Even for the observed luminosity distance DL(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 DL(z) for 1 < ∼ z < 1.7 may confirm or refute this possibility.

Thermodynamic stability of black holes, described by the Rényi formula as equilibrium compatible entropy function, is investigated. It is shown that within this approach, asymptotically flat, Schwarzschild black holes can be in stable equilibrium with thermal radiation at a fixed temperature. This implies that the canonical ensemble exists just like in anti-de Sitter space, and nonextensive effects can stabilize the black holes in a very similar way as it is done by the gravitational potential of an anti-de Sitter space. Furthermore, it is also shown that a Hawking-Page-like black hole phase transition occurs at a critical temperature which depends on the q-parameter of the Rényi formula.

We show that the S 1 -rotating black rings can be superposed by the solution generating technique.We analyze the black di-ring solution for the simplest case of multiple rings. There exists an equilibrium black di-ring where the conical singularities are cured by the suitable choice of physical parameters. Also there are infinite numbers of black di-rings with the same mass and angular momentum. These di-rings can have two different continuous limits of single black rings. Therefore we can transform the fat black ring to the thin ring with the same mass and angular momentum by way of the di-ring solutions.

We investigate the collapse of a spherical cloud of counter-rotating particles. An explicit solution for metric functions is given using an elliptic integral. If the specific angular momentum L(r) = O(r 2 ) at r → 0, no central singularity occurs. With L(r) like that, there is a finite region around the center that bounces. On the other hand, if the order of L(r) is higher than that, a central singularity occurs. In marginally bound collapse with L(r) = 4F (r), a naked singularity occurs, where F (r) is the Misner-Sharp mass. The solution for this case is expressed by elementary functions. For 4 < L/F < ∞ at r → 0, there is a finite region around the center that bounces and a naked singularity occurs. For 0 ≤ L/F < 4 at r → 0, there is no such region. The results suggest that rotation may play a crucial role on the final fate of collapse.PACS numbers: 04.20. Dw, 04.20.Jb, The final fate of gravitational collapse is an important problem of relativistic astrophysics and gravitational physics. A black hole is usually considered as the final state of generic gravitational collapse, and its properties have been investigated [1]. In particular, a cosmic censorship hypothesis [2] is a critical assumption of theorems on black holes. For example, singularity theorems [1] with this hypothesis predict the existence of black holes. Therefore, it is very important to know the behavior of collapse of various kinds of matter in order to obtain the overall picture about the general nature of gravitational collapse. For example, it is well known that spherically symmetric dust collapse from generic initial data results in a naked singularity [3][4][5][6]. This system is rather tractable because of the existence of an explicit expression, i.e., the Lemaître-Tolman-Bondi (LTB) solution. The assumption of dust matter will be considered to be rather unrealistic. In fact, it is obvious that the effect of pressure should be taken into account because the formation of a naked singularity in the LTB solution results in blow up of the energy density. Introducing tangential pressure alone does not lose the merit because this system is also given by an explicit integral [7]. Singh and Witten [8] considered tangential pressure proportional to the energy density and found that in collapse from rest there is a finite region near the center which expands outwards if the tangential pressure is positive. A spherical cloud of counter-rotating particles is an example with tangential pressure but no radial pressure. This system was considered by Datta [9], Bondi [10] and Evans [11]. However, the causal structure of the space-time was not investigated and this is one of our interests.Using comoving coordinates, a spherically symmetric space-time describing a matter with no radial pressure is given bywhere h = h(r, R) gives a relation between the energy density ǫ(r, t) ≡ −T

We report on the first joint search for gravitational waves by the TAMA and LIGO collaborations. We looked for millisecond-duration unmodeled gravitational-wave bursts in 473 hr of coincident data collected during early 2003. No candidate signals were found. We set an upper limit of 0.12 events per day on the rate of detectable gravitational-wave bursts, at 90% confidence level. (2005) 122004-3 simulations, we estimate that our detector network was sensitive to bursts with root-sum-square strain amplitude above approximately 1-3 10 ÿ19 Hz ÿ1=2 in the frequency band 700-2000 Hz. We describe the details of this collaborative search, with particular emphasis on its advantages and disadvantages compared to searches by LIGO and TAMA separately using the same data. Benefits include a lower background and longer observation time, at some cost in sensitivity and bandwidth. We also demonstrate techniques for performing coincidence searches with a heterogeneous network of detectors with different noise spectra and orientations. These techniques include using coordinated software signal injections to estimate the network sensitivity, and tuning the analysis to maximize the sensitivity and the livetime, subject to constraints on the background.