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Tomohiro Harada

Publications and source records attributed to Tomohiro Harada.

At least 163 records · Page 9Linked to original sources
arXiv2003

Stability criterion for self-similar solutions with a scalar field and those with a stiff fluid in general relativity

A stability criterion is derived in general relativity for self-similar solutions with a scalar field and those with a stiff fluid, which is a perfect fluid with the equation of state $P=ρ$. A wide class of self-similar solutions turn out to be unstable against kink mode perturbation. According to the criterion, the Evans-Coleman stiff-fluid solution is unstable and cannot be a critical solution for the spherical collapse of a stiff fluid if we allow sufficiently small discontinuity in the density gradient field in the initial data sets. The self-similar scalar-field solution, which was recently found numerically by Brady {\it et al.} (2002 {\it Class. Quantum. Grav.} {\bf 19} 6359), is also unstable. Both the flat Friedmann universe with a scalar field and that with a stiff fluid suffer from kink instability at the particle horizon scale.

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arXiv2003

A Classification of Spherically Symmetric Kinematic Self-Similar Perfect-Fluid Solutions. II

We give a classification of spherically symmetric kinematic self-similar solutions. This classification is complementary to that given in a previous work by the present authors [Prog. Theor. Phys. 108, 819 (2002)]. Dust solutions of the second, zeroth and infinite kinds, perfect-fluid solutions and vacuum solutions of the first kind are treated. The kinematic self-similarity vector is either parallel or orthogonal to the fluid flow in the perfect-fluid and vacuum cases, while the `tilted' case, i.e., neither parallel nor orthogonal case, is also treated in the dust case. In the parallel case, there are no dust solutions of the second (except when the self-similarity index $α$ is 3/2), zeroth and infinite kinds, and in the orthogonal case, there are no dust solutions of the second and infinite kinds. Except in these cases, the governing equations can be integrated to give exact solutions. It is found that the dust solutions in the tilted case belong to a subclass of the Lema{\^ i}tre-Tolman-Bondi family of solutions for the marginally bound case. The flat Friedmann-Robertson-Walker (FRW) solution is the only dust solution of the second kind with $α=3/2$ in the tilted and parallel cases and of the zeroth kind in the orthogonal case. The flat, open and closed FRW solutions with $p=-μ/3$, where $p$ and $μ$ are the pressure and energy density, respectively, are the only perfect-fluid first-kind self-similar solutions in the parallel case, while a new exact solution with $p=μ$, which we call the ``singular stiff-fluid solution'', is the only such solution in the orthogonal case. The Minkowski solution is the only vacuum first-kind self-similar solution both in the parallel and orthogonal cases. Some important corrections and complements to the authors' previous work are also presented.

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arXiv2003

Nonradial oscillations of quark stars

Recently, it has been reported that a candidate for a quark star may have been observed. In this article, we pay attention to quark stars with radiation radii in the reported range. We calculate nonradial oscillations of $f$-, $w$- and $w_{\rm II}$-modes. Then, we find that the dependence of the $f$-mode quasi-normal frequency on the bag constant and stellar radiation radius is very strong and different from that of the lowest $w_{\rm II}$-mode quasi-normal frequency. Furthermore we deduce a new empirical formula between the $f$-mode frequency of gravitational waves and the parameter of the equation of state for quark stars. The observation of gravitational waves both of the $f$-mode and of the lowest $w_{\rm II}$-mode would provide a powerful probe for the equation of state of quark matter and the properties of quark stars.

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arXiv2003

Computing gravitational waves from slightly nonspherical stellar collapse to black hole: Odd-parity perturbation

Nonspherical stellar collapse to a black hole is one of the most promising gravitational wave sources for gravitational wave detectors. We numerically study gravitational waves from a slightly nonspherical stellar collapse to a black hole in linearized Einstein theory. We adopt a spherically collapsing star as the zeroth-order solution and gravitational waves are computed using perturbation theory on the spherical background. In this paper we focus on the perturbation of odd-parity modes. Using the polytropic equations of state with polytropic indices $n_p=1$ and 3, we qualitatively study gravitational waves emitted during the collapse of neutron stars and supermassive stars to black holes from a marginally stable equilibrium configuration. Since the matter perturbation profiles can be chosen arbitrarily, we provide a few types for them. For $n_p=1$, the gravitational waveforms are mainly characterized by a black hole quasinormal mode ringing, irrespective of perturbation profiles given initially. However, for $n_p=3$, the waveforms depend strongly on the initial perturbation profiles. In other words, the gravitational waveforms strongly depend on the stellar configuration and, in turn, on the ad hoc choice of the functional form of the perturbation in the case of supermassive stars.

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arXiv2003

Criticality and convergence in Newtonian collapse

We study through numerical simulation the spherical collapse of isothermal gas in Newtonian gravity. We observe a critical behavior which occurs at the threshold of gravitational instability leading to core formation. For a given initial density profile, we find a critical temperature, which is of the same order as the virial temperature of the initial configuration. For the exact critical temperature, the collapse converges to a self-similar form, the first member in Hunter's family of self-similar solutions. For a temperature close to the critical value, the collapse first approaches this critical solution. Later on, in the supercritical case, the collapse converges to another self-similar solution, which is called the Larson-Penston solution. In the subcritical case, the gas bounces and disperses to infinity. We find two scaling laws: one for the collapsed mass in the supercritical case and the other for the maximum density reached before dispersal in the subcritical case. The value of the critical exponent is measured to be $\simeq 0.11$ in the supercritical case, which agrees well with the predicted value $\simeq 0.10567$. These critical properties are quite similar to those observed in the collapse of a radiation fluid in general relativity. We study the response of the system to temperature fluctuation and discuss astrophysical implications for the insterstellar medium structure and for the star formation process. Newtonian critical behavior is important not only because it provides a simple model for general relativity but also because it is relevant for astrophysical systems such as molecular clouds.

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arXiv2002

A Classification of Spherically Symmetric Kinematic Self-Similar Perfect-Fluid Solutions

We classify all spherically symmetric spacetimes admitting a kinematic self-similar vector of the second, zeroth or infinite kind. We assume that the perfect fluid obeys either a polytropic equation of state or an equation of state of the form $p=Kμ$, where $p$ and $μ$ are the pressure and the energy density, respectively, and $K$ is a constant. We study the cases in which the kinematic self-similar vector is not only ``tilted'' but also parallel or orthogonal to the fluid flow. We find that, in contrast to Newtonian gravity, the polytropic perfect-fluid solutions compatible with the kinematic self-similarity are the Friedmann-Robertson-Walker solution and general static solutions. We find three new exact solutions which we call the dynamical solutions (A) and (B) and $Λ$-cylinder solution, respectively.

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arXiv2002

Particle velocity in noncommutative space-time

We investigate a particle velocity in the $κ$-Minkowski space-time, which is one of the realization of a noncommutative space-time. We emphasize that arrival time analyses by high-energy $γ$-rays or neutrinos, which have been considered as powerful tools to restrict the violation of Lorentz invariance, are not effective to detect space-time noncommutativity. In contrast with these examples, we point out a possibility that {\it low-energy massive particles} play an important role to detect it.

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arXiv2002

No Go Theorem for Kinematic Self-Similarity with A Polytropic Equation of State

We have investigated spherically symmetric spacetimes which contain a perfect fluid obeying the polytropic equation of state and admit a kinematic self-similar vector of the second kind which is neither parallel nor orthogonal to the fluid flow. We have assumed two kinds of polytropic equations of state and shown in general relativity that such spacetimes must be vacuum.

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arXiv2002

Physical Processes in Naked Singularity Formation

Gravitational collapse is one of the most fruitful subjects in gravitational physics. It is well known that singularity formation is inevitable in complete gravitational collapse. It was conjectured that such a singularity should be hidden by horizons if it is formed from generic initial data with physically reasonable matter fields. Many possible counterexamples to this conjecture have been proposed over the past three decades, although none of them has proved to be sufficiently generic. In these examples, there appears a singularity that is not hidden by horizons. This singularity is called a `naked singularity.' The appearance of a naked singularity represents the formation of an observable high-curvature, strong-gravity region. In this paper we review examples of naked singularity formation and recent progress in research of observable physical processes - gravitational radiation and quantum particle creation - from a forming naked singularity.

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arXiv2001

Have we already detected astrophysical symptoms of space-time noncommutativity ?

We discuss astrophysical implications of $κ$-Minkowski space-time, in which there appears space-time noncommutativity. We first derive a velocity formula for particles based on the motion of a wave packet. The result is that a massless particle moves at a constant speed as in the usual Minkowski space-time, which implies that an arrival time analysis by $γ$-rays from Markarian (Mk) 421 does not exclude space-time noncommutativity. Based on this observation, we analyze reaction processes in $κ$-Minkowski space-time which are related to the puzzling detections of extremely high-energy cosmic rays above the Greisen-Zatsepin-Kuzmin cutoff and of high-energy ($\sim$20 TeV) $γ$-rays from Mk 501.

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arXiv2001

Stability criterion for self-similar solutions with perfect fluids in general relativity

A stability criterion is derived for self-similar solutions with perfect fluids which obey the equation of state $P=kρ$ in general relativity. A wide class of self-similar solutions turn out to be unstable against the so-called kink mode. The criterion is directly related to the classification of sonic points. The criterion gives a sufficient condition for instability of the solution. For a transonic point in collapse, all primary-direction nodal-point solutions are unstable, while all secondary-direction nodal-point solutions and saddle-point ones are stable against the kink mode. The situation is reversed in expansion. Applications are the following: the expanding flat Friedmann solution for $1/3 \le k < 1$ and the collapsing one for $0< k \le 1/3$ are unstable; the static self-similar solution is unstable; nonanalytic self-similar collapse solutions are unstable; the Larson-Penston (attractor) solution is stable for this mode for $0<k\alt 0.036$, while it is unstable for $0.036\alt k $; the Evans-Coleman (critical) solution is stable for this mode for $0<k\alt 0.89$, while it is unstable for $0.89\alt k$. The last application suggests that the Evans-Coleman solution for $0.89\alt k $ is {\em not critical} because it has at least two unstable modes.

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arXiv2001

Critical phenomena in Newtonian gravity

We investigate the stability of self-similar solutions for a gravitationally collapsing isothermal sphere in Newtonian gravity by means of a normal mode analysis. It is found that the Hunter series of solutions are highly unstable, while neither the Larson-Penston solution nor the homogeneous collapse one have an analytic unstable mode. Since the homogeneous collapse solution is known to suffer the kink instability, the present result and recent numerical simulations strongly support a proposition that the Larson-Penston solution will be realized in astrophysical situations. It is also found that the Hunter (A) solution has a single unstable mode, which implies that it is a critical solution associated with some critical phenomena which are analogous to those in general relativity. The critical exponent $γ$ is calculated as $γ\simeq 0.10567$. In contrast to the general relativistic case, the order parameter will be the collapsed mass. In order to obtain a complete picture of the Newtonian critical phenomena, full numerical simulations will be needed.

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arXiv2001

Physical aspects of naked singularity explosion - How does a naked singularity explode? --

The behaviors of quantum stress tensor for the scalar field on the classical background of spherical dust collapse is studied. In the previous works diverging flux of quantum radiation was predicted. We use the exact expressions in a 2D model formulated by Barve et al. Our present results show that the back reaction does not become important during the semiclassical phase. The appearance of the naked singularity would not be affected by this quantum field radiation. To predict whether the naked singularity explosion occurs or not we need the theory of quantum gravity. We depict the generation of the diverging flux inside the collapsing star. The quantum energy is gathered around the center positively. This would be converted to the diverging flux along the Cauchy horizon. The ingoing negative flux crosses the Cauchy horizon. The intensity of it is divergent only at the central naked singularity. This diverging negative ingoing flux is balanced with the outgoing positive diverging flux which propagates along the Cauchy horizon. After the replacement of the naked singularity to the practical high density region the instantaneous diverging radiation would change to more milder one with finite duration.

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arXiv2001

Naked singularities and quantum gravity

There are known models of spherical gravitational collapse in which the collapse ends in a naked shell-focusing singularity for some initial data. If a massless scalar field is quantized on the classical background provided by such a star, it is found that the outgoing quantum flux of the scalar field diverges in the approach to the Cauchy horizon. We argue that the semiclassical approximation (i.e. quantum field theory on a classical curved background) used in these analyses ceases to be valid about one Planck time before the epoch of naked singularity formation, because by then the curvature in the central region of the star reaches Planck scale. It is shown that during the epoch in which the semiclassical approximation is valid, the total emitted energy is about one Planck unit, and is not divergent. We also argue that back reaction in this model does not become important so long as gravity can be treated classically. It follows that the further evolution of the star will be determined by quantum gravitational effects, and without invoking quantum gravity it is not possible to say whether the star radiates away on a short time scale or settles down into a black hole state.

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arXiv2001

Convergence to a self-similar solution in general relativistic gravitational collapse

We study the spherical collapse of a perfect fluid with an equation of state $P=kρ$ by full general relativistic numerical simulations. For $0<k\alt 0.036$, it has been known that there exists a general relativistic counterpart of the Larson-Penston self-similar Newtonian solution. The numerical simulations strongly suggest that, in the neighborhood of the center, generic collapse converges to this solution in an approach to a singularity and that self-similar solutions other than this solution, including a ``critical solution'' in the black hole critical behavior, are relevant only when the parameters which parametrize initial data are fine-tuned. This result is supported by a mode analysis on the pertinent self-similar solutions. Since a naked singularity forms in the general relativistic Larson-Penston solution for $0<k\alt0.0105$, this will be the most serious known counterexample against cosmic censorship. It also provides strong evidence for the self-similarity hypothesis in general relativistic gravitational collapse. The direct consequence is that critical phenomena will be observed in the collapse of isothermal gas in Newton gravity, and the critical exponent $γ$ will be given by $γ\approx 0.11$, though the order parameter cannot be the black hole mass.

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arXiv2000

Power, energy, and spectrum of a naked singularity explosion

Naked singularity occurs in the gravitational collapse of an inhomogeneous dust ball from an initial density profile which is physically reasonable. We show that explosive radiation is emitted during the formation process of the naked singularity. The energy flux is proportional to $(t_{\rm CH}-t)^{-3/2}$ for a minimally coupled massless scalar field, while is proportional to $(t_{\rm CH}-t)^{-1}$ for a conformally coupled massless scalar field, where $t_{\rm CH}-t$ is the `remained time' until the distant observer could observe the singularity if the naked singularity was formed. As a consequence, the radiated energy grows unboundedly for both scalar fields. The amount of the power and the energy depends on parameters which characterize the initial density profile but do not depend on the gravitational mass of the cloud. In particular, there is characteristic frequency $ν_{s}$ of singularity above which the divergent energy is radiated. The energy flux is dominated by particles of which the wave length is about $t_{\rm CH}-t$ at each moment. The observed total spectrum is nonthermal, i.e., $νdN/dν\sim (ν/ν_{s})^{-1}$ for $ν>ν_{s}$. If the naked singularity formation could continue until a considerable fraction of the total energy of the dust cloud is radiated, the radiated energy would reach about $10^{54}(M/M_{\odot})$ erg. The calculations are based on the geometrical optics approximation which turns out to be consistent as a rough order estimate. The analysis does not depend on whether or not the naked singularity occurs in its exact meaning. This phenomenon may provide a new candidate for a source of ultra high energy cosmic rays or a central engine of gamma ray bursts.

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