Probing the size of extra dimension with 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 $\ell$ cannot be static, and it is
dual to a four 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 $\ell$ by performing Fisher analyses. We
found that DECIGO/BBO can put a stronger constraint than the current table-top
result by detecting gravitational waves from small mass BH/BH and BH/neutron
star (NS) binaries. Furthermore, DECIGO/BBO is expected to detect 10$^5$ BH/NS
binaries per year. Taking this advantage, we found that DECIGO/BBO can actually
measure $\ell$ down to $\ell=0.33 \mu$m 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. On the other hand, when we take
eccentricities into binary parameters, the detection limit weakens to $\ell=1.5
\mu$m due to strong degeneracies between $\ell$ and eccentricities. We also
derived the upper bound on $\ell$ from the expected detection number of extreme
mass ratio inspirals (EMRIs) with LISA and BH/NS binaries with DECIGO/BBO,
extending the discussion made recently by McWilliams. We found that these less
robust constraints are weaker than the ones from phase differences.
