Constructing more non-singular Sp-branes

In this note, we construct an array of non-singular Sp (where p = D − 4) branes in arbitrary D dimensions starting from static solutions of black p brane. These solutions carry nontrivial time dependent profiles of dilaton and associated form fields. We also study other non-singular time dependent configurations. These are obtained from proper analytic continuations of non-extremal diholes. E-mail: [email protected] Non-singular time dependent solutions are very rare in gravity theories, be it supergravity or string theory. Therefore, the recent constructions of non-singular Sp-brane solutions [1] have attracted much attention [2]. Sp branes are time dependent gravitational configurations with p longitudinal directions [3]. However, most of these solutions are singular. In a recent paper [1], non-singular S0 brane solutions are constructed by applying double-Wick rotations [1] to known black diholes [6]. Analytic continuation of these solutions give exact, time dependent, non-singular S0-brane in four dimensions. These solutions are non-singular in the sense that, all the conical singularities, which were there in the static solutions of black diholes, can be pushed off to the complex plane of ρ and t. These solutions often lead to accelerating and bouncing cosmologies. In this note, we generalise these non-singular solutions by analytically continuning p branes of [7]. We construct (D − 4) dimensional Sp-brane solutions in D dimensions. These are the solutions of D dimensional maximal supergravity theories and hence can be embedded in string theories. We also construct other non-singular time dependent configurations by analytically continuing the non-extremal diholes of [8], [9]. This letter is organised as follows. First, we construct the non-singular Sp branes by Wick rotating the solutions of [7]. Here, we give various plots to expose the non-singular nature of the solutions. Subsequently, we analyse the double analytic continuation of non-extremal generalisation of black dihole which are different from [1], following the solutions given in [8], [9]. This allow us to construct non-singular S0 branes. A general class of non-extremal black p brane solutions in arbitrary D dimensional space-time was constructed in [7]. The center of the brane sits along the transverse z axis. We take the linear superposition (unlike the non-linear superposition in the case of non-extremal black dihole) of the N individual p-brane potentials to get the potential of N number of branes along the z axis. As non-extremal branes exert forces on each other, the superposition of these branes is a tricky issue. This can be achieved however, if many of them are organised on a circle. This has been discussed in [7]. We start with the general supergravity action in D dimensions of the form S = ∫