The stability of squashed Kaluza-Klein black holes is studied. The squashed Kaluza-Klein black hole looks like five dimensional black hole in the vicinity of horizon and four dimensional Minkowski spacetime with a circle at infinity. In this sense, s
quashed Kaluza-Klein black holes can be regarded as black holes in the Kaluza-Klein spacetimes. Using the symmetry of squashed Kaluza-Klein black holes, $SU(2)times U(1)simeq U(2)$, we obtain master equations for a part of the metric perturbations relevant to the stability. The analysis based on the master equations gives a strong evidence for the stability of squashed Kaluza-Klein black holes. Hence, the squashed Kaluza-Klein black holes deserve to be taken seriously as realistic black holes in the Kaluza-Klein spacetime.
We make a critical comparison between ultra-high energy particle collisions around an extremal Kerr black hole and that around an over-spinning Kerr singularity, mainly focusing on the issue of the timescale of collisions. We show that the time requi
red for two massive particles with the proton mass or two massless particles of GeV energies to collide around the Kerr black hole with Planck energy is several orders of magnitude longer than the age of the Universe for astro-physically relevant masses of black holes, whereas time required in the over-spinning case is of the order of ten million years which is much shorter than the age of the Universe. Thus from the point of view of observation of Planck scale collisions, the over-spinning Kerr geometry, subject to their occurrence, has distinct advantage over their black hole counterparts.
We examine an exact solution which represents a charged black hole in a Kaluza-Klein universe in the five-dimensional Einstein-Maxwell theory. The spacetime approaches to the five-dimensional Kasner solution that describes expanding three dimensions
and shrinking an extra dimension in the far region. The metric is continuous but not smooth at the black hole horizon. There appears a mild curvature singularity that a free-fall observer can traverse the horizon. The horizon is a squashed three-sphere with a constant size, and the metric is approximately static near the horizon.
We propose a simple method to prove non-smoothness of a black hole horizon. The existence of a $C^1$ extension across the horizon implies that there is no $C^{N + 2}$ extension across the horizon if some components of $N$-th covariant derivative of R
iemann tensor diverge at the horizon in the coordinates of the $C^1$ extension. In particular, the divergence of a component of the Riemann tensor at the horizon directly indicates the presence of a curvature singularity. By using this method, we can confirm the existence of a curvature singularity for several cases where the scalar invariants constructed from the Riemann tensor, e.g., the Ricci scalar and the Kretschmann invariant, take finite values at the horizon. As a concrete example of the application, we show that the Kaluza-Klein black holes constructed by Myers have a curvature singularity at the horizon if the spacetime dimension is higher than five.
We present here the observation of the Cygnus Superbubble (CSB) using the Solid-state slit camera (SSC) aboard the Monitor of All-sky X-ray Image. The CSB is a large diffuse structure in the Cygnus region with enhanced soft X-ray emission. By utilizi
ng the CCD spectral resolution of the SSC, we detect Fe, Ne, Mg emission lines from the CSB for the first time. The best fit model implies thin hot plasma of kT ~ 0.3 keV with depleted abundance of 0.26 +/- 0.1 solar. Joint spectrum fitting of the ROSAT PSPC data and MAXI/SSC data enables us to measure precise values of NH and temperature inside the CSB. The results show that all of the regions in the CSB have similar NH and temperature, indicating that the CSB is single unity. The energy budgets calculation suggests that 2-3 Myrs of stellar wind from the Cyg OB2 is enough to power up the CSB, whereas due to its off center position, the origin of the CSB is most likely a Hypernova.
Recently, Banados, Silk and West (BSW) showed that the total energy of two colliding test particles has no upper limit in their center of mass frame in the neighborhood of an extreme Kerr black hole, even if these particles were at rest at infinity i
n the infinite past. We call this mechanism the BSW mechanism or BSW process. The large energy of such particles would generate strong gravity, although this has not been taken into account in the BSW analysis. A similar mechanism is seen in the collision of two spherical test shells in the neighborhood of an extreme Reissner-Nordstrom black hole. In this paper, in order to draw some implications concerning the effects of gravity generated by colliding particles in the BSW process, we study a collision of two spherical dust shells, since their gravity can be exactly treated. We show that the energy of two colliding shells in the center of mass frame observable from infinity has an upper limit due to their own gravity. Our result suggests that an upper limit also exists for the total energy of colliding particles in the center of mass frame in the observable domain in the BSW process due the gravity of the particles.
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 $SU(2) times U(1) simeq U(2)$ symmetry, we can separate the variables of the e
quations 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,pm 2$ and the modes of $K = pm (J + 2)$ are stable against small perturbations from the positivity of the effective potential. As for $J = 0, K=pm 1$ 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 $J = 0, K=pm 1$ modes in general is open issue. However, we can show the stability for $J = 0, K=pm 1$ modes in maximally charged case where the effective potential are positive out side of the horizon.
We have observed the south-east (SE) limb of the Cygnus Loop with {it Suzaku}. Our spatially-resolved spectroscopic study shows that a one-$kT_mathrm{e}$ non-equilibrium ionization model represents our spectra fairly well. We find that the metal abun
dances obtained are all depleted relative to the solar values with a positional dependency along the radial direction of the Cygnus Loop. The abundances in the very edge of the limb shows about half the solar value, whereas other regions inside the Loop show about 0.2 times the solar value which has been believed as a typical value for the Cygnus Loop limb. The enhanced abundance in the very edge in the SE limb is quite similar to that found in the north-east (NE) limb of the Loop, and thus this is another evidence of abundance inhomogeneity in the limb regions of the Loop. The radio map shows a quite different feature: the NE limb is in the radio bright region while the SE limb shows almost no radio. Therefore, the metal abundance variation in the SE limb can not attribute to the non-thermal emission. The abundance inhomogeneity as well as the metal depletion down to 0.2 times the solar value still remain an open question.
