Dynamical p-branes with a cosmological constant

TL;DR

This paper explores dynamical solutions of p-branes in a D-dimensional gravitational theory with a cosmological constant, revealing how brane dynamics depend on the cosmological constant and spacetime dimension, including collision scenarios and asymptotic behaviors.

Contribution

It introduces new dynamical p-brane solutions with a cosmological constant and analyzes their properties and interactions across different spacetime dimensions.

Findings

For D>4, 1-branes approach the Milne universe in the far-brane region.

Negative cosmological constant prevents brane collisions in D>4.

In D=3, colliding 1-branes are possible.

Abstract

We present a class of dynamical solutions in a D-dimensional gravitational theory coupled to a dilaton, a form field strength, and a cosmological constant. We find that for any D due to the presence of a cosmological constant, the metric of solutions depends on a quadratic function of the brane world volume coordinates, and the transverse space cannot be Ricci flat except for the case of 1-branes. We then discuss the dynamics of 1-branes in a D-dimensional spacetime. For a positive cosmological constant, 1-brane solutions with D>4 approach the Milne universe in the far-brane region. On the other hand, for a negative cosmological constant, each 1-brane approaches the others as the time evolves from a positive value, but no brane collision occurs for D>4, since the spacetime close to the 1-branes eventually splits into the separate domains. In contrast, the D=3 case provides an example of colliding 1-branes. Finally, we discuss the dynamics of 0-branes and show that for D>2, they behave like the Milne universe after the infinite cosmic time has passed.