Causal Nature and Dynamics of Trapping Horizons in Black Hole Collapse

In calculations of gravitational collapse to form black holes, trapping horizons (foliated by marginally trapped surfaces) make their first appearance either within the collapsing matter or where it joins on to a vacuum exterior. Those which then move outwards with respect to the matter have been proposed for use in defining black holes, replacing the global concept of an "event horizon" which has some serious drawbacks for practical applications. We here present results from a study of the properties of both outgoing and ingoing trapping horizons, assuming strict spherical symmetry throughout. We have investigated their causal nature (i.e. whether they are spacelike, timelike or null), making contact with the Misner-Sharp- Hernandez formalism, which has often been used for numerical calculations of spherical collapse. We follow two different approaches, one using a geometrical quantity related to expansions of null geodesic congruences, and the other using the horizon velocity measured with respect to the collapsing matter. After an introduction to these concepts, we then implement them within numerical simulations of stellar collapse, revisiting pioneering calculations from the 1960s where some features of the emergence and subsequent behaviour of trapping horizons could already be seen. Our presentation here is aimed firmly at "real world" applications of interest to astrophysicists and includes the effects of pressure, which may be important for the asymptotic behaviour of the ingoing horizon.Comment: 33 pages, 11 figure

Primordial black hole formation in the early universe: critical behaviour and self-similarity

Following on after three previous papers discussing the formation of primordial black holes during the radiative era of the early universe, we present here a further investigation of the critical nature of the process involved, aimed at making contact with some of the basic underlying ideas from the literature on critical collapse. We focus on the intermediate state, which we have found appearing in cases with perturbations close to the critical limit, and examine the connection between this and the similarity solutions which play a fundamental role in the standard picture of critical collapse. We have derived a set of self-similar equations for the null-slicing form of the metric which we are using for our numerical calculations, and have then compared the results obtained by integrating these with the ones coming from our simulations for collapse of cosmological perturbations within an expanding universe. We find that the similarity solution is asymptotically approached in a region which grows to cover both the contracting matter and part of the semi-void which forms outside it. Our main interest is in the situation relevant for primordial black hole formation in the radiative era of the early universe, where the relation between the pressure $p$ and the energy density $e$ can be reasonably approximated by an expression of the form $p = we$ with $w=1/3$. However, we have also looked at other values of $w$, both because these have been considered in previous literature and also because they can be helpful for giving further insight into situations relevant for primordial black hole formation. As in our previous work, we have started our simulations with initial supra-horizon scale perturbations of a type which could have come from inflation.Comment: 23 pages, 8 figures, new abstract, submitted to Classical and Quantum Gravity. This new version of the paper has been completely rewritten with respect the previous one, with several changes and substantial additional wor

Critical Phenomena in Neutron Stars I: Linearly Unstable Nonrotating Models

We consider the evolution in full general relativity of a family of linearly unstable isolated spherical neutron stars under the effects of very small, perturbations as induced by the truncation error. Using a simple ideal-fluid equation of state we find that this system exhibits a type-I critical behaviour, thus confirming the conclusions reached by Liebling et al. [1] for rotating magnetized stars. Exploiting the relative simplicity of our system, we are able carry out a more in-depth study providing solid evidences of the criticality of this phenomenon and also to give a simple interpretation of the putative critical solution as a spherical solution with the unstable mode being the fundamental F-mode. Hence for any choice of the polytropic constant, the critical solution will distinguish the set of subcritical models migrating to the stable branch of the models of equilibrium from the set of subcritical models collapsing to a black hole. Finally, we study how the dynamics changes when the numerically perturbation is replaced by a finite-size, resolution independent velocity perturbation and show that in such cases a nearly-critical solution can be changed into either a sub or supercritical. The work reported here also lays the basis for the analysis carried in a companion paper, where the critical behaviour in the the head-on collision of two neutron stars is instead considered [2].Comment: 15 pages, 9 figure

Mirrors Improve Rabbit Natural Behavior in a Free-Range Breeding System

The aim of this research was to evaluate the possible usefulness of mirrors in improving rabbit behavior in a free-range breeding system. Three groups (each consisting of nine replicates of three animals) were compared: isolated, isolated with mirrors and separated by a wire mesh (possible visual and olfactory contacts). Rabbits allowed to have a visual and olfactory contact showed a significantly higher expression of important natural behaviors (olfactory investigation, gnawing, alertness, stretching, locomotion) compared to the isolated rabbits (with or without mirrors); while rabbits in the mirror group showed higher allo-grooming activity than those isolated and no different locomotion activity than those separated by wire mesh. Thus, mirrors seemed to be able to modify the behavioral repertoire of isolated rabbits by acting on social perception in rabbits reared in small groups in a free-range system. Nevertheless, despite it being advisable to use a combination of different indicators in order to assess the stress level of an animal, the accuracy of serum cortisol, as well as of some secondary stress markers assay, appeared to be limited in this type of breeding

BlinkML: Efficient Maximum Likelihood Estimation with Probabilistic Guarantees

The rising volume of datasets has made training machine learning (ML) models a major computational cost in the enterprise. Given the iterative nature of model and parameter tuning, many analysts use a small sample of their entire data during their initial stage of analysis to make quick decisions (e.g., what features or hyperparameters to use) and use the entire dataset only in later stages (i.e., when they have converged to a specific model). This sampling, however, is performed in an ad-hoc fashion. Most practitioners cannot precisely capture the effect of sampling on the quality of their model, and eventually on their decision-making process during the tuning phase. Moreover, without systematic support for sampling operators, many optimizations and reuse opportunities are lost. In this paper, we introduce BlinkML, a system for fast, quality-guaranteed ML training. BlinkML allows users to make error-computation tradeoffs: instead of training a model on their full data (i.e., full model), BlinkML can quickly train an approximate model with quality guarantees using a sample. The quality guarantees ensure that, with high probability, the approximate model makes the same predictions as the full model. BlinkML currently supports any ML model that relies on maximum likelihood estimation (MLE), which includes Generalized Linear Models (e.g., linear regression, logistic regression, max entropy classifier, Poisson regression) as well as PPCA (Probabilistic Principal Component Analysis). Our experiments show that BlinkML can speed up the training of large-scale ML tasks by 6.26x-629x while guaranteeing the same predictions, with 95% probability, as the full model.Comment: 22 pages, SIGMOD 201

Reducing the data-deficiency of threatened European habitats: Spatial variation of sabellariid worm reefs and associated fauna in the Sicily Channel, Mediterranean Sea

Biogenic reefs, such as those produced by tube-dwelling polychaetes of the genus Sabellaria, are valuable marine habitats which are a focus of protection according to European legislation. The achievement of this goal is potentially hindered by the lack of essential empirical data, especially in the Mediterranean Sea. This study addresses some of the current knowledge gaps by quantifying and comparing multi-scale patterns of abundance and distribution of two habitat-forming species (Sabellaria alveolata and S. spinulosa) and their associated fauna along 190 km of coast on the Italian side of the Sicily Channel. While the abundance of the two sabellariids and the total number of associated taxa did not differ at any of the examined scales (from tens of centimetres to tens-100 of kilometres), the structure (composition in terms of both the identity and the relative abundance of constituting taxa) of the associated fauna and the abundance of several taxa (the polychaetes Eulalia ornata, Syllis pulvinata, S. garciai, Nereis splendida and Arabella iricolor, and the amphipods Apolochus neapolitanus, Tethylembos viguieri and Caprella acanthifera) varied among locations established ~50e100 km apart. Syllis pulvinata also showed significant variation between sites (hundreds of metres apart), analogously to the other syllid polychaetes S. armillaris and S. gracilis, the nereidid polychaete Nereis rava, and the amphipod Gammaropsis ulrici. The largest variance of S. spinulosa, of the structure of the whole associated fauna and of 56% of taxa analysed individually occurred at the scale of replicates (metres apart), while that of the dominant bio-constructor S. alveolata and of 25% of taxa occurred at the scale of sites. The remaining 19% and the total richness of taxa showed the largest variance at the scale of locations. Present findings contribute to meet a crucial requirement of any future effective protection strategy, i.e., identifying relevant scales of variation to be included in protection schemes aiming at preserving representative samples not only of target habitats and organisms, but also of the processes driving such variabilit

Particle creation rate for dynamical black holes

We present the particle creation probability rate around a general black hole as an outcome of quantum fluctuations. Using the uncertainty principle for these fluctuation, we derive a new ultraviolet frequency cutoff for the radiation spectrum of a dynamical black hole. Using this frequency cutoff, we define the probability creation rate function for such black holes. We consider a dynamical Vaidya model, and calculate the probability creation rate for this case when its horizon is in a slowly evolving phase. Our results show that one can expect the usual Hawking radiation emission process in the case of a dynamical black hole when it has a slowly evolving horizon. Moreover, calculating the probability rate for a dynamical black hole gives a measure of when Hawking radiation can be killed off by an incoming flux of matter or radiation. Our result strictly suggests that we have to revise the Hawking radiation expectation for primordial black holes that have grown substantially since they were created in the early universe. We also infer that this frequency cut off can be a parameter that shows the primordial black hole growth at the emission moment.Comment: 10 pages, 1 figure. The paper was rewritten in more clear presentation and one more appendix is adde

Astrophysical constraints on primordial black holes in Brans-Dicke theory

We consider cosmological evolution in Brans-Dicke theory with a population of primordial black holes. Hawking radiation from the primordial black holes impacts various astrophysical processes during the evolution of the Universe. The accretion of radiation by the black holes in the radiation dominated era may be effective in imparting them a longer lifetime. We present a detailed study of how this affects various standard astrophysical constraints coming from the evaporation of primordial black holes. We analyze constraints from the present density of the Universe, the present photon spectrum, the distortion of the cosmic microwave background spectrum and also from processes affecting light element abundances after nucleosynthesis. We find that the constraints on the initial primordial black hole mass fractions are tightened with increased accretion efficiency.Comment: 15 page