Stability criterion for self-similar solutions with a scalar field and those with a stiff fluid in general relativity

A stability criterion is derived in general relativity for self-similar solutions with a scalar field and those with a stiff fluid, which is a perfect fluid with the equation of state $P=\rho$. A wide class of self-similar solutions turn out to be unstable against kink mode perturbation. According to the criterion, the Evans-Coleman stiff-fluid solution is unstable and cannot be a critical solution for the spherical collapse of a stiff fluid if we allow sufficiently small discontinuity in the density gradient field in the initial data sets. The self-similar scalar-field solution, which was recently found numerically by Brady {\it et al.} (2002 {\it Class. Quantum. Grav.} {\bf 19} 6359), is also unstable. Both the flat Friedmann universe with a scalar field and that with a stiff fluid suffer from kink instability at the particle horizon scale.Comment: 15 pages, accepted for publication in Classical and Quantum Gravity, typos correcte

Criticality and convergence in Newtonian collapse

We study through numerical simulation the spherical collapse of isothermal gas in Newtonian gravity. We observe a critical behavior which occurs at the threshold of gravitational instability leading to core formation. For a given initial density profile, we find a critical temperature, which is of the same order as the virial temperature of the initial configuration. For the exact critical temperature, the collapse converges to a self-similar form, the first member in Hunter's family of self-similar solutions. For a temperature close to the critical value, the collapse first approaches this critical solution. Later on, in the supercritical case, the collapse converges to another self-similar solution, which is called the Larson-Penston solution. In the subcritical case, the gas bounces and disperses to infinity. We find two scaling laws: one for the collapsed mass in the supercritical case and the other for the maximum density reached before dispersal in the subcritical case. The value of the critical exponent is measured to be $\simeq 0.11$ in the supercritical case, which agrees well with the predicted value $\simeq 0.10567$. These critical properties are quite similar to those observed in the collapse of a radiation fluid in general relativity. We study the response of the system to temperature fluctuation and discuss astrophysical implications for the insterstellar medium structure and for the star formation process. Newtonian critical behavior is important not only because it provides a simple model for general relativity but also because it is relevant for astrophysical systems such as molecular clouds.Comment: 15 pages, 8 figures, accepted for publication in PRD, figures 1 and 3 at lower resolution than in journal version, typos correcte

Convergence to a self-similar solution in general relativistic gravitational collapse

We study the spherical collapse of a perfect fluid with an equation of state $P=k\rho$ by full general relativistic numerical simulations. For 0, it has been known that there exists a general relativistic counterpart of the Larson-Penston self-similar Newtonian solution. The numerical simulations strongly suggest that, in the neighborhood of the center, generic collapse converges to this solution in an approach to a singularity and that self-similar solutions other than this solution, including a ``critical solution'' in the black hole critical behavior, are relevant only when the parameters which parametrize initial data are fine-tuned. This result is supported by a mode analysis on the pertinent self-similar solutions. Since a naked singularity forms in the general relativistic Larson-Penston solution for 0, this will be the most serious known counterexample against cosmic censorship. It also provides strong evidence for the self-similarity hypothesis in general relativistic gravitational collapse. The direct consequence is that critical phenomena will be observed in the collapse of isothermal gas in Newton gravity, and the critical exponent $\gamma$ will be given by $\gamma\approx 0.11$, though the order parameter cannot be the black hole mass.Comment: 22 pages, 15 figures, accepted for publication in Physical Review D, reference added, typos correcte

Black hole evaporation in a heat bath as a nonequilibrium process and its final fate

When a black hole evaporates, there arises a net energy flow from black hole into its outside environment (heat bath). The existence of energy flow means that the thermodynamic state of the whole system, which consists of the black hole and the heat bath, is in a nonequilibrium state. Therefore, in order to study the detail of evaporation process, the nonequilibrium effects of the energy flow should be taken into account. Using the nonequilibrium thermodynamics which has been formulated recently, this paper shows the following: (1) Time scale of black hole evaporation in a heat bath becomes shorter than that of the evaporation in an empty space (a situation without heat bath), because a nonequilibrium effect of temperature difference between the black hole and heat bath appears as a strong energy extraction from the black hole by the heat bath. (2) Consequently a huge energy burst (stronger than that of the evaporation in an empty space) arises at the end of semi-classical stage of evaporation. (3) It is suggested that a remnant of Planck size remains after the quantum stage of evaporation in order to guarantee the increase of total entropy of the whole system

Black Hole Evaporation in an Expanding Universe

We calculate the quantum radiation power of black holes which are asymptotic to the Einstein-de Sitter universe at spatial and null infinities. We consider two limiting mass accretion scenarios, no accretion and significant accretion. We find that the radiation power strongly depends on not only the asymptotic condition but also the mass accretion scenario. For the no accretion case, we consider the Einstein-Straus solution, where a black hole of constant mass resides in the dust Friedmann universe. We find negative cosmological correction besides the expected redshift factor. This is given in terms of the cubic root of ratio in size of the black hole to the cosmological horizon, so that it is currently of order $10^{-5} (M/10^{6}M_{\odot})^{1/3} (t/14 {Gyr})^{-1/3}$ but could have been significant at the formation epoch of primordial black holes. Due to the cosmological effects, this black hole has not settled down to an equilibrium state. This cosmological correction may be interpreted in an analogy with the radiation from a moving mirror in a flat spacetime. For the significant accretion case, we consider the Sultana-Dyer solution, where a black hole tends to increase its mass in proportion to the cosmological scale factor. In this model, we find that the radiation power is apparently the same as the Hawking radiation from the Schwarzschild black hole of which mass is that of the growing mass at each moment. Hence, the energy loss rate decreases and tends to vanish as time proceeds. Consequently, the energy loss due to evaporation is insignificant compared to huge mass accretion onto the black hole. Based on this model, we propose a definition of quasi-equilibrium temperature for general conformal stationary black holes.Comment: Accepted for publication in Class.Quant.Grav., 18 pages and 3 figure

The Similarity Hypothesis in General Relativity

Self-similar models are important in general relativity and other fundamental theories. In this paper we shall discuss the ``similarity hypothesis'', which asserts that under a variety of physical circumstances solutions of these theories will naturally evolve to a self-similar form. We will find there is good evidence for this in the context of both spatially homogenous and inhomogeneous cosmological models, although in some cases the self-similar model is only an intermediate attractor. There are also a wide variety of situations, including critical pheneomena, in which spherically symmetric models tend towards self-similarity. However, this does not happen in all cases and it is it is important to understand the prerequisites for the conjecture.Comment: to be submitted to Gen. Rel. Gra

Bounded excursion stable gravastars and black holes

Dynamical models of prototype gravastars were constructed in order to study their stability. The models are the Visser-Wiltshire three-layer gravastars, in which an infinitely thin spherical shell of stiff fluid divides the whole spacetime into two regions, where the internal region is de Sitter, and the external is Schwarzschild. It is found that in some cases the models represent the "bounded excursion" stable gravastars, in which the thin shell is oscillating between two finite radii, while in other cases they collapse until the formation of black holes. In the phase space, the region for the ``bounded excursion" gravastars is very small in comparison to that of black holes, but not empty. Therefore, although the existence of gravastars cannot be excluded from such dynamical models, our results do indicate that, even if gravastars indeed exist, they do not exclude the existence of black holes.Comment: Revtex4, 12 figures. Version published in JCAP, 06 (2008) 02

Differential cross-section measurements of the production of four charged leptons in association with two jets using the ATLAS detector

Differential cross-sections are measured for the production of four charged leptons in association with two jets. These measurements are sensitive to final states in which the jets are produced via the strong interaction as well as to the purely-electroweak vector boson scattering process. The analysis is performed using proton-proton collision data collected by ATLAS at √s = 13 TeV and with an integrated luminosity of 140 fb−1. The data are corrected for the effects of detector inefficiency and resolution and are compared to state-of-the-art Monte Carlo event generator predictions. The differential cross-sections are used to search for anomalous weak-boson self-interactions that are induced by dimension-six and dimension-eight operators in Standard Model effective field theory