arXiv subjects

Kota Ogasawara

Publications and source records attributed to Kota Ogasawara.

24 records · Page 2Linked to original sources

arXiv2017

Particle collision with an arbitrarily high center-of-mass energy near a Bañados-Teitelboim-Zanelli black hole

We consider a particle collision with a high center-of-mass energy near a Bañados-Teitelboim-Zanelli (BTZ) black hole. We obtain the center-of-mass energy of two general colliding geodesic particles in the BTZ black hole spacetime. We show that the center-of-mass energy of two ingoing particles can be arbitrarily large on an event horizon if either of the two particles has a critical angular momentum and the other has a non-critical angular momentum. We also show that the motion of a particle with a subcritical angular momentum is allowed near an extremal rotating BTZ black hole and that a center-of-mass energy for a tail-on collision at a point can be arbitrarily large in a critical angular momentum limit.

gr-qc↗

arXiv2017

Escape probability of the super-Penrose process

We consider a head-on collision of two massive particles that move in the equatorial plane of an extremal Kerr black hole, which results in the production of two massless particles. Focusing on a typical case, where both of the colliding particles have zero angular momenta, we show that a massless particle produced in such a collision can escape to infinity with arbitrarily large energy in the near-horizon limit of the collision point. Furthermore, if we assume that the emission of the produced massless particles is isotropic in the center-of-mass frame but confined to the equatorial plane, the escape probability of the produced massless particle approaches $5/12$ and almost all escaping massless particles have arbitrarily large energy at infinity and an impact parameter approaching $2GM/c^2$, where $M$ is the mass of the black hole.

gr-qc↗

arXiv2016

Empirical Uncertain Bayes Methods in Area-level Models

Random effects model can account for the lack of fitting a regression model and increase precision of estimating area-level means. However, in case that the synthetic mean provides accurate estimates, the prior distribution may inflate an estimation error. Thus it is desirable to consider the uncertain prior distribution, which is expressed as the mixture of a one-point distribution and a proper prior distribution. In this paper, we develop an empirical Bayes approach for estimating area-level means, using the uncertain prior distribution in the context of a natural exponential family, which we call the empirical uncertain Bayes (EUB) method. The regression model considered in this paper includes the Poisson-gamma and the binomial-beta, and the normal-normal (Fay-Herriot) model, which are typically used in small area estimation. We obtain the estimators of hyperparameters based on the marginal likelihood by using a well-known Expectation-Maximization algorithm, and propose the EUB estimators of area means. For risk evaluation of the EUB estimator, we derive a second-order unbiased estimator of a conditional mean squared error by using some techniques of numerical calculation. Through simulation studies and real data applications, we evaluate a performance of the EUB estimator and compare it with the usual empirical Bayes estimator.

stat.ME↗

arXiv2016

Bayesian Nonparametric Instrumental Variable Regression Approach to Quantile Inference

This study extends the Bayesian nonparametric instrumental variable regression model to determine the structural effects of covariates on the conditional quantile of the response variable. The error distribution is nonparametrically modelled using a Dirichlet mixture of bivariate normal distributions. The mean functions include the smooth effects of the covariates represented using the spline functions in an additive manner. The conditional variance of the second-stage error is also modelled using the spline functions such that it varies smoothly with the covariates. Accordingly, the proposed model allows for considerable flexibility in the shape of the quantile function while correcting for an endogeneity effect. The posterior inference for the proposed model is based on the Markov chain Monte Carlo method that requires no Metropolis-Hastings update. The approach is demonstrated using simulated and real data on the death rate in Japan during the inter-war period.

stat.ME↗

arXiv2016

Consistent analytic approach to the efficiency of collisional Penrose process

We propose a consistent analytic approach to the efficiency of collisional Penrose process in the vicinity of a maximally rotating Kerr black hole. We focus on a collision with arbitrarily high center-of-mass energy, which occurs if either of the colliding particles has its angular momentum fine-tuned to the critical value to enter the horizon. We show that if the fine-tuned particle is ingoing on the collision, the upper limit of the efficiency is $(2+\sqrt{3})(2-\sqrt{2})\simeq 2.186$, while if the fine-tuned particle is bounced back before the collision, the upper limit is $(2+\sqrt{3})^{2}\simeq 13.93$. Despite earlier claims, the former can be attained for inverse Compton scattering if the fine-tuned particle is massive and starts at rest at infinity, while the latter can be attained for various particle reactions, such as inverse Compton scattering and pair annihilation, if the fine-tuned particle is either massless or highly relativistic at infinity. We discuss the difference between the present and earlier analyses.

gr-qc↗

arXiv2015

High efficiency of collisional Penrose process requires heavy particle production

The center-of-mass energy of two particles can become arbitrarily large if they collide near the event horizon of an extremal Kerr black hole, which is called the Ba$\rm \tilde n$ados-Silk-West (BSW) effect. We consider such a high-energy collision of two particles which started from infinity and follow geodesics in the equatorial plane and investigate the energy extraction from such a high-energy particle collision and the production of particles in the equatorial plane. We analytically show that, on the one hand, if the produced particles are as massive as the colliding particles, the energy-extraction efficiency is bounded by $2.19$ approximately. On the other hand, if a very massive particle is to be produced as a result of the high-energy collision, which has negative energy and necessarily falls into the black hole, the upper limit of the energy-extraction efficiency is increased to $(2+\sqrt{3})^2 \simeq 13.9$. Thus, higher efficiency of the energy extraction, which is typically as large as 10, provides strong evidence for the production of a heavy particle.

gr-qc↗