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.Comment: 19 pages, 10 figures. Published in PRD, typos corrected, references and footnotes adde

Hawking temperature for near-equilibrium black holes

We discuss the Hawking temperature of near-equilibrium black holes using a semiclassical analysis. We introduce a useful expansion method for slowly evolving spacetime, and evaluate the Bogoliubov coefficients using the saddle point approximation. For a spacetime whose evolution is sufficiently slow, such as a black hole with slowly changing mass, we find that the temperature is determined by the surface gravity of the past horizon. As an example of applications of these results, we study the Hawking temperature of black holes with null shell accretion in asymptotically flat space and the AdS-Vaidya spacetime. We discuss implications of our results in the context of the AdS/CFT correspondence.Comment: 13 pages, 7 figures, REVTeX4; published in PR

Constructing new optimal entanglement witnesses

We provide a new class of indecomposable entanglement witnesses. In 4 x 4 case it reproduces the well know Breuer-Hall witness. We prove that these new witnesses are optimal and atomic, i.e. they are able to detect the "weakest" quantum entanglement encoded into states with positive partial transposition (PPT). Equivalently, we provide a new construction of indecomposable atomic maps in the algebra of 2k x 2k complex matrices. It is shown that their structural physical approximations give rise to entanglement breaking channels. This result supports recent conjecture by Korbicz et. al.Comment: 9 page

Facial structures for various notions of positivity and applications to the theory of entanglement

In this expository note, we explain facial structures for the convex cones consisting of positive linear maps, completely positive linear maps, decomposable positive linear maps between matrix algebras, respectively. These will be applied to study the notions of entangled edge states with positive partial transposes and optimality of entanglement witnesses.Comment: An expository note. Section 7 and Section 8 have been enlarge

Quantum Back Reaction to asymptotically AdS Black Holes

We analyze the effects of the back reaction due to a conformal field theory (CFT) on a black hole spacetime with negative cosmological constant. We study the geometry numerically obtained by taking into account the energy momentum tensor of CFT approximated by a radiation fluid. We find a sequence of configurations without a horizon in thermal equilibrium (CFT stars), followed by a sequence of configurations with a horizon. We discuss the thermodynamic properties of the system and how back reaction effects alter the space-time structure. We also provide an interpretation of the above sequence of solutions in terms of the AdS/CFT correspondence. The dual five-dimensional description is given by the Karch-Randall model, in which a sequence of five-dimensional floating black holes followed by a sequence of brane localized black holes correspond to the above solutions.Comment: 13 pages, 10 figure