the context of the braneworld paradigm, where a single scalar field can act as both the inflaton field in the very early universe and also as strong, self-interacting dark matter in the post-inflationary universe. Reheating proceeds due to the overproduction and subsequent evaporation of primordial black holes. Observational constraints, most notably from gravitational waves, are satisfied if the probability of PBH formation is sufficiently high.
We reformulate boundary conditions for axisymmetric codimension-2 braneworlds in a way which is applicable to linear perturbation with various gauge conditions. Our interest is in the thin brane limit and thus this scheme assumes that the perturbations are also axisymmetric and that the surface energy-momentum tensor of the brane is proportional to its induced metric. An advantage of our scheme is that it allows much more freedom for convenient coordinate choices than the other methods. This is because in our scheme, the coordinate system in the bulk and that on the brane are completely disent…
We explore cosmology of intersecting braneworlds with induced gravity on the branes. We find the cosmological equations that control the evolution of a moving codimension one brane and a codimension two brane that sits at the intersection. We study the Friedmann equation at the intersection, finding new contributions from the six dimensional bulk. These higher dimensional contributions allow us to find new examples of self-accelerating configurations for the codimension two brane at the intersection and we discuss their features.
We consider the case of a generic braneworld geometry in the presence of one or more moduli fields (e.g., the dilaton) that vary throughout the bulk spacetime. Working in an arbitrary conformal frame, using the generalized junction conditions of gr-qc/0008008 and the Gauss--Codazzi equations, we derive the effective ``induced'' on-brane gravitational equations. As usual in braneworld scenarios, these equations do not form a closed system in that the bulk can exchange both information and stress-energy with the braneworld. We work with an arbitrary number of moduli fields described by an arbitr…
We propose a codimension two warped braneworld model within the teleparallel $f(T)$ gravity. By assuming a global vortex as the source, we found a $l=0$ vortex solution that yields to a thick string-like brane. Asymptotically, the bulk geometry converges to an $AdS_6$ spacetime whose cosmological constant is produced by the torsion parameters. Furthermore, the torsion induces an $AdS-dS$ transition on the exterior region. Inside the brane core, the torsion produces an internal structure even for a single complex scalar field. As the torsion parameters vary, the brane undergoes a phase transiti…
A static self-tuning SO(3)xZ_2 symmetric and translation invariant braneworld setup with flat brane is considered. We discuss the null energy conditions (NEC) for matter on the brane and in the bulk and prove that for the static regular background with broken Lorentz invariance the NEC and positiveness of the total energy density on the brane and NEC in the bulk cannot be satisfied simultaneously. Then we give some examples and elaborate some special cases. For instance, we provide a macroscopic solution for a background with Lifshitz scaling.
Braneworld models with induced gravity have the potential to replace dark energy as the explanation for the current accelerating expansion of the Universe. The original model of Dvali, Gabadadze and Porrati (DGP) demonstrated the existence of a ``self--accelerating'' branch of background solutions, but suffered from the presence of ghosts. We present a new large class of braneworld models which generalize the DGP model. Our models have negative curvature in the bulk, allow a second brane, and have general brane tensions and localized curvature terms. We exhibit three different kinds of ghosts,…
We investigate the stability of the extra dimensions in a warped, codimension two braneworld that is based upon an Einstein-Maxwell-dilaton theory with a non-vanishing scalar field potential. The braneworld solution has two 3-branes, which are located at the positions of the conical singularities. For this type of brane solution the relative positions of the branes (the shape modulus) is determined via the tension-deficit relations, if the brane tensions are fixed. However, the volume of the extra dimensions (the volume modulus) is not fixed in the context of the classical theory, implying we …
Conical brane singularities in six-dimensional flux compactification models can be resolved by introducing cylindrical codimension-one branes with regular caps instead of 3-branes (a la Kaluza-Klein braneworlds with fluxes). In this paper, we consider such a regularized braneworld with axial symmetry in six-dimensional Einstein-Maxwell theory. We derive a low energy effective theory on the regularized brane by employing the gradient expansion approach, and show that standard four-dimensional Einstein gravity is recovered at low energies. Our effective equations extend to the nonlinear gravity …
We compute the matching conditions for a general thick codimension 2 brane, a necessary previous step towards the investigation of gravitational phenomena in codimension 2 braneworlds. We show that, provided the brane is weakly curved, they are specified by the integral in the extra dimensions of the brane energy-momentum, independently of its detailed internal structure. These general matching conditions can then be used as boundary conditions for the bulk solution. By evaluating Einstein equations at the brane boundary we are able to write an evolution equation for the induced metric on the …
We investigate in detail recent suggestions that codimension-two braneworlds in six dimensional supergravity might circumvent Weinberg's no-go theorem for self-tuning of the cosmological constant. The branes are given finite thickness in order to regularize mild singularities in their vicinity, and we allow them to have an arbitrary equation of state. We study perturbatively the time evolution of the solutions by solving the equations of motion linearized around a static background. Even allowing for the most general possibility of warping and nonconical singularities, the geometry does not re…
In this article we study closed inflationary universe models proposed by Linde in a brane world cosmological context. In this scenario we determine and characterize the existence of a closed universe, in presence of one self-interacting scalar field with an inflationary stage. Our results are compared to those found in General Relativity.
We discuss the backreaction of a massless, minimally coupled, quantized scalar field on a thick, two-dimensional de Sitter (dS) brane as an extension of our previous work. We show that a finite brane thickness naturally regularizes the backreaction on the brane. The quantum backreaction exhibits a quadratic divergence in the thin wall limit. We also give a theoretical bound on the brane thickness, in terms of the brane self-consistency of the quantum corrected Einstein equation, namely the requirement that the size of the backreaction should be smaller than that of the background stress-energy…
It has been believed that topology and signature change of the universe can only happen accompanied by singularities, in classical, or instantons, in quantum, gravity. In this note, we point out however that in the braneworld context, such an event can be understood as a classical, smooth event. We supply some explicit examples of such cases, starting from the Dirac-Born-Infeld action. Topology change of the brane universe can be realised by allowing self-intersecting branes. Signature change in a braneworld is made possible in an everywhere Lorentzian bulk spacetime. In our examples, the boun…
We consider the static domain wall braneworld scenario constructed from the Palatini formalism $f(\mathcal{R})$ theory. We check the self-consistency under scalar perturbations. By using the scalar-tensor formalism we avoid dealing with the higher-order equations. We develop the techniques to deal with the coupled system. We show that under some conditions, the scalar perturbation simply oscillates with time, which guarantees the stability. We also discuss the localization condition of the scalar mode by analyzing the effective potential and the fifth dimensional profile of the scalar mode. We…
We consider five-dimensional Einstein-Maxwell-Kalb-Ramond system self-consistently coupled to a lightlike 3-brane, where the latter acts as material, charge and variable cosmological constant source. We find wormhole-like solutions whose total space-time manifold consists of either (a) two "universes", which are identical copies of the exterior space-time region (beyond the horizon) of 5-dimensional Schwarzschild-anti-de Sitter black hole, or (b) a "right" "universe" comprising the exterior space-time region of Reissner-Nordstroem-anti-de Sitter black hole and a "left" "universe" being the Rin…
We study gravitational waves in the black string Randall-Sundrum braneworld. We present a reasonably self-contained and complete derivation of the equations governing the evolution of gravitational perturbations in the presence of a brane localized source, and then specialize to the case of spherical radiation from a pointlike body in orbit around the black string. We solve for the resulting gravitational waveform numerically for a number of different orbital parameters.
We investigate five-dimensional braneworld setups with broken Lorentz invariance continuing the developments of our previous paper (arXiv:0712.1136), where a family of static self-tuning braneworld solutions was found. We show that several known braneworld models can be embedded into this family. Then we give a qualitative analysis of spectra of field fluctuations in backgrounds with broken Lorentz invariance. We also elaborate on one particular model and study spectra of scalar and spinor fields in it. It turns out that the spectra we have found possess very peculiar and unexpected properties…
We propose a braneworld scenario in a modified symmetric teleparallel gravitational theory, where the dynamics for the gravitational field is encoded in the nonmetricity tensor rather than in the curvature. Assuming a single real scalar field with a sine-Gordon self-interaction, the generalized quadratic nonmetricity invariant $\mathbb{Q}$ controls the brane width while keeping the shape of the energy density. By considering power corrections of the invariant $\mathbb{Q}$ in the gravitational Lagrangian, the sine-Gordon potential is modified exhibiting new barriers and false vacuum. As a resul…
We investigated the effects of the spacetime curvature and extra dimensions on the excitations of a self-interacting vector field known as the bumblebee field. The self-interacting quadratic potential breaks the gauge invariance and the vacuum expectation value (VEV) of the bumblebee field $b_M$ violates the local particle Lorentz symmetry. By assuming the bumblebee field living in a $AdS_{5}$ bulk, we found an exponential suppression of the self-interacting constant $λ$ and the bumblebee VEV along the extra dimension. The fluctuations of the bumblebee upon the VEV can be decomposed into trans…
We consider the 6D Cascading DGP model, a braneworld model which is a promising candidate to realize the phenomenon of the degravitation of vacuum energy. Focusing on a recently proposed thin limit description of the model, we study solutions where the induced metric on the codimension-2 brane is of the de Sitter form. While these solutions have already been recovered in the literature imposing by hand the bulk to be flat, we show that it is possible to derive them without making this assumption, by solving a suitably chosen subset of the bulk equations.
We raise on theoretical grounds the question of the physical relevance of Israel matching conditions and their generalizations to higher codimensions, the standard cornerstone of the braneworld and other membrane scenarios. Our reasoning is twofold: First, the incapability of the conventional matching conditions to accept the Nambu-Goto probe limit (even the geodesic limit of the Israel matching conditions is not acceptable since being the geodesic equation a kinematical fact it should be preserved for all gravitational theories or defects, which is not the case for these conditions). Second, …
Our main objective is to study how braneworld models of higher codimension differ from the 5D case and traditional Kaluza-Klein compactifications. We first derive the classical dynamics describing the physical fluctuations in a wide class of models incorporating gravity, non-Abelian gauge fields, the dilaton and two-form potential, as well as 3-brane sources. Next, we use these results to study braneworld compactifications in 6D supergravity, focusing on the bosonic fields in the minimal model; composed of the supergravity-tensor multiplet and the U(1) gauge multiplet whose flux supports the c…
We consider the critical behavior at the threshold of black hole formation for the five dimensional vacuum Einstein equations satisfying the cohomogeneity-two triaxial Bianchi IX ansatz. Exploiting a discrete symmetry present in this model we predict the existence of a codimension-two attractor. This prediction is confirmed numerically and the codimension-two attractor is identified as a discretely self-similar solution with two unstable modes.
