R-charged AdS bubble

We construct R-charged adS bubbles in D = 5, N = 8 supergravity. These bubbles are charecterised by four parameters. The asymptotic boundary of these solutions are deSitter times a circle. By comparing boundary energies, we study the possibility of a transition from certain class of black holes to these bubbles below a critical radius of the boundary circle. We argue that this may occur when four parameters of the bubble satisfy a constraint among themselves. Electronic address: anindyab,tanay, [email protected] In this Letter, we first construct the bubble solutions of D = 5, N = 8 gauged IIB supergravity [1, 2] . These bubbles carry the R-charges that correspond to the three U(1) Cartan subalgebra of the gauge group SO(6). At asymptotic boundary, these solutions approach S × dS. This is similar to the adS-Schwarzschild bubbles [4, 5]∗. We then compute various components of the boundary stress-energy tensors associated with these R-charged bubbles. One of the main motivation for us to study these bubbles is an issue pointed out in [8]†. It was found earlier that a certain class of five dimensional black holes [9, 10] (which are higher dimensional analogue of BTZ black holes) had same asymptotic boundary metric as that of the adS-Schwarzschild bubbles. As far as the boundary geometry is concerned, the only difference is that, for the black hole, the boundary radius of the S (say parametrised by χ) has no restriction. However, for the bubble, the size of S has an upper bound (say ∆χc). Otherwise, for ∆χ > ∆χc, the space-time becomes singular‡. Furthermore, it was found in [11] that the components of the boundary stress tensor of these holes are exactly same as that of a bubble in the limit of zero bubble radius. In general, however, the energy of the bubble space-time is lower than that of a black hole. Now suppose that we start with a black hole with large ∆χ which parametrises the period of S at the boundary. As we tune ∆χ below the critical value ∆χc, the bubble solution for the bulk becomes available whose energy is less than that of a black hole. One would then expect a transition from the black hole to the bubble configuration. In the case of R-charged bubble, we also find a possibility of such a transition. Here the transition is infact from the same adS orbifold (with some radiation of massless matter) to R-charged bubble below certain critical radius of the boundary circle. In the following we construct the bubbles and then discuss the possibility of such a transition. In particular, this happens when the parameters specifying the solution satisfy certain relation among themselves. Due to the conjectured dS/CFT correspondence, one would then expect to see the signature of such a transition in the gauge theory on the boundary. One would also like to understand this phenomenon better in terms of string theory in the bulk. Neither of these issues are clear to us at this moment. We only offer some possibilities at the end of this Letter. The bubble solution in D = 5, N = 8 gauged type IIB supergravity has the following form§: ds = Hfdχ +H(fdr − rdτ + r cosh τdΩ22). (1) where Hi = 1− qi/r, (2)