Probing the size of extra dimension from gravitational wave astronomy

In Randall-Sundrum II (RS-II) braneworld model, it has been conjectured according to the AdS/CFT correspondence that brane-localized black hole (BH) larger than the bulk AdS curvature scale ℓ cannot be static , and it is dual to a 4 dimensional BH emitting the Hawking radiation through some quantum fields. In this scenario, the number of the quantum field species is so large that this radiation changes the orbital evolution of a BH binary. We derived the correction to the gravitational waveform phase due to this effect and estimated the upper bounds on ℓ by performing Fisher analyses. DECIGO/BBO is expected to detect 10⁵ BH/NS binaries per year. Taking this advantage, we found that DECIGO/BBO can actually measure ℓ down to ℓ = 0.328 μm for 5 year observation if we know that binaries are circular a priori. This is about 40 times smaller than the upper bound obtained from the table-top experiment.