How close can we approach the event horizon of the Kerr black hole from the detection of the gravitational quasinormal modes?

Using the WKB method, we show that the peak location ($r_{\rm peak}$) of the potential, which determines the quasinormal mode frequency of the Kerr black hole, obeys an accurate empirical relation as a function of the specific angular momentum $a$ and the gravitational mass $M$. If the quasinormal mode with $a/M \sim 1$ is observed by gravitational wave detectors, we can confirm the black-hole space-time around the event horizon, $r_{\rm peak}=r_+ +O(\sqrt{1-q})$ where $r_+$ is the event horizon radius. While if the quasinormal mode is different from that of general relativity, we are forced to seek the true theory of gravity and/or face to the existence of the naked singularity.Comment: 8 pages, 4 figure

Possible confirmation of the existence of ergoregion by the Kerr quasinormal mode in gravitational waves from Pop III massive black hole binary

The existence of the ergoregion of the Kerr space-time has not been confirmed observationally yet. We show that the confirmation would be possible by observing the quasinormal mode in gravitational waves. As an example, using the recent population synthesis results of Pop III binary black holes, we find that the peak of the final merger mass ($M_f$) is about $50~\rm M_{\odot}$, while the fraction of the final spin $q_f = a_f/M_f > 0.7$ needed for the confirmation of a part of ergoregion is $\sim 77\%$. To confirm the frequency of the quasinormal mode, ${\rm SNR} > 35$ is needed. The standard model of Pop III population synthesis tells us that the event rate for the confirmation of more than $50\%$ of the ergoregion by the second generation gravitational wave detectors is $\sim 2.3$ ${\rm events\ yr^{-1}\ (SFR_p/(10^{-2.5}\ M_\odot yr^{-1}\ Mpc^{-3}))} \cdot (\rm [f_b/(1+f_b)]/0.33)$ where ${\rm SFR_p}$ and ${\rm f_b}$ are the peak value of the Pop III star formation rate and the fraction of binaries, respectively.Comment: Accepted for publication in PTEP. Comments welcom

Gravitational wave quasinormal mode from Population III massive black hole binaries in various models of population synthesis

Focusing on the remnant black holes after merging binary black holes, we show that ringdown gravitational waves of Population III binary black holes mergers can be detected with the rate of $5.9-500~{\rm events~yr^{-1}}~({\rm SFR_p}/ (10^{-2.5}~M_\odot~{\rm yr^{-1}~Mpc^{-3}})) \cdot ({\rm [f_b/(1+f_b)]/0.33})$ for various parameters and functions. This rate is estimated for the events with SNR$>8$ for the second generation gravitational wave detectors such as KAGRA. Here, ${\rm SFR_p}$ and ${\rm f_b}$ are the peak value of the Population III star formation rate and the fraction of binaries, respectively. When we consider only the events with SNR$>35$, the event rate becomes $0.046-4.21~{\rm events~yr^{-1}}~({\rm SFR_p}/ (10^{-2.5}~M_\odot~{\rm yr^{-1}~Mpc^{-3}})) \cdot ({\rm [f_b/(1+f_b)]/0.33})$. This suggest that for remnant black hole's spin $q_f>0.95$ we have the event rate with SNR$>35$ less than $0.037~{\rm events~yr^{-1}}~({\rm SFR_p}/ (10^{-2.5}~M_\odot~{\rm yr^{-1}~Mpc^{-3}})) \cdot ({\rm [f_b/(1+f_b)]/0.33})$, while it is $3-30~{\rm events~yr^{-1}}~({\rm SFR_p}/ (10^{-2.5}~M_\odot~{\rm yr^{-1}~Mpc^{-3}})) \cdot ({\rm [f_b/(1+f_b)]/0.33})$ for the third generation detectors such as Einstein Telescope. If we detect many Population III binary black holes merger, it may be possible to constrain the Population III binary evolution paths not only by the mass distribution but also by the spin distribution.Comment: Submitted to PTEP. comments welcom

Changing Rural Japan

Paper by Takashi Nakan

Quarkyonic matter in lattice QCD at strong coupling

We study the phase diagram of quark matter at finite temperature and density in the strong coupling lattice QCD with one species of unrooted staggered fermions including finite coupling ($1/g^2$) effects for color SU($N_c$). We find that we may have partially chiral restored medium density matter at $N_c=3$, which would correspond to the quarkyonic matter suggested at large $N_c$.Comment: 9 pages, 4 figure

Chiral and deconfinement transitions in strong coupling lattice QCD with finite coupling and Polyakov loop effects

We investigate chiral and deconfinement transitions in the framework of the strong coupling lattice QCD for color SU(3) with one species of unrooted staggered fermion at finite temperature and quark chemical potential. We take account of the leading order Polyakov loop terms as well as the next-to-next-to-leading order (1/g^4) fermionic terms of the strong coupling expansion in the effective action. We investigate the Polyakov loop effects by comparing two approximation schemes, a Haar measure method (no fluctuation from the mean field) and a Weiss mean-field method (with fluctuations). The effective potential is obtained in both cases, and we analytically clarify the Polyakov loop contributions to the effective potential. The Polyakov loop is found to suppress the chiral condensate and to reduce the chiral transition temperature at mu=0, and the chiral transition temperature roughly reproduces the Monte Carlo results at beta=2N_c/g^2 \lesssim 4. The deconfinement transition is found to be the crossover and first order for light (am_0 \lesssim 4 at beta=4) and heavy quark masses, respectively.Comment: 13 pages, 15 figures. v2; More dicussions added, figures improved, and typos correcte