Can a brane fluctuate freely?

TL;DR

This paper demonstrates that a self-gravitating vacuum brane cannot fluctuate freely and its dynamics are essentially governed by gravitational waves, contrasting with the intuitive picture of independent brane fluctuations.

Contribution

It clarifies the relationship between the dynamics of self-gravitating branes and non-gravitating branes, bridging the gap between full gravitational perturbation analysis and the Nambu-Goto approximation.

Findings

Self-gravitating branes lack independent dynamical degrees of freedom.

Under weak backreaction, brane dynamics resemble non-gravitating branes.

The full perturbation equations show no free brane fluctuations.

Abstract

No, it cannot in the following sense if a self-gravitating vacuum brane is concerned. Once we write down the full set of linear perturbation equations of the system containing a self-gravitating brane, we will see that such a brane does not have its own dynamical degrees of freedom independent of those of gravitational waves which propagate in the surrounding spacetime. This statement seems to contradict with our intuition that a brane fluctuates freely on a given background spacetime in the lowest order approximation. Based on this intuition, we usually think that the dynamics of a brane can be approximately described by the equations derived from the Nambu-Goto action. In this paper we fill the gap residing between these two descriptions, showing that the dynamics of a self-gravitating brane is in fact similar to that described by a non-gravitating brane on a fixed background spacetime when the weak backreaction condition we propose in this paper is satisfied.