arXiv subjects

Hideki Maeda

Publications and source records attributed to Hideki Maeda.

At least 73 records · Page 4Linked to original sources

arXiv2008

Self-similar cosmological solutions with dark energy. II: black holes, naked singularities and wormholes

We use a combination of numerical and analytical methods, exploiting the equations derived in a preceding paper, to classify all spherically symmetric self-similar solutions which are asymptotically Friedmann at large distances and contain a perfect fluid with equation of state $p=(γ-1)μ$ with $0<γ<2/3$. The expansion of the Friedmann universe is accelerated in this case. We find a one-parameter family of self-similar solutions representing a black hole embedded in a Friedmann background. This suggests that, in contrast to the positive pressure case, black holes in a universe with dark energy can grow as fast as the Hubble horizon if they are not too large. There are also self-similar solutions which contain a central naked singularity with negative mass and solutions which represent a Friedmann universe connected to either another Friedmann universe or some other cosmological model. The latter are interpreted as self-similar cosmological white hole or wormhole solutions. The throats of these wormholes are defined as two-dimensional spheres with minimal area on a spacelike hypersurface and they are all non-traversable because of the absence of a past null infinity.

gr-qc↗

arXiv2007

Black Hole Evaporation in an Expanding Universe

We calculate the quantum radiation power of black holes which are asymptotic to the Einstein-de Sitter universe at spatial and null infinities. We consider two limiting mass accretion scenarios, no accretion and significant accretion. We find that the radiation power strongly depends on not only the asymptotic condition but also the mass accretion scenario. For the no accretion case, we consider the Einstein-Straus solution, where a black hole of constant mass resides in the dust Friedmann universe. We find negative cosmological correction besides the expected redshift factor. This is given in terms of the cubic root of ratio in size of the black hole to the cosmological horizon, so that it is currently of order $10^{-5} (M/10^{6}M_{\odot})^{1/3} (t/14 {Gyr})^{-1/3}$ but could have been significant at the formation epoch of primordial black holes. Due to the cosmological effects, this black hole has not settled down to an equilibrium state. This cosmological correction may be interpreted in an analogy with the radiation from a moving mirror in a flat spacetime. For the significant accretion case, we consider the Sultana-Dyer solution, where a black hole tends to increase its mass in proportion to the cosmological scale factor. In this model, we find that the radiation power is apparently the same as the Hawking radiation from the Schwarzschild black hole of which mass is that of the growing mass at each moment. Hence, the energy loss rate decreases and tends to vanish as time proceeds. Consequently, the energy loss due to evaporation is insignificant compared to huge mass accretion onto the black hole. Based on this model, we propose a definition of quasi-equilibrium temperature for general conformal stationary black holes.

gr-qc↗

arXiv2007

Origin of matter out of pure curvature

We propose a mechanism for origin of matter in the universe in the framework of Einstein-Gauss-Bonnet gravity in higher dimensions. The recently discovered new static black hole solution by the authors \cite{md2006} with the Kaluza-Klein split up of spacetime as a product of the usual ${\ma M}^4$ with a space of negative constant curvature is indeed a pure gravitational creation of a black hole which is also endowed with a Maxwell-like {\it gravitational charge} in four-dimensional vacuum spacetime. Further it could be envisioned as being formed from anti-de Sitter spacetime by collapse of radially inflowing charged null dust. It thus establishes the remarkable reciprocity between matter and gravity - as matter produces gravity (curvature), gravity too produces matter.

hep-th↗

arXiv2007

Global structure and physical interpretation of the Fonarev solution for a scalar field with exponential potential

We discuss the physical interpretation of a dynamical and inhomogeneous spherically symmetric solution obtained by Fonarev for a scalar field with an exponential potential. There is a single parameter $w$ in the solution which can be set to $\pm1$ if it is non-zero, in addition to the steepness parameter $λ$ in the potential. The spacetime is conformally static and asymptotically flat Friedmann-Robertson-Walker spacetime. The solution reduces to the Friedmann-Robertson-Walker solution for $w=0$. There are two curvature singularities, of which one is a timelike central singularity and the other is a big-bang or big-crunch type singularity. Depending on the parameters, the spacetime can possess a future outer trapping horizon in the collapsing case. Then the solution represents a dynamical black hole in the sense of Hayward although there is a locally naked singularity at the center and no black-hole event horizon. This demonstrates a weak point of the local definition of a black hole in terms of a trapping horizon.

gr-qc↗

arXiv2007

Matter without matter: novel Kaluza-Klein spacetime in Einstein-Gauss-Bonnet gravity

We consider Einstein-Gauss-Bonnet gravity in $n(\ge 6)$-dimensional Kaluza-Klein spacetime ${\ma M}^{4} \times {\ma K}^{n-4}$, where ${\ma K}^{n-4}$ is the Einstein space with negative curvature. In the case where ${\ma K}^{n-4}$ is the space of negative constant curvature, we have recently obtained a new static black-hole solution (Phys. Rev. D {\bf 74}, 021501(R) (2006), hep-th/0605031) which is a pure gravitational creation including Maxwell field in four-dimensional vacuum spacetime. The solution has been generalized to make it radially radiate null radiation representing gravitational creation of charged null dust. The same class of solutions though exists in spacetime ${\ma M}^{d} \times {\ma K}^{n-d}$ for $d=3,4$, however the gravitational creation of the Maxwell field is achieved only for $d=4$. Also, Gauss-Bonnet effect could be brought down to ${\ma M}^d$ only for $d=4$. Further some new exact solutions are obtained including its analogue in Taub-NUT spacetime on ${\ma M}^4$ for $d=4$.

hep-th↗

arXiv2006

Non-existence of self-similar solutions containing a black hole in a universe with a stiff fluid or scalar field or quintessence

We consider the possible existence of self-similar solutions containing black holes in a Friedmann background with a stiff fluid or a scalar field. We carefully study the relationship between the self-similar equations in these two cases and emphasize the crucial role of the similarity horizon. We show that there is no self-similar black hole solution surrounded by an exact or asymptotically flat Friedmann background containing a massless scalar field. This result also applies for a scalar field with a potential, providing the universe is decelerating. However, if there is a potential and the universe is accelerating (as in the quintessence scenario), the result only applies for an exact Friedmann background. This extends the result previously found in the stiff fluid case and strongly suggests that accretion onto primordial black holes is ineffective even during scalar field domination. It also contradicts recent claims that such black holes can grow appreciably by accreting quintessence. Appreciable growth might be possible with very special matter fields but this requires {\it ad hoc} and probably unphysical conditions.

astro-ph↗

arXiv2006

Kaluza-Klein black hole with negatively curved extra dimensions in string generated gravity models

We obtain a new exact black-hole solution in Einstein-Gauss-Bonnet gravity with a cosmological constant which bears a specific relation to the Gauss-Bonnet coupling constant. The spacetime is a product of the usual 4-dimensional manifold with a $(n-4)$-dimensional space of constant negative curvature, i.e., its topology is locally ${\ma M}^n \approx {\ma M}^4 \times {\ma H}^{n-4}$. The solution has two parameters and asymptotically approximates to the field of a charged black hole in anti-de Sitter spacetime. The most interesting and remarkable feature is that the Gauss-Bonnet term acts like a Maxwell source for large $r$ while at the other end it regularizes the metric and weakens the central singularity.

hep-th↗

arXiv2006

Final fate of spherically symmetric gravitational collapse of a dust cloud in Einstein-Gauss-Bonnet gravity

We give a model of the higher-dimensional spherically symmetric gravitational collapse of a dust cloud in Einstein-Gauss-Bonnet gravity. A simple formulation of the basic equations is given for the spacetime $M \approx M^2 \times K^{n-2}$ with a perfect fluid and a cosmological constant. This is a generalization of the Misner-Sharp formalism of the four-dimensional spherically symmetric spacetime with a perfect fluid in general relativity. The whole picture and the final fate of the gravitational collapse of a dust cloud differ greatly between the cases with $n=5$ and $n \ge 6$. There are two families of solutions, which we call plus-branch and the minus-branch solutions. Bounce inevitably occurs in the plus-branch solution for $n \ge 6$, and consequently singularities cannot be formed. Since there is no trapped surface in the plus-branch solution, the singularity formed in the case of $n=5$ must be naked. In the minus-branch solution, naked singularities are massless for $n \ge 6$, while massive naked singularities are possible for $n=5$. In the homogeneous collapse represented by the flat Friedmann-Robertson-Walker solution, the singularity formed is spacelike for $n \ge 6$, while it is ingoing-null for $n=5$. In the inhomogeneous collapse with smooth initial data, the strong cosmic censorship hypothesis holds for $n \ge 10$ and for $n=9$ depending on the parameters in the initial data, while a naked singularity is always formed for $5 \le n \le 8$. These naked singularities can be globally naked when the initial surface radius of the dust cloud is fine-tuned, and then the weak cosmic censorship hypothesis is violated.

gr-qc↗

arXiv2006

Effects of Lovelock terms on the final fate of gravitational collapse: analysis in dimensionally continued gravity

We find an exact solution in dimensionally continued gravity in arbitrary dimensions which describes the gravitational collapse of a null dust fluid. Considering the situation that a null dust fluid injects into the initially anti-de Sitter spacetime, we show that a naked singularity can be formed. In even dimensions, a massless ingoing null naked singularity emerges. In odd dimensions, meanwhile, a massive timelike naked singularity forms. These naked singularities can be globally naked if the ingoing null dust fluid is switched off at a finite time; the resulting spacetime is static and asymptotically anti-de Sitter spacetime. The curvature strength of the massive timelike naked singularity in odd dimensions is independent of the spacetime dimensions or the power of the mass function. This is a characteristic feature in Lovelock gravity.

gr-qc↗

arXiv2006

Effects of Gauss-Bonnet term on the final fate of gravitational collapse

We obtain a general spherically symmetric solution of a null dust fluid in $n (\geq 4)$-dimensions in Gauss-Bonnet gravity. This solution is a generalization of the $n$-dimensional Vaidya-(anti)de Sitter solution in general relativity. For $n=4$, the Gauss-Bonnet term in the action does not contribute to the field equations, so that the solution coincides with the Vaidya-(anti)de Sitter solution. Using the solution for $n \ge 5$ with a specific form of the mass function, we present a model for a gravitational collapse in which a null dust fluid radially injects into an initially flat and empty region. It is found that a naked singularity is inevitably formed and its properties are quite different between $n=5$ and $n \ge 6$. In the $n \ge 6$ case, a massless ingoing null naked singularity is formed, while in the $n=5$ case, a massive timelike naked singularity is formed, which does not appear in the general relativistic case. The strength of the naked singularities is weaker than that in the general relativistic case. These naked singularities can be globally naked when the null dust fluid is turned off after a finite time and the field settles into the empty asymptotically flat spacetime.

gr-qc↗

arXiv2005

Spacetime structure of static solutions in Gauss-Bonnet gravity: charged case

We have studied spacetime structures of static solutions in the $n$-dimensional Einstein-Gauss-Bonnet-Maxwell-$Λ$ system. Especially we focus on effects of the Maxwell charge. We assume that the Gauss-Bonnet coefficient $α$ is non-negative and $4{\tilde α}/\ell^2\leq 1$ in order to define the relevant vacuum state. Solutions have the $(n-2)$-dimensional Euclidean sub-manifold whose curvature is $k=1,~0$, or -1. In Gauss-Bonnet gravity, solutions are classified into plus and minus branches. In the plus branch all solutions have the same asymptotic structure as those in general relativity with a negative cosmological constant. The charge affects a central region of the spacetime. A branch singularity appears at the finite radius $r=r_b>0$ for any mass parameter. There the Kretschmann invariant behaves as $O((r-r_b)^{-3})$, which is much milder than divergent behavior of the central singularity in general relativity $O(r^{-4(n-2)})$. Some charged black hole solutions have no inner horizon in Gauss-Bonnet gravity. Although there is a maximum mass for black hole solutions in the plus branch for $k=-1$ in the neutral case, no such maximum exists in the charged case. The solutions in the plus branch with $k=-1$ and $n\geq6$ have an "inner" black hole, and inner and the "outer" black hole horizons. Considering the evolution of black holes, we briefly discuss a classical discontinuous transition from one black hole spacetime to another.

hep-th↗

arXiv2005

Spacetime structure of static solutions in Gauss-Bonnet gravity: neutral case

We study the spacetime structures of the static solutions in the $n$-dimensional Einstein-Gauss-Bonnet-$Λ$ system systematically. We assume the Gauss-Bonnet coefficient $α$ is non-negative. The solutions have the $(n-2)$-dimensional Euclidean sub-manifold, which is the Einstein manifold with the curvature $k=1,~0$ and -1. We also assume $4{\tilde α}/\ell^2\leq 1$, where $\ell$ is the curvature radius, in order for the sourceless solution (M=0) to be defined. The general solutions are classified into plus and minus branches. The structures of the center, horizons, infinity and the singular point depend on the parameters $α$, $\ell^2$, $k$, $M$ and branches complicatedly so that a variety of global structures for the solutions are found. In the plus branch, all the solutions have the same asymptotic structure at infinity as that in general relativity with a negative cosmological constant. For the negative mass parameter, a new type of singularity called the branch singularity appears at non-zero finite radius $r=r_b>0$. The divergent behavior around the singularity in Gauss-Bonnet gravity is milder than that around the central singularity in general relativity. In the $k=1,~0$ cases the plus-branch solutions do not have any horizon. In the $k=-1$ case, the radius of the horizon is restricted as $r_h<\sqrt{2\tildeα}$ ($r_h>\sqrt{2\tildeα}$) in the plus (minus) branch. There is also the extreme black hole solution with positive mass in spite of the lack of electromagnetic charge. We briefly discuss the effect of the Gauss-Bonnet corrections on black hole formation in a collider and the possibility of the violation of third law of the black hole thermodynamics.

hep-th↗

arXiv2005

Novel Cauchy-horizon instability

The evolution of weak discontinuity is investigated on horizons in the $n$-dimensional static solutions in the Einstein-Maxwell-scalar-$Λ$ system, including the Reissner-Nordström-(anti) de Sitter black hole. The analysis is essentially local and nonlinear. We find that the Cauchy horizon is unstable, whereas both the black-hole event horizon and the cosmological event horizon are stable. This new instability, the so-called kink instability, of the Cauchy horizon is completely different from the well-known ``infinite-blueshift'' instability. The kink instability makes the analytic continuation beyond the Cauchy horizon unstable.

gr-qc↗

arXiv2005

Quantum Effect and Curvature Strength of Naked Singularities

There are many solutions to the Einstein field equations that demonstrate naked singularity (NS) formation after regular evolution. It is possible, however, that such a quantum effect as particle creation prevents NSs from forming. We investigate the relation between the curvature strength and the quantum effects of NSs in a very wide class of spherical dust collapse. Through a perturbative calculation, we find that if the NS is very strong, the quantum particle creation diverges as the Cauchy horizon is approached, while if the NS is very weak, the creation should be finite. In the context of cosmic censorship, strong NSs will be subjected to the backreaction of quantum effects and may disappear or be hidden behind horizons, while weak NSs will not.

gr-qc↗

arXiv2004

Kink instability and stabilization of the Friedmann universe with scalar fields

The evolution of weak discontinuity is investigated in the flat FRW universe with a single scalar field and with multiple scalar fields. We consider both massless scalar fields and scalar fields with exponential potentials. Then we find that a new type of instability, i.e. kink instability develops in the flat FRW universe with massless scalar fields. The kink instability develops with scalar fields with considerably steep exponential potentials, while less steep exponential potentials do not suffer from kink instability. In particular, assisted inflation with multiple scalar fields does not suffer from kink instability. The stability of general spherically symmetric self-similar solutions is also discussed.

gr-qc↗

arXiv2004

Kinematic self-similar solutions in general relativity

The gravitational interaction is scale-free in both Newtonian gravity and general theory of relativity. The concept of self-similarity arises from this nature. Self-similar solutions reproduce themselves as the scale changes. This property results in great simplification of the governing partial differential equations. In addition, some self-similar solutions can describe the asymptotic behaviors of more general solutions. Newtonian gravity contains only one dimensional constant, the gravitational constant, while the general relativity contains another dimensional constant, the speed of light, besides the gravitational constant. Due to this crucial difference, incomplete similarity can be more interesting in general relativity than in Newtonian gravity. Kinematic self-similarity has been defined and studied as an example of incomplete similarity in general relativity, in an effort to pursue a wider application of self-similarity in general relativity. We review the mathematical and physical aspects of kinematic self-similar solutions in general relativity.

gr-qc↗

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.

gr-qc↗

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.

gr-qc↗