Detecting Extra Dimensions with Gravity-Wave Spectroscopy: The Black-String Brane World

Using the black string between two branes as a model of a brane-world black hole, we compute the gravity-wave perturbations and identify the features arising from the additional polarizations of the graviton. The standard four-dimensional gravitational wave signal acquires late-time oscillations due to massive modes of the graviton. The Fourier transform of these oscillations shows a series of spikes associated with the masses of the Kaluza-Klein modes, providing in principle a spectroscopic signature of extra dimensions.

Figure 1

Schematic of the black string.

Figure 2

The allowed region in parameter space. The stability boundary is well approximated by $GM/\ell =0.1122e^{d/\ell }$.

Figure 3

The $s$-wave potential for varying $\mu$. The critical potential is indicated by the heavy line. For $\mu <{\mu }_{\mathrm{crit}}$, there is a bound state with ${\omega }^2<0$, indicating an instability.

Figure 4

Gravity-wave signals associated with 3 massive KK modes and the 0-mode of $l=2$ axial perturbations, for a marginally stable black string. The inset shows the zero-mode signal on a logarithmic scale.

Figure 5

Composite $l=2$ axial gravity-wave signal (normalized) from the 9 lowest mass modes of a marginally stable black string. The upper panel corresponds to “truncated zero-mode” bulk initial data with $d/\ell =6$, the lower panel to Gaussian bulk initial data with $d/\ell =20$. The insets show the Fourier transform of the respective waveforms for $300\le \tau \le 1000$. The percentage of energy in the 4D zero-mode part of the signal is 99.96% (upper panel) and $2.281\times {10}^{-13}\%$ (lower panel).