Gravitational Collapse of a Radiating Shell

We study the collapse of a self-gravitating and radiating shell. Matter constituting the shell is quantized and the construction is viewed as a semiclassical model of possible black hole formation. It is shown that the shell internal degrees of freedom are excited by the quantum non-adiabaticity of the collapse and, consequently, on coupling them to a massless scalar field, the collapsing matter emits a burst of coherent (thermal) radiation.Comment: LaTeX, 34 pages, 21 EPS figures include

Generalized cohesiveness

We study some generalized notions of cohesiveness which arise naturally in connection with effective versions of Ramsey's Theorem. An infinite set $A$ of natural numbers is $n$--cohesive (respectively, $n$--r--cohesive) if $A$ is almost homogeneous for every computably enumerable (respectively, computable) $2$--coloring of the $n$--element sets of natural numbers. (Thus the $1$--cohesive and $1$--r--cohesive sets coincide with the cohesive and r--cohesive sets, respectively.) We consider the degrees of unsolvability and arithmetical definability levels of $n$--cohesive and $n$--r--cohesive sets. For example, we show that for all $n \ge 2$, there exists a $\Delta^0_{n+1}$ $n$--cohesive set. We improve this result for $n = 2$ by showing that there is a $\Pi^0_2$ $2$--cohesive set. We show that the $n$--cohesive and $n$--r--cohesive degrees together form a linear, non--collapsing hierarchy of degrees for $n \geq 2$. In addition, for $n \geq 2$ we characterize the jumps of $n$--cohesive degrees as exactly the degrees {\bf \geq \jump{0}{(n+1)}} and show that each $n$--r--cohesive degree has jump {\bf > \jump{0}{(n)}}

Entanglement and Nonunitary Evolution

We consider a collapsing relativistic spherical shell for a free quantum field. Once the center of the wavefunction of the shell passes a certain radius R, the degrees of freedom inside R are traced over. We show that an observer outside this region will determine that the evolution of the system is nonunitary. We argue that this phenomenon is generic to entangled systems, and discuss a possible relation to black hole physics.Comment: 14 pages, 1 figure; Added a clarification regarding the relation with black hole physic

Possible effects of tilt order on phase transitions of a fixed connectivity surface model

We study the phase structure of a phantom tethered surface model shedding light on the internal degrees of freedom (IDOF), which correspond to the three-dimensional rod like structure of the lipid molecules. The so-called tilt order is assumed as IDOF on the surface model. The model is defined by combining the conventional spherical surface model and the XY model, which describes not only the interaction between lipids but also the interaction between the lipids and the surface. The interaction strength between IDOF and the surface varies depending on the interaction strength between the variables of IDOF. We know that the model without IDOF undergoes a first-order transition of surface fluctuations and a first-order collapsing transition. We observe in this paper that the order of the surface fluctuation transition changes from first-order to second-order and to higher-order with increasing strength of the interaction between IDOF variables. On the contrary, the order of collapsing transition remains first-order and is not influenced by the presence of IDOF.Comment: 20 pages, 14 figure

Collapse and dispersal of a homogeneous spin fluid in Einstein-Cartan theory

In the present work, we revisit the process of gravitational collapse of a spherically symmetric homogeneous dust fluid which is known as the Oppenheimer-Snyder (OS) model [1]. We show that such a scenario would not end in a spacetime singularity when the spin degrees of freedom of fermionic particles within the collapsing cloud are taken into account. To this purpose, we take the matter content of the stellar object as a homogeneous Weyssenhoff fluid which is a generalization of perfect fluid in general relativity (GR) to include the spin of matter. Employing the homogeneous and isotropic FLRW metric for the interior spacetime setup, it is shown that the spin of matter, in the context of a negative pressure, acts against the pull of gravity and decelerates the dynamical evolution of the collapse in its later stages. Our results bode a picture of gravitational collapse in which the collapse process halts at a finite radius whose value depends on the initial configuration. We thus show that the spacetime singularity that occurs in the OS model is replaced by a non-singular bounce beyond which the collapsing cloud re-expands to infinity. Depending on the model parameters, one can find a minimum value for the boundary of the collapsing cloud or correspondingly a threshold value for the mass content below which the horizon formation can be avoided. Our results are supported by a thorough numerical analysis.Comment: 16 pages, 5 figures, revised versio

A Systematic Examination of Particle Motion in a Collapsing Magnetic Trap Model for Solar Flares

Context. It has been suggested that collapsing magnetic traps may contribute to accelerating particles to high energies during solar flares. Aims. We present a detailed investigation of the energization processes of particles in collapsing magnetic traps, using a specific model. We also compare for the first time the energization processes in a symmetric and an asymmetric trap model. Methods. Particle orbits are calculated using guiding centre theory. We systematically investigate the dependence of the energization process on initial position, initial energy and initial pitch angle. Results. We find that in our symmetric trap model particles can gain up to about 50 times their initial energy, but that for most initial conditions the energy gain is more moderate. Particles with an initial position in the weak field region of the collapsing trap and with pitch angles around 90 degrees achieve the highest energy gain, with betatron acceleration of the perpendicular energy the dominant energization mechanism. For particles with smaller initial pitch angle, but still outside the loss cone, we find the possibility of a significant increase in parallel energy. This increase in parallel energy can be attributed to the curvature term in the parallel equation of motion and the associated energy gain happens in the center of the trap where the field line curvature has its maximum. We find qualitatively similar results for the asymmetric trap model, but with smaller energy gains and a larger number of particles escaping from the trap.Comment: 11 pages, 13 figures. To be published in Astronomy and Astrophysic

On the Aggregation of Multimarker Information for Marker-Set and Sequencing Data Analysis: Genotype Collapsing vs. Similarity Collapsing

Methods that collapse information across genetic markers when searching for association signals are gaining momentum in the literature. Although originally developed to achieve a better balance between retaining information and controlling degrees of freedom when performing multimarker association analysis, these methods have recently been proven to be a powerful tool for identifying rare variants that contribute to complex phenotypes. The information among markers can be collapsed at the genotype level, which focuses on the mean of genetic information, or the similarity level, which focuses on the variance of genetic information. The aim of this work is to understand the strengths and weaknesses of these two collapsing strategies. Our results show that neither collapsing strategy outperforms the other across all simulated scenarios. Two factors that dominate the performance of these strategies are the signal-to-noise ratio and the underlying genetic architecture of the causal variants. Genotype collapsing is more sensitive to the marker set being contaminated by noise loci than similarity collapsing. In addition, genotype collapsing performs best when the genetic architecture of the causal variants is not complex (e.g., causal loci with similar effects and similar frequencies). Similarity collapsing is more robust as the complexity of the genetic architecture increases and outperforms genotype collapsing when the genetic architecture of the marker set becomes more sophisticated (e.g., causal loci with various effect sizes or frequencies and potential non-linear or interactive effects). Because the underlying genetic architecture is not known a priori, we also considered a two-stage analysis that combines the two top-performing methods from different collapsing strategies. We find that it is reasonably robust across all simulated scenarios