Hideo Iguchi

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 (2002), 819]. 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 Lemaître-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.

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 λ 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 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 the Λ-cylinder solution.

Even for the observed luminosity distance D_L(z), which suggests the existence of dark energy, we show that an inhomogeneous dust universe solution without dark energy is possible in general. Future observation of D_L(z) for 1 ≲z < 1.7 may confirm or refute this possibility.

We investigate 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 assume two kinds of polytropic equations of state and show in general relativity that such spacetimes must be a vacuum, which is in contrast with the result in the Newtonian case.

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.

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.

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 the 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.