arXiv subjects

Ken-ichi Nakao

Publications and source records attributed to Ken-ichi Nakao.

At least 55 records · Page 3Linked to original sources

arXiv2010

Visible borders of spacetime generated by high-energy collisions

Several years ago, two of the present authors proposed the concept of the border of spacetime as a generalization of spacetime singularities. Visible borders of spacetime, which replace naked singularities of classical theory, are not only necessary for the mathematical completeness of general relativity but they also provide a window into new physics of strongly curved spacetime, which is observable in principle. By employing simple geometrical and dimensional arguments, we show that not only black holes but also visible borders of spacetime will be generated at, for example, the CERN Large Hadron Collider, provided that the energy scale of quantum gravity is near 1 TeV in the framework of the large extra-dimension scenario.

gr-qc↗

arXiv2010

CMB observations in LTB universes: Part I: Matching peak positions in the CMB spectrum

Acoustic peaks in the spectrum of the cosmic microwave background in spherically symmetric inhomogeneous cosmological models are studied. At the photon-baryon decoupling epoch, the universe may be assumed to be dominated by non-relativistic matter, and thus we may treat radiation as a test field in the universe filled with dust which is described by the Lemaître-Tolman-Bondi (LTB) solution. First, we give an LTB model whose distance-redshift relation agrees with that of the concordance $Λ$CDM model in the whole redshift domain and which is well approximated by the Einstein-de Sitter universe at and before decoupling. We determine the decoupling epoch in this LTB universe by Gamow's criterion and then calculate the positions of acoustic peaks. Thus obtained results are not consistent with the WMAP data. However, we find that one can fit the peak positions by appropriately modifying the LTB model, namely, by allowing the deviation of the distance-redshift relation from that of the concordance $Λ$CDM model at $z>2$ where no observational data are available at present. Thus there is still a possibility of explaining the apparent accelerated expansion of the universe by inhomogeneity without resorting to dark energy if we abandon the Copernican principle. Even if we do not take this extreme attitude, it also suggests that local, isotropic inhomogeneities around us may seriously affect the determination of the density contents of the universe unless the possible existence of such inhomogeneities is properly taken into account.

astro-ph.CO↗

arXiv2009

Einstein-Rosen waves and the self-similarity hypothesis in cylindrical symmetry

The self-similarity hypothesis claims that in classical general relativity, spherically symmetric solutions may naturally evolve to a self-similar form in certain circumstances. In this context, the validity of the corresponding hypothesis in nonspherical geometry is very interesting as there may exist gravitational waves. We investigate self-similar vacuum solutions to the Einstein equation in the so-called whole-cylinder symmetry. We find that those solutions are reduced to part of the Minkowski spacetime with a regular or conically singular axis and with trivial or nontrivial topology if the homothetic vector is orthogonal to the cylinders of symmetry. These solutions are analogous to the Milne universe, but only in the direction parallel to the axis. Using these solutions, we discuss the nonuniqueness (and nonvanishing nature) of C energy and the existence of a cylindrical trapping horizon in Minkowski spacetime. Then, as we generalize the analysis, we find a two-parameter family of self-similar vacuum solutions, where the homothetic vector is not orthogonal to the cylinders in general. The family includes the Minkowski, the Kasner and the cylindrical Milne solutions. The obtained solutions describe the interior to the exploding (imploding) shell of gravitational waves or the collapse (explosion) of gravitational waves involving singularities from nonsingular initial data in general. Since recent numerical simulations strongly suggest that one of these solutions may describe the asymptotic behavior of gravitational waves from the collapse of a dust cylinder, this means that the self-similarity hypothesis is naturally generalized to cylindrical symmetry.

gr-qc↗

arXiv2009

Accelerated cosmic expansion in a scalar-field universe

We consider here a spherically symmetric but inhomogeneous universe filled with a massless scalar field. The model obeys two constraints. The first one is that the gradient of the scalar field is timelike everywhere. The second constraint is that the radial coordinate basis vector is a unit vector field in the comoving coordinate system. We find that the resultant dynamical solutions compose a one-parameter family of self-similar models which is known as the Roberts solution. The solutions are divided into three classes. The first class consists of solutions with only one spacelike singularity in the synchronous-comoving chart. The second class consists of solutions with two singularities which are null and spacelike, respectively. The third class consists of solutions with two spacelike singularities which correspond to the big bang and big crunch, respectively. We see that, in the first case, a comoving volume exponentially expands as in an inflationary period; the fluid elements are accelerated outwards form the symmetry center, even though the strong energy condition is satisfied. This behavior is very different from that observed in the homogeneous and isotropic universe in which the fluid elements would move outwards with deceleration, if the strong energy conditions are satisfied. We are thus able to achieve the accelerated expansion of the universe for the models considered here, without a need to violate the energy conditions. The cosmological features of the models are examined in some detail.

gr-qc↗

arXiv2009

Solving the Inverse Problem with Inhomogeneous Universes

We construct the Lemaître-Tolman-Bondi (LTB) dust universe whose distance-redshift relation is equivalent to that in the concordance $Λ$ cold dark matter ($Λ$CDM) cosmological model. In our model, the density distribution and velocity field are not homogeneous, whereas the big-bang time is uniform, which implies that the universe is homogeneous at its beginning. We also study the effects of local clumpiness in the density distribution as well as the effects of large-scale inhomogeneities on the distance-redshift relation, and show that these effects may reduce the amplitude of large-scale inhomogeneities necessary for having a distance-redshift relation that is the same as that of the concordance $Λ$CDM universe. We also study the temporal variation of the cosmological redshift and show that, by the observation of this quantity, we can distinguish our LTB universe model from the concordance $Λ$CDM model, even if their redshift-distance relations are equivalent to each other.

astro-ph↗

arXiv2009

Maximal slicing of D-dimensional spherically-symmetric vacuum spacetime

We study the foliation of a $D$-dimensional spherically symmetric black-hole spacetime with $D\ge 5$ by two kinds of one-parameter family of maximal hypersurfaces: a reflection-symmetric foliation with respect to the wormhole slot and a stationary foliation that has an infinitely long trumpet-like shape. As in the four-dimensional case, the foliations by the maximal hypersurfaces have the singularity avoidance nature irrespective of dimensionality. This indicates that the maximal slicing condition will be useful for simulating higher-dimensional black-hole spacetimes in numerical relativity. For the case of D=5, we present analytic solutions of the intrinsic metric, the extrinsic curvature, the lapse function, and the shift vector for the foliation by the stationary maximal hypersurfaces. This data will be useful for checking five-dimensional numerical relativity codes based on the moving puncture approach.

gr-qc↗

arXiv2009

Relativistic Gravitational Collapse of a Cylindrical Shell of Dust II: Settling Down Boundary Condition

We numerically study the dynamics of an imploding hollow cylinder composed of dust. Since there is no cylindrical black hole in 4-dimensional spacetime with physically reasonable energy conditions, a collapsed dust cylinder involves a naked singularity accompanied by its causal future, or a fatal singularity which terminates the history of the whole universe. In a previous paper, the present authors have shown that if the dust is assumed to be composed of collisionless particles such that these particles go through the symmetry axis of the cylinder, then the scalar polynomial singularity formed on the symmetry axis is so weak that almost all of geodesics are complete, and thus effectively no singularity forms by the collapse of a hollow dust cylinder. By contrast, in this paper, we assume that whole of the collapsed dust settles down on the symmetry axis by changing its equation of state. Obtained solutions are the straightforward extension of Morgan's null dust solution, in which no gravitational radiation is emitted. However, in the present case with timelike dust, infinite amount of $C$-energy initially stored in the system is released through gravitational radiation. We also show that the gravitational waves asymptotically behave in a self-similar manner.

gr-qc↗

arXiv2008

Magnification Probability Distribution Functions of Standard Candles in a Clumpy Universe

Lensing effects on light rays from point light sources, such like Type Ia supernovae, are simulated in a clumpy universe model. In our universe model, it is assumed that all matter in the universe takes the form of randomly distributed objects each of which has finite size and is transparent for light rays. Monte-Carlo simulations are performed for several lens models, and we compute probability distribution functions of magnification. In the case of the lens models that have a smooth density profile or the same degree of density concentration as the spherical NFW (Navarro-Frenk-White) lens model at the center, the so-called gamma distributions fit well the magnification probability distribution functions if the size of lenses is sufficiently larger than the Einstein radius. In contrast, the gamma distributions do not fit the magnification probability distribution functions in the case of the SIS (Singular Isothermal Sphere) lens model. We find, by using the power law cusp model, that the magnification probability distribution function is fitted well using the gamma distribution only when the slope of the central density profile is not very steep. These results suggest that we may obtain information about the slope of the central density profiles of dark matter halo from the lensing effect of Type Ia supernovae.

astro-ph↗

arXiv2008

High-Speed Collapse of a Hollow Sphere of Type I Matter

In this paper, we study the dynamics of a hollow spherical matter collapsing with very large initial velocity. The spacetime is initially very similar to the Vaidya solution, and the deviations from this background are treated perturbatively. The equations of state for radial pressure $p_{\rm R}=kρ$ and tangential one $p_{\rm T}=wρ$ with constant $k$ and $w$ are assumed. We find for the case of equations of state $k< 1$ and $0<w\leq1$ that the initial velocity, which is nearly the speed of light, is strongly decelerated. This result implies that the pressure is essential to the property of singularity formation in gravitational collapse even for initially nearly light-speed collapse. By contrast, in cases with the negative tangential pressure, the present result implies that the central naked singularity similar to that of the Vaidya spacetime can be formed, even though the radial pressure is positive, and the weak, strong and dominant energy conditions hold. Especially, in the case of $w<-(1-k)/4$, the high-speed collapse will produce the spacetime structure very similar to that of the Vaidya spacetime.

gr-qc↗

arXiv2007

New instability in relativistic cylindrically symmetric system

We investigate an infinitesimally thin cylindrical shell composed of counter-rotating dust particles. This system was studied by Apostolatos and Thorne in terms of the C-energy for a bounded domain. In this paper, we reanalyze this system by evaluating the C-energy on the future null infinity. We find that some class of momentarily static and radiation-free initial data does not settle down into static, equilibrium configurations, and otherwise infinite amount of the gravitational radiation is emitted to the future null infinity. Our result implies the existence of an instability in this system. In the framework of the Newtonian gravity, a cylindrical shell composed of counter-rotating dust particles can be in a steady state with oscillation by the gravitational attraction and centrifugal repulsion, and hence a static state is not necessarily realized as a final state. By contrast, in the framework of general relativity, the steady oscillating state will be impossible since the gravitational radiation will carry the energy of the oscillation to infinity. Thus, this instability has no counterpart in the Newtonian gravity.

gr-qc↗

arXiv2007

Critical Collapse of Einstein Cluster

We observe critical phenomena in spherically symmetric gravitational collapse of Einstein Cluster. We show analytically that the collapse evolution ends either in formation of a black hole or in dispersal depending on the values of initial parameters which characterize initial density and angular momentum of the collapsing cloud. Near the threshold of black hole formation, we obtain scaling relation for the mass of the black hole and find the critical exponent value to be 3/2. We numerically confirm that there exist wide ranges of initial parameter values around the critical configuration for which the model remains shell-crossing free.

gr-qc↗

arXiv2007

Relativistic Gravitational Collapse of a Cylindrical Shell of Dust

The gravitational collapse of a thick cylindrical shell of dust matter is investigated. It is found that a spacetime singularity forms on the symmetry axis and that it is necessarily naked, i.e., observable in principle. We propose a physically reasonable boundary condition at this naked singularity to construct the solution including its causal future. This boundary condition enables us to construct the unique continuation of spacetime beyond the naked singularity and ensures that the dust shell passes through the naked singularity. When the cylindrical shell leaves its symmetry axis away, the naked singularity disappears, and regularity is recovered. We construct numerical solutions with this feature. This result implies that the gravity produced by a thick cylindrical shell of dust is too weak to bind the shell even if it engenders the formation of a curvature singularity which is so strong as to satisfy the limiting focusing condition. For this reason, this naked singularity is very weak in the extended spacetime; the metric tensor is $C^{1-}$ even at the naked singularity, and the extended spacetime is complete for almost all geodesics. This feature is also seen for singular hypersurfaces. Such an extended spacetime can be regarded as phenomenological in the sense that it is valid if the relevant microphysics length scale is sufficiently small compared to the scale of interest.

gr-qc↗

arXiv2007

Lensing Effects on Gravitational Waves in a Clumpy Universe -Effects of Inhomogeneity on the Distance-Redshift Relation-

The distance-redshift relation determined by means of gravitational waves in the clumpy universe is simulated numerically by taking into account the effects of gravitational lensing. It is assumed that all of the matter in the universe takes the form of randomly distributed point masses, each of which has the identical mass $M_L$. Calculations are carried out in two extreme cases: $λ\gg GM_L/c^2$ and $λ\ll GM_L/c^2$, where $λ$ denotes the wavelength of gravitational waves. In the first case, the distance-redshift relation for the fully homogeneous and isotropic universe is reproduced with a small distance dispersion, whereas in the second case, the distance dispersion is larger. This result suggests that we might obtain information about the typical mass of lens objects through the distance-redshift relation gleaned through observation of gravitational waves of various wavelengths. In this paper, we show how to set limitations on the mass $M_L$ through the observation of gravitational waves in the clumpy universe model described above.

astro-ph↗

arXiv2006

The universe out of a monopole in the laboratory?

To explore the possibility that an inflationary universe can be created out of a stable particle in the laboratory, we consider the classical and quantum dynamics of a magnetic monopole in the thin-shell approximation. Classically there are three types of solutions: stable, collapsing and inflating monopoles. We argue that the transition from a stable monopole to an inflating one could occur either by collision with a domain wall or by quantum tunneling.

gr-qc↗

arXiv2006

Naked singularity resolution in cylindrical collapse

In this paper, we study the gravitational collapse of null dust in the cylindrically symmetric spacetime. The naked singularity necessarily forms at the symmetry axis. We consider the situation in which null dust is emitted again from the naked singularity formed by the collapsed null dust and investigate the back-reaction by this emission for the naked singularity. We show a very peculiar but physically important case in which the same amount of null dust as that of the collapsed one is emitted from the naked singularity as soon as the ingoing null dust hits the symmetry axis and forms the naked singularity. In this case, although this naked singularity satisfies the strong curvature condition by Królak (limiting focusing condition), geodesics which hit the singularity can be extended uniquely across the singularity. Therefore we may say that the collapsing null dust passes through the singularity formed by itself and then leaves for infinity. Finally the singularity completely disappears and the flat spacetime remains.

gr-qc↗

arXiv2005

Hoop Conjecture in Five-dimensios -Violation of Cosmic Censorship-

We study the condition of black hole formation in five-dimensional space-time. We analytically solve the constraint equations of five-dimensional Einstein equations for momentarily static and conformally flat initial data of a spheroidal mass. We numerically search for an apparent horizon in various initial hypersurfaces and find both necessary and sufficient conditions for the horizon formation in terms of inequalities relating a geometric quantity and a mass defined in an appropriate manner. In the case of infinitely thin spheroid, our results suggest a possibility of naked singularity formation by the spindle gravitational collapse in five-dimensional space-time.

gr-qc↗

arXiv2005

Black Strings in Our World

The brane world scenario is a new approach to resolve the problem on how to compactify the higher dimensional spacetime to our 4-dimensional world. One of the remarkable features of this scenario is the higher dimensional effects in classical gravitational interactions at short distances. Due to this feature, there are black string solutions in our 4-dimensional world. In this paper, assuming the simplest model of complex minimally coupled scalar field with the local U(1) symmetry, we show a possibility of black-string formation by merging processes of type I long cosmic strings in our 4-dimensional world. No fine tuning for the parameters in the model might be necessary.

gr-qc↗

arXiv2005

Gravitational Radiation from Cylindrical Naked Singularity

We construct an approximate solution which describes the gravitational emission from a naked singularity formed by the gravitational collapse of a cylindrical thick shell composed of dust. The assumed situation is that the collapsing speed of the dust is very large. In this situation, the metric variables are obtained approximately by a kind of linear perturbation analysis in the background Morgan solution which describes the motion of cylindrical null dust. The most important problem in this study is what boundary conditions for metric and matter variables should be imposed at the naked singularity. We find a boundary condition that all the metric and matter variables are everywhere finite at least up to the first order approximation. This implies that the spacetime singularity formed by this high-speed dust collapse is very similar to that formed by the null dust and thus the gravitational emission from a naked singularity formed by the cylindrical dust collapse can be gentle.

gr-qc↗