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ABSTRACT: 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.
01/2013;
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ABSTRACT: 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.
04/2012;
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ABSTRACT: 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 $\kappa$ in a homogeneous and isotropic universe
within the region observable for the observer. We introduce additional
anisotropic perturbations with a dimensionless small parameter $\epsilon$,
whose evolution is of interest. Then, we solve perturbation equations up to
order $\kappa \epsilon$ 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.
02/2012;
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ABSTRACT: 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.
12/2011;
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ABSTRACT: We explore the Reissner-Nordstr\"{o}m 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-Nordstr\"{o}m 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.
08/2011;
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ABSTRACT: 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.
05/2011;
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ABSTRACT: It is known that the Meissner-like effect is seen in a magnetosphere without an electric current in black hole space–time: 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 space–time. 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.
Monthly Notices of the Royal Astronomical Society 04/2011; 412(4):2417 - 2432. · 4.90 Impact Factor
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ABSTRACT: 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 the 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≲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.
Phys. Rev. D. 02/2011; 83(4).
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ABSTRACT: We explore equilibrium solutions of nontopological 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 be responsible for baryon asymmetry and dark matter. Therefore, observational signals of the new solitons would give us more information on the early Universe and supersymmetric theories.
Phys. Rev. D. 11/2010; 84(10).
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ABSTRACT: 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-Nordstr\"om 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.
10/2010;
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ABSTRACT: We study the redshift drift, i.e., the time derivative of the cosmological
redshift in the Lema\^itre-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.
10/2010;
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ABSTRACT: The kinematic Sunyaev-Zel'dovich (kSZ) effect in a Lemtre-Tolman-Bondi (LTB) universe is discussed. We use the LTB universe model whose distance redshift relation coincides with the concordance ΛCDM model. The physical degrees of freedom on the last scattering surface (LSS) are fixed by using Gamow's criterion and other additional convenient conditions. We simulate the kSZ effect by solving the null geodesic equations numerically. The observational results with adiabatic inhomogeneities on the LSS seem to be difficult to explain. This difficulty would be resolved by introducing an inhomogeneity of the matter-to-photon ratio on the LSS.
Journal- Korean Physical Society 10/2010; 57:610-614. · 0.45 Impact Factor
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ABSTRACT: We study the kinematic Sunyaev-Zel'dovich (kSZ) effect in a Lem\^itre-Tolman-Bondi (LTB) universe model whose distance-redshift relation agrees with that of the concordance $\Lambda$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. Comment: 20 pages, 8 figures
08/2010;
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ABSTRACT: 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. Comment: 9 pages
07/2010;
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ABSTRACT: 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 Lema\^itre-Tolman-Bondi (LTB) solution. First, we give an LTB model whose distance-redshift relation agrees with that of the concordance $\Lambda$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 $\Lambda$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. Comment: 20 pages, 5 figures
05/2010;
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ABSTRACT: 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. Comment: 20 pages, 8 figures
08/2009;
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ABSTRACT: 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. Comment: 24 pages, 10 figures
05/2009;
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ABSTRACT: 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. Comment: 21 pages, 10 figure files, revised version, accepted for publication in Physical Review D, minor correction, erratum added
12/2008;
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ABSTRACT: 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 $p_{\rm R}=k\rho$ and tangential one $p_{\rm T}=w\rho$ 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.
12/2008;
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ABSTRACT: We construct the Lema\^itre-Tolman-Bondi (LTB) dust universe whose distance-redshift relation is equivalent to that in the concordance $\Lambda$ cold dark matter ($\Lambda$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 $\Lambda$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 $\Lambda$CDM model, even if their redshift-distance relations are equivalent to each other. Comment: 28 pages,12 figures,PTP accepted version,typo corrected
07/2008;
