Black branes on the linear dilaton background

TL;DR

This paper demonstrates that static black p-branes can have two distinct asymptotic behaviors, including a new exact solution with a linear dilaton background, and establishes their uniqueness and thermodynamic properties.

Contribution

It provides the first direct integration proof that asymptotically linear dilaton background p-branes are exact solutions and introduces a new uniqueness theorem for static p-branes.

Findings

Asymptotically LDB p-branes are exact supergravity solutions.

A new uniqueness theorem for static p-branes is established.

Solutions satisfy the first law of thermodynamics.

Abstract

We show that the complete static black p-brane supergravity solution with a single charge contains two and only two branches with respect to behavior at infinity in the transverse space. One branch is the standard family of asymptotically flat black branes, and another is the family of black branes which asymptotically approach the linear dilaton background with antisymmetric form flux (LDB). Such configurations were previously obtained in the near-horizon near-extreme limit of the dilatonic asymptotically flat p-branes, and used to describe the thermal phase of field theories involved in the DW/QFT dualities and the thermodynamics of little string theory in the case of the NS5-brane. Here we show by direct integration of the Einstein equations that the asymptotically LDB p-branes are indeed exact supergravity solutions, and we prove a new uniqueness theorem for static p-brane solutions satisfying cosmic censorship. In the non-dilatonic case, our general non-asymptotically flat p-branes are uncharged black branes on the background $AdS_{p+2}\times S^{D-p-2}$ supported by the form flux. We develop the general formalism of quasilocal quantities for non-asymptotically flat supergravity solutions with antisymmetric form fields, and show that our solutions satisfy the first law of theormodynamics. We also suggest a constructive procedure to derive rotating asymptotically LDB brane solutions.