Brane Solutions with Tension

TL;DR

This paper constructs and analyzes charged brane solutions with tension in higher-dimensional gravity, identifying conditions for regularity and connections to known M-branes, advancing understanding of brane configurations with tension.

Contribution

It introduces a special metric ansatz to simplify equations and constructs new charged brane solutions with tension, including conditions for regularity and relations to M2 and M5 branes.

Findings

Charged brane solutions characterized by mass, tension, and charge.

Regularity conditions depend on specific tension values.

Solutions reduce to M2 and M5 branes under certain limits.

Abstract

In this note, we apply a special metric ansatz to simplify the equations of motion for gravitational systems. Then we construct charged brane solutions in $D=n+p+2$ dimensions which have spherical symmetry of $S^n$ and translational symmetry along $p$ directions. They are characterized by mass density, uniform tension and electric/magnetic charges, and nonsingular only for specific tension. In particular, we find the limits and the coordinate transformations which reduce the charged brane solutions to $M2$- and $M5$-branes. We also obtain the regularity condition for an electrically charged two-brane solution which has two tensions.