74 | | [[latex($\rho_1 =$)]] |

| 74 | [[latex($\rho_1 \propto e^{-i i [4 \pi G \rho_0 (1-\frac{\lambda_J^2}{\lambda^2})]t}$)]] |

| 75 | |

| 76 | which gives |

| 77 | |

| 78 | [[latex($\rho_1 = C \cos(kx) e^{[4 \pi G \rho_0 (1-\frac{\lambda_J^2}{\lambda^2})]t}$)]] |

| 79 | |

| 80 | |

| 81 | Thus we have found the condition on [[latex($\omega$)]] which gives unstable perturbation modes. Now, the growth rate of these modes is given by |

| 82 | |

| 83 | [[latex($\Gamma = 4 \pi G \rho_0 (1-\frac{\lambda_J^2}{\lambda^2})$)]] |

| 84 | |

| 85 | and so the characteristic timescale for exponential growth, that is the time in which the perturbation increases by a factor of e, is given by |

| 86 | |

| 87 | [[latex($\tau = \frac{1}{\Gamma}$)]] |