We study the evolution of linear density perturbations in a large spherical void universe which accounts for the acceleration of the cosmic volume expansion without introducing dark energy. The density contrast of this void is not large within the light cone of an observer at the center of the void. Therefore, we describe the void structure as a perturbation with a dimensionless small parameter κ in a homogeneous and isotropic universe within the region observable for the observer. We introduce additional anisotropic perturbations with a dimensionless small parameter ǫ, whose evolution is of interest. Then, we solve perturbation equations up to order κǫ by applying secondorder perturbation theory in the homogeneous and isotropic universe model. By this method, we can know the evolution of anisotropic perturbations affected by the void structure. We show that the growth rate of the anisotropic density perturbations in the large void universe is significantly different from that in the homogeneous and isotropic universe. This result suggests that the observation of the distribution of galaxies may give a strong constraint on the large void universe model. *

We study gravitational and electromagnetic perturbation around the squashed Kaluza-Klein black holes with charge. Since the black hole spacetime focused on this paper have SU (2) × U (1) ≃ U (2) symmetry, we can separate the variables of the equations for perturbations by using Wigner function D J KM which is the irreducible representation of the symmetry. In this paper, we mainly treat J = 0 modes which preserve SU (2) symmetry. We derive the master equations for the J = 0 modes and discuss the stability of these modes. We show that the modes of J = 0 and K = 0, ±2 and the modes of K = ±(J + 2) are stable against small perturbations from the positivity of the effective potential. As for J = 0, K = ±1 modes, since there are domains where the effective potential is negative except for maximally charged case, it is hard to show the stability of these modes in general. To show stability for J = 0, K = ±1 modes in general is open issue. However, we can show the stability for J = 0, K = ±1 modes in maximally charged case where the effective potential are positive out side of the horizon.call the higher-dimensional black holes on the spacetime with compact extra dimensions Kaluza-Klein black holes. In general, it is difficult to construct exact solutions describing Kaluza-Klein black holes because of the less symmetry than the asymptotically flat case.However, if we consider the spacetime with twisted extra-dimensions, we can construct such exact solutions, i.e. squashed Kaluza-Klein (SqKK) black holes [27,28] in the class of cohomogeneity-one symmetry. The topology of the horizon of this SqKK black holes is S 3 , while it looks like four-dimensional black holes with a circle as an internal space in the asymptotic region.Recently, much effort has been devoted to reveal the properties of squashed Kaluza-Klein black holes. In [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47] generalizations of SqKK black holes are studied. Several aspects of SqKK black holes are also discussed, e.g. thermodynamics [48-50], Hawking radiation [51-53], gravitational collapse [54], behavior of Klein-Gordon equation [55], stabil-

We study the two-point correlation function of density perturbations in a spherically symmetric void universe model which does not employ the Copernican principle. First we solve perturbation equations in the inhomogeneous universe model and obtain density fluctuations by using a method of non-linear perturbation theory which was adopted in our previous paper. From the obtained solutions, we calculate the two-point correlation function and show that it has a local anisotropy at the off-center position differently from those in homogeneous and isotropic universes. This anisotropy is caused by the tidal force in the off-center region of the spherical void. Since no tidal force exists in homogeneous and isotropic universes, we may test the inhomogeneous universe by observing statistical distortion of the two-point galaxy correlation function. *

Recently, the present authors studied perturbations in the Lemaître-Tolman-Bondi cosmological model by applying the second-order perturbation theory in the dust Friedmann-Lemaître-Robertson-Walker universe model. Before this work, the same subject was studied in some papers by analyzing linear perturbations in the Lemaître-Tolman-Bondi cosmological model under the assumption proposed by Clarkson, Clifton and February, in which two of perturbation variables are negligible. However, it is a non-trivial issue in what situation the Clarkson-Clifton-February assumption is valid. In this paper, we investigate differences between these two approaches. It is shown that, in general, these two approaches are not compatible with each other. That is, in our perturbative procedure, the Clarkson-Clifton-February assumption is not valid at the order of our interest. *

Usually the effects of isotropic inhomogeneities are not seriously taken into account in the determination of the cosmological parameters because of Copernican principle whose statement is that we do not live in the privileged domain in the universe. But Copernican principle has not been observationally confirmed yet in sufficient accuracy, and there is the possibility that there are non-negligible large-scale isotropic inhomogeneities in our universe. In this paper, we study the effects of the isotropic inhomogeneities on the determination of the cosmological parameters and show the probability that non-Copernican isotropic inhomogeneities mislead us into believing, for example, the phantom energy of the equation of state, p = wρ with w < −1, even in case that w = −1 is the true value.