We study the instability of charged anti-de Sitter black holes in four or higher-dimension under fragmentation. The instability of fragmentation breaks the black hole into two black holes. We have found that the region near extremal or massive black holes become unstable under fragmentation. These regions depend not only on the mass and charge of initial black hole but also those of the fragmented one. The instability in higher-dimension is qualitatively similar to that of four-dimension. The detailed instabilities are numerically investigated.

A Fubini instanton is a bounce solution which describes the decay of a vacuum state located at the top of the tachyonic potential via the tunneling without a barrier. We investigate various types of Fubini instantons of a self-gravitating scalar field under a tachyonic quartic potential. With gravity taken into account, we show there exist various types of unexpected solutions including oscillating bounce solutions. We present numerically oscillating Fubini bounce solutions in anti-de Sitter and de Sitter spaces. We construct the parametric phase diagrams of the solutions, which is the extension of our previous work. Of particular significance is that there always exist solutions in all parameter spaces in anti-de Sitter space. The regions are divided depending on the number of oscillations. On the other hand, de Sitter space allows solutions with codimension-one in parameter spaces. We numerically evaluate semiclassical exponents which give the finite tunneling probabilities.

We study Fubini instantons of a self-gravitating scalar field. The Fubini instanton describes the decay of a vacuum state under tunneling instead of rolling in the presence of a tachyonic potential. The tunneling occurs from the maximum of the potential, which is a vacuum state, to any arbitrary state, belonging to the tunneling without any barrier. We consider two different types of the tachyonic potential. One has only a quartic term. The other has both the quartic and quadratic terms. We show that, there exist several kinds of new O(4)-symmetric Fubini instanton solution, which are possible only if gravity is taken into account. One type of them has the structure with Z 2 symmetry. This type of the solution is possible only in the de Sitter background. We discuss on the interpretation of the solutions with Z 2 symmetry.

We investigate the time-dependent entanglement entropy in the AdS space with a dS boundary which represents an expanding spacetime. On this time-dependent spacetime, we show that the Ryu–Takayanagi formula, which is usually valid in the static spacetime, provides a leading contribution to the time-dependent entanglement entropy. We also study the leading behavior of the entanglement entropy between the visible and invisible universes in an inflationary cosmology. The result shows that the quantum entanglement monotonically decreases with time and finally saturates a constant value inversely proportional to the square of the Hubble constant. Intriguingly, we find that even in the expanding universes, the time-dependent entanglement entropy still satisfies the area law determined by the physical distance.

We study a hairy black hole solution in the dilatonic Einstein-Gauss-Bonnet theory of gravitation, in which the Gauss-Bonnet term is nonminimally coupled to the dilaton field. Hairy black holes with spherical symmetry seem to be easily constructed with a positive Gauss-Bonnet (GB) coefficient α within the coupling function, f (φ) = αe γφ , in an asymptotically flat spacetime, i.e., no-hair theorem seems to be easily evaded in this theory. Therefore, it is natural to ask whether this construction can be expanded into the case with the negative coefficient α. In this paper, we numerically present the dilaton black hole solutions with a negative α, and we analyze the properties of GB term through the aspects of the black hole mass. We construct the new integral constraint allowing the existence of the hairy solutions with the negative α. Through this procedure, we expand the evasion of the no-hair theorem for hairy black hole solutions.