Geometrical properties of the trans-spherical solutions in higher dimensions

Abstract

We investigate the geometrical properties of static vacuum $p$-brane solutions of Einstein gravity in $D=n+p+3$ dimensions, which have spherical symmetry of $S^{n+1}$ orthogonal to the $p$-directions and are invariant under the translation along them. % The solutions are characterized by mass density and $p$ tension densities. % The causal structure of the higher dimensional solutions is essentially the same as that of the five dimensional ones. Namely, a naked singularity appears for most solutions except for the Schwarzschild black $p$-brane and the Kaluza-Klein bubble. % We show that some important geometric properties such as the area of $S^{n+1}$ and the total spatial volume are characterized only by the three parameters such as the mass density, the sum of tension densities and the sum of tension density squares rather than individual tension densities. These geometric properties are analyzed in detail in this parameter space and are compared with those of 5-dimensional case.

14 pages, 2 figures, Title changed

References in corpus (18)

• Black Strings and p-Branes are Unstable
• The evolution of unstable black holes in anti-de Sitter space
• Intersection Rules for Non-Extreme $p$-Branes
• General Definition of Gravitational Tension
• Origin of black string instability
• Five-dimensional black strings in Einstein-Gauss-Bonnet gravity
• On the stability of AdS black strings
• A Positivity Theorem for Gravitational Tension in Brane Spacetimes
• Complete Intersecting Non-Extreme p-Branes
• Classical Stability of Black D3-branes
• Black String Solutions with arbitrary Tension
• Extra Dimensions and Possible Space-Time Signature Changes
• Extraordinary vacuum black string solutions
• Spacetime structure of 5D hypercylindrical vacuum solutions with tension
• Geodesic Properties and Orbits in 5-dimensional Hypercylindrical Spacetime
• p-Brane Black Holes as Stability Islands
• Stationary vacuum hyper-cylindrical solution in 4+1 dimensions
• Geometrical features of (4+d) gravity

Cited by in corpus (6)

• Geodesic Properties and Orbits in 5-dimensional Hypercylindrical Spacetime
• Brane Solutions with Tension
• String or branelike solutions in four-dimensional Einstein gravity in the presence of cosmological constant
• Classification of Hypercylindrical Spacetimes with Momentum Flow
• Geodesic motions in extraordinary string geometry
• Toroidal AdS Charged Branes and Toda Equations