Complete Intersecting Non-Extreme p-Branes

We give general intersecting brane solutions without assuming any restriction on the metric in supergravity coupled to a dilaton and antisymmetric tensor fields in arbitrary dimensions D. The result is a general class of intersecting brane solutions which interpolate the non-extreme solutions of type 1 and 2. We also discuss the relation of our solutions to the known single brane solution. e-mail address: [email protected] e-mail address: [email protected] Understanding classical solutions of supergravities in eleven and ten dimensions is an important subject in the current particle physics. These are the low-energy effective theories of string and M theories. An important class of solutions in such theories are the extended objects called branes [1]-[4], which have played significant role in our study of nonperturbative effects in strings and field theories realized on the branes. In particular non-extreme solutions give rise to non-extreme black holes and thus are very important in studying the properties of realistic black holes. Various supersymmetric and non-extreme solutions, and their intersections have been studied so far [5]-[18]. It has been known that there are two possible ways to construct non-extreme solutions, classified as type 1 and 2 in ref. [12]. Type 1 has the metric ds = edxp+1 + e (dr + rdΩ d̃+1 ), (1) where the dimension of the space-time is given as D = p+ d̃+3 and there is no restriction on the functions A and B except that they are functions of r only. The usual extreme solutions are obtained under the condition [5] (p+ 1)A+ d̃B = 0, (2) which can be understood as ‘no-force’ or BPS condition. By type 1 non-extreme solutions, we mean that the restriction (2) is removed. The metric for type 2 solutions is taken as ds = e(−fdt + dxp) + e(fdr + r2dΩ2d̃+1), (3) with the restriction (2). Here the function f gives the non-extreme extension. There have been many works on these two kinds of non-extreme solutions separately [3]-[19], but to the best of our knowledge neither clarification of the connection of these solutions nor attempt at interpolating these two classes of solutions have been made. In view of the importance of both these solutions, it is interesting to examine if there are more general solutions that include both classes of solutions and hence interpolate these in the particular limits of the parameters. The purpose of this paper is to show that this is indeed possible by deriving complete intersecting brane solutions without the restriction (2). We also discuss their relations to other known solutions. 2 The method adopted here is a simple generalization of that developed by one of the present authors some time ago [15] for the type 2 solutions. There the field equations were solved with a simplifying ansatz which generalizes the condition (2). What we show here is that it is in fact possible to solve the field equations without this ansatz, and the result is a very general class of solutions that involve additional integration constants, and their appropriate choices give both the solutions of type 1 and 2. Let us start with the general action for gravity coupled to a dilaton φ and m different nA-form field strengths: I = 1 16πGD ∫