Trap Target Studies

This research was sponsored by the National Science Foundation Grant NSF PHY-931478

CE-30 - Toward a Trapped Particle Target

This research was sponsored by the National Science Foundation Grant NSF PHY-931478

Trapped surfaces in prolate collapse in the Gibbons-Penrose construction

We investigate existence and properties of trapped surfaces in two models of collapsing null dust shells within the Gibbons-Penrose construction. In the first model, the shell is initially a prolate spheroid, and the resulting singularity forms at the ends first (relative to a natural time slicing by flat hyperplanes), in analogy with behavior found in certain prolate collapse examples considered by Shapiro and Teukolsky. We give an explicit example in which trapped surfaces are present on the shell, but none exist prior to the last flat slice, thereby explicitly showing that the absence of trapped surfaces on a particular, natural slicing does not imply an absence of trapped surfaces in the spacetime. We then examine a model considered by Barrabes, Israel and Letelier (BIL) of a cylindrical shell of mass M and length L, with hemispherical endcaps of mass m. We obtain a "phase diagram" for the presence of trapped surfaces on the shell with respect to essential parameters $\lambda \equiv M/L$ and $\mu \equiv m/M$. It is found that no trapped surfaces are present on the shell when $\lambda$ or $\mu$ are sufficiently small. (We are able only to search for trapped surfaces lying on the shell itself.) In the limit $\lambda \to 0$, the existence or nonexistence of trapped surfaces lying within the shell is seen to be in remarkably good accord with the hoop conjecture.Comment: 22 pages, 6 figure

No-horizon theorem for spacetimes with spacelike G1 isometry groups

We consider four-dimensional spacetimes $(M,{\mathbf g})$ which obey the Einstein equations ${\mathbf G}={\mathbf T}$, and admit a global spacelike $G_{1}={\mathbb R}$ isometry group. By means of dimensional reduction and local analyis on the reduced (2+1) spacetime, we obtain a sufficient condition on ${\mathbf T}$ which guarantees that $(M,{\mathbf g})$ cannot contain apparent horizons. Given any (3+1) spacetime with spacelike translational isometry, the no-horizon condition can be readily tested without the need for dimensional reduction. This provides thus a useful and encompassing apparent horizon test for $G_{1}$-symmetric spacetimes. We argue that this adds further evidence towards the validity of the hoop conjecture, and signals possible violations of strong cosmic censorship.Comment: 8 pages, LaTeX, uses IOP package; published in Class. Quantum Gra

Does the generalized second law require entropy bounds for a charged system?

We calculate the net change in generalized entropy occurring when one carries out the gedanken experiment in which a box initially containing energy $E$, entropy $S$ and charge $Q$ is lowered adiabatically toward a Reissner-Nordstr\"{o}m black hole and then dropped in. This is an extension of the work of Unruh-Wald to a charged system (the contents of the box possesses a charge $Q$). Their previous analysis showed that the effects of acceleration radiation prevent violation of the generalized second law of thermodynamics. In our more generic case, we show that the properties of the thermal atmosphere are equally important when charge is present. Indeed, we prove here that an equilibrium condition for the the thermal atmosphere and the physical properties of ordinary matter are sufficient to enforce the generalized second law. Thus, no additional assumptions concerning entropy bounds on the contents of the box need to be made in this process. The relation between our work and the recent works of Bekenstein and Mayo, and Hod (entropy bound for a charged system) are also discussed.Comment: 18pages, RevTex, no figure

A Reformulation of the Hoop Conjecture

A reformulation of the Hoop Conjecture based on the concept of trapped circle is presented. The problems of severe compactness in every spatial direction, and of how to superpose the hoops with the surface of the black hole, are resolved. A new conjecture concerning "peeling" properties of dynamical/trapping horizons is propounded. A novel geometric Hoop inequality is put forward. The possibility of carrying over the results to arbitrary dimension is discussed.Comment: 6 pages, no figures. New references included, typos corrected, explanatory comments added. Much shorter version, in order to match EPL length restrictions. To be published in EP

Moving black holes via singularity excision

We present a singularity excision algorithm appropriate for numerical simulations of black holes moving throughout the computational domain. The method is an extension of the excision procedure previously used to obtain stable simulations of single, non-moving black holes. The excision procedure also shares elements used in recent work to study the dynamics of a scalarfield in the background of a single, boosted black hole. The robustness of our excision method is tested with single black-hole evolutions using a coordinate system in which the coordinate location of the black hole, and thus the excision boundary, moves throughout the computational domain.Comment: 9 pages and 11 figure

Non-Archimedean character of quantum buoyancy and the generalized second law of thermodynamics

Quantum buoyancy has been proposed as the mechanism protecting the generalized second law when an entropy--bearing object is slowly lowered towards a black hole and then dropped in. We point out that the original derivation of the buoyant force from a fluid picture of the acceleration radiation is invalid unless the object is almost at the horizon, because otherwise typical wavelengths in the radiation are larger than the object. The buoyant force is here calculated from the diffractive scattering of waves off the object, and found to be weaker than in the original theory. As a consequence, the argument justifying the generalized second law from buoyancy cannot be completed unless the optimal drop point is next to the horizon. The universal bound on entropy is always a sufficient condition for operation of the generalized second law, and can be derived from that law when the optimal drop point is close to the horizon. We also compute the quantum buoyancy of an elementary charged particle; it turns out to be negligible for energetic considerations. Finally, we speculate on the significance of the absence from the bound of any mention of the number of particle species in nature.Comment: RevTeX, 16 page

Absence of trapped surfaces and singularities in cylindrical collapse

The gravitational collapse of an infinite cylindrical thin shell of generic matter in an otherwise empty spacetime is considered. We show that geometries admitting two hypersurface orthogonal Killing vectors cannot contain trapped surfaces in the vacuum portion of spacetime causally available to geodesic timelike observers. At asymptotic future null infinity, however, congruences of outgoing radial null geodesics become marginally trapped, due to convergence induced by shear caused by the interaction of a transverse wave component with the geodesics. The matter shell itself is shown to be always free of trapped surfaces, for this class of geometries. Finally, two simplified matter models are analytically examined. For one model, the weak energy condition is shown to be a necessary condition for collapse to halt; for the second case, it is a sufficient condition for collapse to be able to halt.Comment: 26 pages, revtex4, 1 eps figure; matches version to appear in Phys. Rev. D (in press