Brane Solutions with Tension

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.