We extent our previous study on spherically symmetric braneworld solutions with induced gravity, including non-local bulk effects. We find the most general static four-dimensional black hole solutions with g tt = −g −1 rr . They satisfy a closed system of equations on the brane and represent the strong-gravity corrections to the Schwarzschild-(A)dS 4 spacetime. These new solutions have extra terms which give extra attraction relative to the Newtonian-(A)dS 4 force; however, the conventional limits are easily obtained. These terms, when defined asymptotically, behave like AdS 4 in this regime, while when defined at infinitely short distances predict either an additional attractive Newtonian potential or an attractive potential which scales approximately as √ r. One of the solutions found gives extra deflection of light compared to Newtonian deflection.

We study the regularization of the codimension-2 singularities in six-dimensional Einstein-Maxwell axisymmetric models with warping. These singularities are replaced by codimension-1 branes of a ring form, situated around the axis of symmetry. We assume that there is a brane scalar field with Goldstone dynamics, which is known to generate a brane energy momentum tensor of a particular structure necessary for the above regularization to be successful. We study these compactifications in both a non-supersymmetric and a supersymmetric setting. We see that in the non-supersymmetric case, there is a restriction to the admissible warpings and furthermore to the quantum numbers of the bulk gauge field and the brane scalar field. On the contrary, in the supersymmetric case, the warping can be arbitrary.

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.A growing interest in codimension-2 braneworlds, i.e a brane embedded in a bulk with two extra dimensions, has recently appeared. The most attractive feature of these models is that the vacuum energy (tension) of the brane instead of curving the brane world-volume, merely induces a deficit angle in the bulk around the brane [1]. This property was used to solve the cosmological constant problem [2]. However, soon it was realized [3] that one can only find nonsingular solutions if the brane stress tensor is proportional to its induced metric. To obtain the Einstein equation on the brane one has to introduce a cut-off (brane thickness) [4], loosing the predictability of the theory, or alternatively, one can modify the gravitational action by including a Gauss-Bonnet term [5] or a scalar curvature term (induced gravity) on the brane [6].We still lack an understanding of time dependent cosmological solutions in codimension-2 braneworlds. In the thin brane limit, because the energy momentum tensors on the brane and in the bulk are related, we cannot get the standard cosmology on the brane [7,8]. One then has to regularize the codimension-2 branes by introducing some thickness and then consider matter on them [9,10]. A cosmological evolution on the regularized branes requires an expanding brane world-volume and in general also a time evolving bulk. An alternatively approach was followed in [11] by considering a codimension-1 brane moving in the regularized static background. The resulting cosmology, however, was unrealistic having a negative Newton's constant (for a review see [12]).Moreover, the issue of localization of a black hole on the brane and its extension to the bulk is not fully understood. In codimension-1 braneworlds, a first attempt was to consider the black string extension in the bulk of a Schwarzschild metric [13]. Unfortunately, this string is unstable to classical linear perturbations [14] (for a review see [15]). Further attempts deal with the Einstein equations projected on the brane, which include an unknown bulk dependent term, the Weyl tensor projection. Due to this reason the system is not closed, and some assumptions have to be made either in the form of the metric or in the Weyl term [16]. The stability and thermodynamics of these solutions were worked out in [17].A lower dimensional version of a black hole living on a (2+1)-dimensional braneworld was considered in [18] by Emparan, Horowitz, and Myers. They based their analysis on the so-called C-metric [19] modified by a cosmological constant term. They found a BTZ black hole [20] on the brane which can be extended as a BTZ string in a four-dimensional AdS bulk. Their thermodynamical stability analysis showed that the black string remains a stable configuration when its transverse size is compara...

We consider a six-dimensional Einstein-Maxwell system compactified in an axisymmetric two-dimensional space with one capped regularized conical brane of codimension one. We study the cosmological evolution which is induced on the regularized brane as it moves in between known static bulk and cap solutions. Looking at the resulting Friedmann equation, we see that the brane cosmology at high energies is dominated by a five-dimensional ρ 2 energy density term. At low energies, we obtain a Friedmann equation with a term linear to the energy density with, however, negative coefficient in the small four-brane radius limit (i.e., with negative effective Newton's constant). We discuss ways out of this problem.

We study the slow-roll inflationary dynamics in a self-gravitating induced gravity braneworld model with bulk cosmological constant. For E ≫ M 3 5 /M 2 4 we find important corrections to the four-dimensional Friedmann equation which bring the standard chaotic inflationary scenario in closer agreement with recent observations. For M 3 5 /M 2 P l ≪ E ≪ M 3 5 /M 2 4 we find five-dimensional corrections to the Friedmann equation, which give the known Randall-Sundrum results of the inflationary parameters. a