arXiv subjects

Ken-ichi Nakao

Publications and source records attributed to Ken-ichi Nakao.

At least 37 records · Page 2Linked to original sources

arXiv2015

Systematic error due to isotropic inhomogeneities

Usually the effects of isotropic inhomogeneities are not seriously taken into account in the determination of the cosmological parameters because of Copernican principle whose statement is that we do not live in the privileged domain in the universe. But Copernican principle has not been observationally confirmed yet in sufficient accuracy, and there is the possibility that there are non-negligible large-scale isotropic inhomogeneities in our universe. In this paper, we study the effects of the isotropic inhomogeneities on the determination of the cosmological parameters and show the probability that non-Copernican isotropic inhomogeneities mislead us into believing, for example, the phantom energy of the equation of state, $p=wρ$ with $w<-1$, even in case that $w=-1$ is the true value.

astro-ph.CO↗

arXiv2014

How small can an over-spinning body be in general relativity?

The angular momentum of the Kerr singularity should not be larger than a threshold value so that it is enclosed by an event horizon: The Kerr singularity with the angular momentum exceeding the threshold value is naked. This fact suggests that if the cosmic censorship exists in our Universe, an over-spinning body without releasing its angular momentum cannot collapse to spacetime singularities. A simple kinematical estimate of two particles approaching each other supports this expectation and suggests the existence of a minimum size of an over-spinning body. But this does not imply that the geometry near the naked singularity cannot appear. By analyzing initial data, i.e., a snapshot of a spinning body, we see that an over-spinning body may produce a geometry close to the Kerr naked singularity around itself at least as a transient configuration.

gr-qc↗

arXiv2014

Comparison of two approximation schemes for solving perturbations in a LTB cosmological model

Recently, the present authors studied perturbations in the Lemaitre-Tolman-Bondi cosmological model by applying the second-order perturbation theory in the dust Friedmann-Lemaitre-Robertson-Walker universe model. Before this work, the same subject was studied in some papers by analyzing linear perturbations in the Lemaitre-Tolman-Bondi cosmological model under the assumption proposed by Clarkson, Clifton and February, in which two of perturbation variables are negligible. However, it is a non-trivial issue in what situation the Clarkson-Clifton-February assumption is valid. In this paper, we investigate differences between these two approaches. It is shown that, in general, these two approaches are not compatible with each other. That is, in our perturbative procedure, the Clarkson-Clifton-February assumption is not valid at the order of our interest.

astro-ph.CO↗

arXiv2014

Newtonian self-gravitating system in a relativistic huge void universe model

We consider a test of the Copernican Principle through observations of the large-scale structures, and for this purpose we study the self-gravitating system in a relativistic huge void universe model which does not invoke the Copernican Principle. If we focus on the the weakly self-gravitating and slowly evolving system whose spatial extent is much smaller than the scale of the cosmological horizon in the homogeneous and isotropic background universe model, the cosmological Newtonian approximation is available. Also in the huge void universe model, the same kind of approximation as the cosmological Newtonian approximation is available for the analysis of the perturbations contained in a region whose spatial size is much smaller than the scale of the huge void: the effects of the huge void are taken into account in a perturbative manner by using the Fermi-normal coordinates. By using this approximation, we derive the equations of motion for the weakly self-gravitating perturbations whose elements have relative velocities much smaller than the speed of light, and show the derived equations can be significantly different from those in the homogeneous and isotropic universe model, due to the anisotropic volume expansion in the huge void. We linearize the derived equations of motion and solve them. The solutions show that the behaviors of linear density perturbations are very different from those in the homogeneous and isotropic universe model.

gr-qc↗

arXiv2013

Black Hole Universe: Time Evolution

Time evolution of a black hole lattice universe is simulated. The vacuum Einstein equations in a cubic box with a black hole at the origin are numerically solved with periodic boundary conditions on all pairs of opposite faces. Defining effective scale factors by using the area of a surface and the length of an edge of the cubic box, we compare them with that in the Einstein-deSitter universe. It is found that the behaviour of the effective scale factors is well approximated by that in the Einstein-deSitter universe. Our result suggests that local inhomogeneities do not significantly affect the global expansion law of the universe even if the inhomogeneity is extremely nonlinear.

gr-qc↗

arXiv2013

What wormhole is traversable?: A case of a wormhole supported by a spherical thin shell

We analytically explore the effect of falling matter on a spherically symmetric wormhole supported by a spherical shell composed of exotic matter located at its throat. The falling matter is assumed to be also a thin spherical shell concentric with the shell supporting the wormhole, and its self-gravity is completely taken into account. We treat these spherical thin shells by Israel's formalism of metric junction. When the falling spherical shell goes through the wormhole, it necessarily collides with the shell supporting the wormhole. To treat this collision, we assume the interaction between these shells is only gravity. We show the conditions on the parameters that characterize this model in which the wormhole persists after the spherical shell goes through it.

gr-qc↗

arXiv2013

Two-point correlation function of density perturbations in a large void universe

We study the two-point correlation function of density perturbations in a spherically symmetric void universe model which does not employ the Copernican principle. First we solve perturbation equations in the inhomogeneous universe model and obtain density fluctuations by using a method of non-linear perturbation theory which was adopted in our previous paper. From the obtained solutions, we calculate the two-point correlation function and show that it has a local anisotropy at the off-center position differently from those in homogeneous and isotropic universes. This anisotropy is caused by the tidal force in the off-center region of the spherical void. Since no tidal force exists in homogeneous and isotropic universes, we may test the inhomogeneous universe by observing statistical distortion of the two-point galaxy correlation function.

astro-ph.CO↗

arXiv2013

Ultra-high energy collision with neither black hole nor naked singularity

We explore the collision between two concentric spherical thin shells. The inner shell is charged, whereas the outer one is either neutral or charged. In the situation we consider, the charge of the inner shell is larger than its gravitational mass, and the inside of it is empty and regular. Hence the domain just outside it is described by the overcharged Reissner-Nordstrom geometry whereas the inside of it is Minkowski. First, the inner shell starts to shrink form infinity with finite kinetic energy, and then the outer shell starts to shrink from infinity with vanishing kinetic energy. The inner shell bounces on the potential wall and collides with the ingoing outer shell. The energy of collision between these shells at "their center of mass frame" does not exceed the total energy of the system. By contrast, by virtue of the very large gamma factor of the relative velocity of the shells, the energy of collision between two of the constituent particles of these shells at their center of mass frame can be much larger than the Planck scale. This result suggests that the black hole or naked singularity is not necessary for ultra-high energy collision of particles.

gr-qc↗

arXiv2012

Acceleration of particles and shells by Reissner-Nordström naked singularities

We explore the Reissner-Nordström naked singularities with a charge $Q$ larger than its mass $M$ from the perspective of the particle acceleration. We first consider a collision between two test particles following the radial geodesics in the Reissner-Nordström naked singular geometry. An initially radially ingoing particle turns back due to the repulsive effect of gravity in the vicinity of naked singularity. Such a particle then collides with an another radially ingoing particle. We show that the center of mass energy of collision taking place at $r \approx M$ is unbound, in the limit where the charge transcends the mass by arbitrarily small amount $0<1-M/Q\ll1$.The acceleration process we described avoids fine tuning of the parameters of the particle geodesics for the unbound center of mass energy of collisions and the proper time required for the process is also finite. We show that the coordinate time required for the trans-Plankian collision to occur around one solar mass naked singularity is around million years while it is many orders of magnitude larger than Hubble time in the black hole case. We then study the collision of the neutral spherically symmetric shells made up of dust particles. In this case, it is possible to treat the situation by exactly taking into account the gravity due to the shells using Israel`s thin shell formalism, and thus this treatment allows us to go beyond the test particle approximation. The center of mass energy of collision of the shells is then calculated in a situation analogous to the test particle case and is shown to be bounded above. However, we find thatthe energy of a collision between two of constituent particles of the shells at the center of mass frame can exceed the Planck energy.

gr-qc↗

arXiv2012

Black Hole Universe: Construction and Analysis of Initial Data

We numerically construct an one-parameter family of initial data of an expanding inhomogeneous universe model which is composed of regularly aligned black holes with an identical mass. They are initial data for vacuum solutions of the Einstein equations. We call this universe model the "black hole universe" and analyze the structure of these initial data. We study the relation between the mean expansion rate of the 3-space, which corresponds to the Hubble parameter, and the mass density of black holes. The result implies that the same relation as that of the Einstein-de Sitter universe is realized in the limit of the large separation between neighboring black holes. The applicability of the cosmological Newtonian $N$-body simulation to the dark matter composed of black holes is also discussed. The deviation of the spatial metric of the cosmological Newtonian $N$-body system from that of the black hole universe is found to be smaller than about 1% in a region distant from the particles, if the separation length between neighboring particles is 20 times larger than their gravitational radius. By contrast, the deviation of the square of the Hubble parameter of the cosmological Newtonian $N$-body system from that of the black hole universe is about 20% for the same separation length.

gr-qc↗

arXiv2012

Evolution of density perturbations in large void universe

We study the evolution of linear density perturbations in a large spherical void universe which accounts for the acceleration of the cosmic volume expansion without introducing dark energy. The density contrast of this void is not large within the light cone of an observer at the center of the void. Therefore, we describe the void structure as a perturbation with a dimensionless small parameter $κ$ in a homogeneous and isotropic universe within the region observable for the observer. We introduce additional anisotropic perturbations with a dimensionless small parameter $ε$, whose evolution is of interest. Then, we solve perturbation equations up to order $κε$ by applying second-order perturbation theory in the homogeneous and isotropic universe model. By this method, we can know the evolution of anisotropic perturbations affected by the void structure. We show that the growth rate of the anisotropic density perturbations in the large void universe is significantly different from that in the homogeneous and isotropic universe. This result suggests that the observation of the distribution of galaxies may give a strong constraint on the large void universe model.

astro-ph.CO↗

arXiv2011

Dynamical instability in a relativistic cylindrical shell composed of counter rotating particles

We give a perturbative analysis for an infinitesimally thin cylindrical shell composed of counter rotating collisionless particles, originally devised by Apostolatos and Thorne. They found a static solution of the shell and concluded by C-energy argument that it is stable. Recently, the present authors and Ida reanalyzed this system by evaluating the C-energy on the future null infinity and found that the system has an instability, though it was not shown how the system is unstable. In this paper, it is shown in the framework of the linear perturbation theory that, if the constituent particles move slowly, the static shell is unstable in the sense that the perturbation of its circumferential radius oscillates with exponentially growing amplitude, whereas if the speed of the constituent particle exceeds a critical value, the shell just expands or contracts exponentially with time.

gr-qc↗

arXiv2011

Q-tubes and Q-crusts

We explore equilibrium solutions of non-topological solitons in a general class of scalar field theories which include global U(1) symmetry. We find new types of solutions, tube-shaped and crust-shaped objects, and investigate their stability. Like Q-balls, the new solitons can exist in supersymmetric extensions of the Standard Model, which may responsible for baryon asymmetry and dark matter. Therefore, observational signals of the new solitons would give us more informations on the early universe and supersymmetric theories.

hep-th↗

arXiv2011

Is super-Planckian physics visible? -- Scattering of black holes in 5 dimensions

It may be widely believed that probing short-distance physics is limited by the presence of the Planck energy scale above which scale any information is cloaked behind a horizon. If this hypothesis is correct, we could observe quantum behavior of gravity only through a black hole of Planck mass. We numerically show that in a scattering of two black holes in the 5-dimensional spacetime, a visible domain, whose curvature radius is much shorter than the Planck length, can be formed. Our result indicates that super-Planckian phenomena may be observed without an obstruction by horizon formation in particle accelerators.

gr-qc↗

arXiv2011

Acceleration of colliding shells around a black hole: Validity of the test particle approximation in the Banados-Silk-West process

Recently, Banados, Silk and West (BSW) showed that the total energy of two colliding test particles has no upper limit in their center of mass frame in the neighborhood of an extreme Kerr black hole, even if these particles were at rest at infinity in the infinite past. We call this mechanism the BSW mechanism or BSW process. The large energy of such particles would generate strong gravity, although this has not been taken into account in the BSW analysis. A similar mechanism is seen in the collision of two spherical test shells in the neighborhood of an extreme Reissner-Nordström black hole. In this paper, in order to draw some implications concerning the effects of gravity generated by colliding particles in the BSW process, we study a collision of two spherical dust shells, since their gravity can be exactly treated. We show that the energy of two colliding shells in the center of mass frame observable from infinity has an upper limit due to their own gravity. Our result suggests that an upper limit also exists for the total energy of colliding particles in the center of mass frame in the observable domain in the BSW process due the gravity of the particles.

gr-qc↗

arXiv2010

Perturbative Analysis of a Stationary Magnetosphere in an Extreme Black Hole Spacetime : On the Meissner-like Effect of an Extreme Black Hole

It is known that the Meissner-like effect is seen in a magnetosphere without an electric current in black hole spacetime: no non-monopole component of magnetic flux penetrates the event horizon if the black hole is extreme. In this paper, in order to see how an electric current affects the Meissner-like effect, we study a force-free electromagnetic system in a static and spherically symmetric extreme black hole spacetime. By assuming that the rotational angular velocity of the magnetic field is very small, we construct a perturbative solution for the Grad-Shafranov equation, which is the basic equation to determine a stationary, axisymmetric electromagnetic field with a force-free electric current. Our perturbation analysis reveals that, if an electric current exists, higher multipole components may be superposed upon the monopole component on the event horizon, even if the black hole is extreme.

gr-qc↗

arXiv2010

Redshift Drift in LTB Void Universes

We study the redshift drift, i.e., the time derivative of the cosmological redshift in the Lemaître-Tolman-Bondi (LTB) solution in which the observer is assumed to be located at the symmetry center. This solution has often been studied as an anti-Copernican universe model to explain the acceleration of cosmic volume expansion without introducing the concept of dark energy. One of decisive differences between LTB universe models and Copernican universe models with dark energy is believed to be the redshift drift. The redshift drift is negative in all known LTB universe models, whereas it is positive in the redshift domain $z \lesssim 2$ in Copernican models with dark energy. However, there have been no detailed studies on this subject. In the present paper, we prove that the redshift drift of an off-center source is always negative in the case of LTB void models. We also show that the redshift drift can be positive with an extremely large hump-type inhomogeneity. Our results suggest that we can determine whether we live near the center of a large void without dark energy by observing the redshift drift.

astro-ph.CO↗

arXiv2010

CMB observations in LTB universes: Part II: the kSZ effect in an LTB universe

We study the kinematic Sunyaev-Zel'dovich (kSZ) effect in a Lemître-Tolman-Bondi (LTB) universe model whose distance-redshift relation agrees with that of the concordance $Λ$CDM model at redshifts $z\lesssim2$. This LTB universe model has a void with size comparable to the Hubble horizon scale. We first determine the decoupling epoch in this LTB universe model by an approximate analytical condition under a few simplified assumptions on the physical quantities at that epoch. Then we calculate the cosmic microwave background (CMB) anisotropy observed in the rest frame of clusters of galaxies which are assumed to be at rest in the spatial comoving coordinates of the LTB universe model. We find that the obtained temperature anisotropies are dominated by dipole, although there may exist higher multi-poles in general. We may interpret this dipole anisotropy as the drift velocity of a cluster of galaxies relative to the CMB rest frame. Hence it gives rise to the kSZ effect. We calculate this effect and compare it with observational data. We find that if we assume the conventional adiabatic perturbation scenario at the time of decoupling, the drift velocity of clusters of galaxies becomes unacceptably large. Conversely, this observational constraint may be relaxed by introducing a non-adiabatic (i.e., primordially isocurvature) component of inhomogeneities at the time of decoupling. However, our result indicates that the necessary isocurvature perturbation amplitude is very large.

astro-ph.CO↗