The angular momentum of the Kerr singularity should not be larger than a threshold value so that it is enclosed by an event horizon: The Kerr singularity with the angular momentum exceeding the threshold value is naked. This fact suggests that if the
cosmic censorship exists in our Universe, an over-spinning body without releasing its angular momentum cannot collapse to spacetime singularities. A simple kinematical estimate of two particles approaching each other supports this expectation and suggests the existence of a minimum size of an over-spinning body. But this does not imply that the geometry near the naked singularity cannot appear. By analyzing initial data, i.e., a snapshot of a spinning body, we see that an over-spinning body may produce a geometry close to the Kerr naked singularity around itself at least as a transient configuration.
We analytically explore the effect of falling matter on a spherically symmetric wormhole supported by a spherical shell composed of exotic matter located at its throat. The falling matter is assumed to be also a thin spherical shell concentric with t
he shell supporting the wormhole, and its self-gravity is completely taken into account. We treat these spherical thin shells by Israels formalism of metric junction. When the falling spherical shell goes through the wormhole, it necessarily collides with the shell supporting the wormhole. To treat this collision, we assume the interaction between these shells is only gravity. We show the conditions on the parameters that characterize this model in which the wormhole persists after the spherical shell goes through it.
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.
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.
We consider here a spherically symmetric but inhomogeneous universe filled with a massless scalar field. The model obeys two constraints. The first one is that the gradient of the scalar field is timelike everywhere. The second constraint is that the
radial coordinate basis vector is a unit vector field in the comoving coordinate system. We find that the resultant dynamical solutions compose a one-parameter family of self-similar models which is known as the Roberts solution. The solutions are divided into three classes. The first class consists of solutions with only one spacelike singularity in the synchronous-comoving chart. The second class consists of solutions with two singularities which are null and spacelike, respectively. The third class consists of solutions with two spacelike singularities which correspond to the big bang and big crunch, respectively. We see that, in the first case, a comoving volume exponentially expands as in an inflationary period; the fluid elements are accelerated outwards form the symmetry center, even though the strong energy condition is satisfied. This behavior is very different from that observed in the homogeneous and isotropic universe in which the fluid elements would move outwards with deceleration, if the strong energy conditions are satisfied. We are thus able to achieve the accelerated expansion of the universe for the models considered here, without a need to violate the energy conditions. The cosmological features of the models are examined in some detail.
We study the foliation of a $D$-dimensional spherically symmetric black-hole spacetime with $Dge 5$ by two kinds of one-parameter family of maximal hypersurfaces: a reflection-symmetric foliation with respect to the wormhole slot and a stationary fol
iation 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.
We investigate an infinitesimally thin cylindrical shell composed of counter-rotating dust particles. This system was studied by Apostolatos and Thorne in terms of the C-energy for a bounded domain. In this paper, we reanalyze this system by evaluati
ng the C-energy on the future null infinity. We find that some class of momentarily static and radiation-free initial data does not settle down into static, equilibrium configurations, and otherwise infinite amount of the gravitational radiation is emitted to the future null infinity. Our result implies the existence of an instability in this system. In the framework of the Newtonian gravity, a cylindrical shell composed of counter-rotating dust particles can be in a steady state with oscillation by the gravitational attraction and centrifugal repulsion, and hence a static state is not necessarily realized as a final state. By contrast, in the framework of general relativity, the steady oscillating state will be impossible since the gravitational radiation will carry the energy of the oscillation to infinity. Thus, this instability has no counterpart in the Newtonian gravity.
