ar X iv : h ep - t h / 97 02 07 9 v 1 1 0 Fe b 19 97 Non - extremal Intersecting p - branes in Various Dimensions

Non-extremal intersecting p-brane solutions of gravity coupled with several antisymmetric fields and dilatons in various space-time dimensions are constructed. The construction uses the same algebraic method of finding solutions as in the extremal case and a modified “no-force” conditions. We justify the “deformation” prescription. It is shown that the non-extremal intersecting p-brane solutions satisfy harmonic superposition rule and the intersections of non-extremal p-branes are specified by the same characteristic equations for the incidence matrices as for the extremal p-branes. We show that S-duality holds for non-extremal p-brane solutions. Generalized T -duality takes place under additional restrictions to the parameters of the theory, which are the same as in the extremal case. e-mail: [email protected] e-mail: [email protected] 1 A recent study of duality [1]–[5] and the microscopic interpretation of the BekensteinHawking entropy within string theory [6, 7] has stimulated investigations of the intersecting (composite) p-brane solutions. An extension of the D-brane entropy counting to near-extremal black p-branes is a problem of the valuable interest. There has been recently considerable progress in the study of classical extremal [8] -[28] and non-extremal p-brane solutions [30]-[34] in higher dimensional gravity coupled with matter. Heuristic scheme of construction of p-brane intersections was based on string theory representation of the branes, duality and supersymmetry. This construction involves the harmonic function superposition rule for the intersecting p-branes. The rule was formulated in [8] based on [10] for extremal solutions in D = 11 and D = 10 space-time dimensions. This rule was proved in [25] in arbitrary dimensions by using an algebraic method [18, 19, 22] of solutions of the Einstein equations. It has been shown that there is a prescription for “deformation” of a certain class of extremal p-branes to give non-extremal ones [30, 31]. The harmonic function superposition rule for the intersecting p-branes has also been extended to non-extremal solutions with a single “non-extremality” parameter specifying a deviation from the BPS-limit [33]. Nonextremal black hole solutions from intersecting M-branes which are characterized by two non-extremal deformation parameters have found in [34]. Another approach to the construction of p-brane solutions was elaborated in the papers [18, 19, 22, 24, 25, 26, 28]. In these papers a general class of p-brane intersection solutions was found. One starts from the equations of motion and by using a special ansatz for the metric and the matter fields specified by the incidence matrix one reduces them to the Laplace equation and to a system of algebraic equations. The aim of this letter is to extend this approach to the non-extremal case and to derive an explicit formula (40), see below, for solutions. We justify the harmonic function superposition rule and show that Sand T-dualities for intersecting non-extremal p-branes hold. Let us consider the theory with the following action I = 1 2κ2 ∫