The Complete Black Brane Solutions in D-dimensional Coupled Gravity System

TL;DR

The paper derives a complete analytic family of black-brane solutions in a $D$-dimensional gravity–dilaton–antisymmetric-tensor system by solving the coupled equations of motion with a quasi-Poincaré invariant ansatz. Central to the construction is reformulating the remaining equation as a Schwarzian derivative problem, which yields a seed solution $g_0(r)$ and, via $SL(2,\mathbb{R})$ transformations, a full nine-parameter solution; imposing flat-space behavior at infinity reduces to four physical parameters, with special choices reproducing the BPS and standard black-brane solutions. The authors provide explicit closed-form expressions for all metric factors, the dilaton, and the antisymmetric-tensor sector, and show how the celebrated Strominger–DuffaDuff black brane emerges as a corollary of their general solution, accessible also through a Schwarzschild-like coordinate change. The results offer a unified, complete analytic description of brane solutions in this class and lay groundwork for exploring their physical properties in diverse dimensions.

Abstract

In this paper, we use only the equation of motion for an interacting system of gravity, dilaton and antisymmetric tensor to study the black brane solutions. By making use of the property of Schwarzian derivative, we obtain the complete solution of this system of equations. For some special values we obtain the well-known BPS brane and black brane solutions.