arXiv subjects

Tomohiro Harada

Publications and source records attributed to Tomohiro Harada.

176 records · Page 10Linked to original sources

arXiv2000

Response of Interferometric Detectors to Scalar Gravitational Waves

We rigorously analyze the frequency response functions and antenna sensitivity patterns of three types of interferometric detectors to scalar mode of gravitational waves which is predicted to exist in the scalar-tensor theory of gravity. By a straightforward treatment, we show that the antenna sensitivity pattern of the simple Michelson interferometric detector depends strongly on the wave length $λ_{\rm SGW}$ of the scalar mode of gravitational waves if $λ_{\rm SGW}$ is comparable to the arm length of the interferometric detector. For the Delay-Line and Fabry-Perot interferometric detectors with arm length much shorter than $λ_{\rm SGW}$, however, the antenna sensitivity patterns depend weakly on $λ_{\rm SGW}$ even though $λ_{\rm SGW}$ is comparable to the effective path length of those interferometers. This agrees with the result obtained by Maggiore and Nicolis.

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arXiv2000

Naked Singularity Explosion

It is known that the gravitational collapse of a dust ball results in naked singularity formation from an initial density profile which is physically reasonable. In this paper, we show that explosive radiation is emitted during the formation process of the naked singularity.

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arXiv2000

Causal Structure of an Inflating Magnetic Monopole

We clarify the causal structure of an inflating magnetic monopole. The spacetime diagram shows explicitly that this model is free from ``graceful exit'' problem, while the monopole itself undergoes ``eternal inflation''. We also discuss general nature of inflationary spacetimes.

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arXiv2000

Gravitational Radiation from a Naked Singularity. II - Even-Parity Perturbation -

A naked singularity occurs in the generic collapse of an inhomogeneous dust ball. We study the even-parity mode of gravitational waves from a naked singularity of the Lema\^ıtre-Tolman-Bondi spacetime. The wave equations for gravitational waves are solved by numerical integration using the single null coordinate. The result implies that the metric perturbation grows when it approaches the Cauchy horizon and diverges there, although the naked singularity is not a strong source of even-parity gravitational radiation. Therefore, the Cauchy horizon in this spacetime should be unstable with respect to linear even-parity perturbations.

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arXiv1999

Distance-redshift relation in an isotropic inhomogeneous universe II: Spherically symmetric dust-shell universe

The relation between the angular diameter distance and redshift in a spherically symmetric dust-shell universe is studied. We have discovered that the relation agrees with that of an appropriate Friedmann-Lemaitre (FL) model if we set a ``homogeneous'' expansion law and a ``homogeneous'' averaged density field. This will support the averaging hypothesis that a universe looks like a FL model in spite of small-scale fluctuations of density field, if its averaged density field is homogeneous on large scales. We also study the connection of the proper mass of a shell with the mass of gravitationally bound objects. Combining this with the results of the distance-redshift relation, we discuss an impact of the local inhomogeneities on determination of the cosmological parameters through the observation of the locally inhomogeneous universe.

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arXiv1999

Gravitational Radiation from a Naked Singularity -- Odd-Parity Perturbation --

It has been suggested that a naked singularity may be a good candidate for a strong gravitational wave burster. The naked singularity occurs in the generic collapse of an inhomogeneous dust ball. We study odd-parity mode of gravitational waves from a naked singularity of the Lema\^ıtre-Tolman-Bondi space-time. The wave equation for gravitational waves are solved by numerical integration using the single null coordinate. The result is that the naked singularity is not a strong source of the odd-parity gravitational radiation although the metric perturbation grows in the central region. Therefore, the Cauchy horizon in this space-time would be marginally stable against odd-parity perturbations.

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arXiv1999

Nakedness and curvature strength of shell-focusing singularity in the spherically symmetric space-time with vanishing radial pressure

It was recently shown that the metric functions which describe a spherically symmetric space-time with vanishing radial pressure can be explicitly integrated. We investigate the nakedness and curvature strength of the shell-focusing singularity in that space-time. If the singularity is naked, the relation between the circumferential radius and the Misner-Sharp mass is given by $R\approx 2y_{0} m^β$ with $ 1/3<β\le 1$ along the first radial null geodesic from the singularity. The $β$ is closely related to the curvature strength of the naked singularity. For example, for the outgoing or ingoing null geodesic, if the strong curvature condition (SCC) by Tipler holds, then $β$ must be equal to 1. We define the ``gravity dominance condition'' (GDC) for a geodesic. If GDC is satisfied for the null geodesic, both SCC and the limiting focusing condition (LFC) by Królak hold for $β=1$ and $y_{0}\ne 1$, not SCC but only LFC holds for $1/2\le β<1$, and neither holds for $1/3<β<1/2$, for the null geodesic. On the other hand, if GDC is satisfied for the timelike geodesic $r=0$, both SCC and LFC are satisfied for the timelike geodesic, irrespective of the value of $β$. Several examples are also discussed.

gr-qc↗

arXiv1998

Final fate of the spherically symmetric collapse of a perfect fluid

The final fate of the spherically symmetric collapse of a perfect fluid which follows the $γ$-law equation of state and adiabatic condition is investigated. Full general relativistic hydrodynamics is solved numerically using a retarded time coordinate, the so-called observer time coordinate. Thanks to this coordinate, the causal structure of the resultant space-time is automatically constructed. Then, it is found that a globally naked, shell-focusing singularity can occur at the center from relativistically high-density, isentropic and time symmetric initial data if $γ\alt 1.01$ within the numerical accuracy. The result is free from the assumption of self-similarity. The upper limit of $γ$ with which a naked singularity can occur from generic initial data is consistent with the result of Ori and Piran based on the assumption of self-similarity.

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arXiv1998

Distance-redshift relation in an isotropic inhomogeneous universe: Spherically symmertic dust-shell universe

The relation between angular diameter distance and redshift in a spherically symmetric dust-shell universe is studied. This model has large inhomogeneities of matter distribution on small scales. We have discovered that the relation agrees with that of an appropriate Friedmann-Lemaitre(FL) model if we set a ``homogeneous'' expansion law and a ``homogeneous'' averaged density field. This will support the averaging hypothesis that a universe looks like a FL model in spite of small-scale fluctuations of density field, if its averaged density field is homogeneous on large scales.

gr-qc↗

arXiv1998

Naked singularity formation in the collapse of a spherical cloud of counterrotating particles

We investigate collapse of a spherical cloud of counter-rotating particles. An explicit solution is given using an elliptic integral. If the specific angular momentum $L(r)=O(r^2)$ at $r\to 0$, no central singularity occurs. With $L(r)$ like that, there is a finite region around the center that bounces. On the other hand, if the order of $L(r)$ is higher than that, a central singularity occurs. In marginally bound collapse with $L(r)=4F(r)$, a naked singularity occurs, where $F(r)$ is the Misner-Sharp mass. The solution for this case is expressed by elementary functions. For $ 4 <L/F<\infty$ at $r\to0$, there is a finite region around the center that bounces and a naked singularity occurs. For $ 0 \le L/F< 4$ at $r\to0$, there is no such region. The results suggests that rotation may play a crucial role on the final fate of collapse.

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arXiv1998

Gravitational Waves around a Naked Singularity -- Odd-Parity Perturbation of Lemaitre-Tolman-Bondi Space-Time --

The motion of a spherical dust cloud is described by the Lemaitre-Tolman-Bondi solution and is completely specified by initial values of distributions of the rest mass density and specific energy of the dust fluid. From generic initial conditions of this spherically symmetric collapse, there appears a naked singularity at the symmetric center in the course of the gravitational collapse of the dust cloud. So this might be a counter example to the cosmic censorship hypothesis. To investigate the genericity of this example, we examine the stability of the `nakedness' of this singularity against odd-parity modes of non-spherical linear perturbations for the metric, i.e., linear gravitational waves. We find that the perturbations do not diverge but are well-behaved even in the neighborhood of the central naked singularity. This means that the naked singularity formation process is marginally stable against the odd-parity modes of linear gravitational waves.

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arXiv1998

Neutron stars in scalar-tensor theories of gravity and catastrophe theory

We investigate neutron stars in scalar-tensor theories. We examine their secular stability against spherically symmetric perturbations by use of a turning point method. For some choices of the coupling function contained in the theories, the number of the stable equilibrium solutions changes and the realized equilibrium may change discontinuously as the asymptotic value of the scalar field or total baryon number is changed continuously. The behaviour of the stable equilibrium solutions is explained by fold and cusp catastrophes. Whether the cusp catastrophe appears or not depends on the choices of the coupling function. These types of the catastrophes are structurally stable. Recently discovered spontaneous scalarization, which is non-perturbative strong-field phenomenon due to the presence of the gravitational scalar field, is well described in terms of the cusp catastrophe.

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arXiv1997

Stability Analysis of Spherically Symmetric Star in Scalar-Tensor Theories of Gravity

A stability analysis of a spherically symmetric star in scalar-tensor theories of gravity is given in terms of the frequencies of quasi-normal modes. The scalar-tensor theories have a scalar field which is related to gravitation. There is an arbitrary function, the so-called coupling function, which determines the strength of the coupling between the gravitational scalar field and matter. Instability is induced by the scalar field for some ranges of the value of the first derivative of the coupling function. This instability leads to significant discrepancies with the results of binary-pulsar-timing experiments and hence, by the stability analysis, we can exclude the ranges of the first derivative of the coupling function in which the instability sets in. In this article, the constraint on the first derivative of the coupling function from the stability of relativistic stars is found. Analysis in terms of the quasi-normal mode frequencies accounts for the parameter dependence of the wave form of the scalar gravitational waves emitted from the Oppenheimer-Snyder collapse. The spontaneous scalarization is also discussed.

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arXiv1997

Scalar gravitational wave from Oppenheimer-Snyder collapse in scalar- tensor theories of gravity

Unlike general relativity, scalar-tensor theories of gravity predict scalar gravitational waves even from a spherically symmetric gravitational collapse. We solve numerically the generation and propagation of the scalar gravitational wave from a spherically symmetric and homogeneous dust collapse under the approximation that we can neglect the back reaction of the scalar wave on the space-time, and examine how the amplitude, characteristic frequency and wave form of the observed scalar gravitational wave depend on the initial radius and mass of the dust and parameters contained in the theory. In the Brans-Dicke theory, through the observation of the scalar gravitational wave, it is possible to determine the initial radius and mass and a parameter contained in the theory. In the scalar-tensor theories, it would be possible to get the information of the first derivative of the coupling function contained in the theory because the wave form of the scalar gravitational wave greatly depends on it.

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