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, fixed by the present horizon size, are related via the conical deficit angle of the six-dimensional bulk solution, which is a free parameter.
We examine the deSitter entropy in the braneworld model with the Gauss-Bonnet/Lovelock terms. Then, we can see that the deSitter entropy computed through the Euclidean action exactly coincides with the holographic entanglement entropy.
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…
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…
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.
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 present matching conditions for distributional sources of arbitrary codimension in the context of Lovelock gravity. Then we give examples, treating maximally symmetric distributional p-branes, embedded in flat, de Sitter and anti-de Sitter spacetime. Unlike Einstein theory, distributional defects of locally smooth geometry and codimension greater than 2 are demonstrated to exist in Lovelock theories. The form of the matching conditions depends on the parity of the brane codimension. For odd codimension, the matching conditions involve discontinuities of Chern-Simons forms and are thus simil…
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.
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 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 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.
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…
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 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 give the equations of motion for a self-gravitating Dirac p-brane embedded in an even co-dimension spacetime. The dynamics of the bulk are dictated by Lovelock gravity and permit matching conditions, even when the codimension is strictly greater than 2. We show that the equations of motion involve both induced Lovelock densities on the brane and regular extrinsic curvature terms. The brane dynamics can be derived from an exact (p+1)-dimensional induced action. The Dirac charge is carried by an overall (solid) angle defect which sets the Planck scale on the brane. In particular, if the codim…
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 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 …
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 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…
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 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 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…
We study codimension-even conical defects that contain a deficit solid angle around each point along the defect. We show that they lead to a delta function contribution to the Lovelock scalar and we compute the contribution by two methods. We then show that these codimension-even defects appear as Euclidean brane solutions in higher dimensional topological AdS gravity which is Lovelock-Chern-Simons gravity without torsion. The theory possesses a holographic Weyl anomaly that is purely of type-A and proportional to the Lovelock scalar. Using the formula for the defect contribution, we prove a h…
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…
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 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…
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 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 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…
The recently proposed gravitational entropy generalize the usual black hole entropy to Euclidean solutions without U(1) symmetry in the framework of Einstein gravity. The entropy of such smooth configuration is given by the area of minimal surface, therefore explaining the Ryu-Takayanagi formula of holographic entanglement entropy. In this note we investigate the generalized gravitational entropy for general Lovelock gravity in arbitrary dimensions. We use the replica trick and consider the Euclidean bulk spacetime with conical singularity localized at a codimension two surface. We obtain a co…
Lovelock gravity is an important extension of General Relativity that provides a promising framework to study curvature corrections to the Einstein action, while avoiding ghosts and keeping second order field equations. This paper derives the greybody factors for D-dimensional black holes arising in a theory with a Gauss-Bonnet curvature-squared term. These factors describe the non-trivial coupling between black holes and quantum fields during the evaporation process: they can be used both from a theoretical viewpoint to investigate the intricate spacetime structure around such a black hole, a…
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 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, …
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.
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…
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 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…
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, …
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 investigate the vacuum expectation value of the surface energy-momentum tensor for a massive scalar field with general curvature coupling parameter obeying the Robin boundary conditions on two codimension one parallel branes in a (D+1)-dimensional background spacetime $AdS_{D_{1}+1}\times Σ$ with a warped internal space $Σ$. These vacuum densities correspond to a gravitational source of the cosmological constant type for both subspaces of the branes. Using the generalized zeta function technique in combination with contour integral representations, the surface energies on the branes are pre…
