Practical Issues in the Application of Direct Metal Laser Sintering

Direct Metal Laser Sintering (DMLS) was introduced to meet the objective of producing metal parts directly from CAD data. CRDM has accumulated six years of experience in applying this technique, mostly to prototyping parts for evaluation. For some applications, such as blow moulds, porosity generated in DMLS has proved to be beneficial, but for others a concession on tolerances or finish are necessary and/or complementary operations are required, which add to manufacturing time and cost. This paper examines such issues through some well chosen examples of parts to demonstrate both the strengths and weaknesses of the DMLS process.Mechanical Engineerin

Construction of N = 2 Chiral Supergravity Compatible with the Reality Condition

We construct N = 2 chiral supergravity (SUGRA) which leads to Ashtekar's canonical formulation. The supersymmetry (SUSY) transformation parameters are not constrained at all and auxiliary fields are not required in contrast with the method of the two-form gravity. We also show that our formulation is compatible with the reality condition, and that its real section is reduced to the usual N = 2 SUGRA up to an imaginary boundary term.Comment: 16 pages, late

Destroying black holes with test bodies

If a black hole can accrete a body whose spin or charge would send the black hole parameters over the extremal limit, then a naked singularity would presumably form, in violation of the cosmic censorship conjecture. We review some previous results on testing cosmic censorship in this way using the test body approximation, focusing mostly on the case of neutral black holes. Under certain conditions a black hole can indeed be over-spun or over-charged in this approximation, hence radiative and self-force effects must be taken into account to further test cosmic censorship.Comment: Contribution to the proceedings of the First Mediterranean Conference on Classical and Quantum Gravity (talk given by T. P. S.). Summarizes the results of Phys. Rev. Lett. 103, 141101 (2009), arXiv:0907.4146 [gr-qc] and considers further example

The great dichotomy of the Solar System: small terrestrial embryos and massive giant planet cores

The basic structure of the solar system is set by the presence of low-mass terrestrial planets in its inner part and giant planets in its outer part. This is the result of the formation of a system of multiple embryos with approximately the mass of Mars in the inner disk and of a few multi-Earth-mass cores in the outer disk, within the lifetime of the gaseous component of the protoplanetary disk. What was the origin of this dichotomy in the mass distribution of embryos/cores? We show in this paper that the classic processes of runaway and oligarchic growth from a disk of planetesimals cannot explain this dichotomy, even if the original surface density of solids increased at the snowline. Instead, the accretion of drifting pebbles by embryos and cores can explain the dichotomy, provided that some assumptions hold true. We propose that the mass-flow of pebbles is two-times lower and the characteristic size of the pebbles is approximately ten times smaller within the snowline than beyond the snowline (respectively at heliocentric distance $r<r_{ice}$ and $r>r_{ice}$, where $r_{ice}$ is the snowline heliocentric distance), due to ice sublimation and the splitting of icy pebbles into a collection of chondrule-size silicate grains. In this case, objects of original sub-lunar mass would grow at drastically different rates in the two regions of the disk. Within the snowline these bodies would reach approximately the mass of Mars while beyond the snowline they would grow to $\sim 20$ Earth masses. The results may change quantitatively with changes to the assumed parameters, but the establishment of a clear dichotomy in the mass distribution of protoplanets appears robust, provided that there is enough turbulence in the disk to prevent the sedimentation of the silicate grains into a very thin layer.Comment: In press in Icaru

Spinning Black Holes as Particle Accelerators

It has recently been pointed out that particles falling freely from rest at infinity outside a Kerr black hole can in principle collide with arbitrarily high center of mass energy in the limiting case of maximal black hole spin. Here we aim to elucidate the mechanism for this fascinating result, and to point out its practical limitations, which imply that ultra-energetic collisions cannot occur near black holes in nature.Comment: 3 pages; v2: references added, minor modifications to match version published in PR

Hawking radiation without black hole entropy

In this Letter I point out that Hawking radiation is a purely kinematic effect that is generic to Lorentzian geometries. Hawking radiation arises for any test field on any Lorentzian geometry containing an event horizon regardless of whether or not the Lorentzian geometry satisfies the dynamical Einstein equations of general relativity. On the other hand, the classical laws of black hole mechanics are intrinsically linked to the Einstein equations of general relativity (or their perturbative extension into either semiclassical quantum gravity or string-inspired scenarios). In particular, the laws of black hole thermodynamics, and the identification of the entropy of a black hole with its area, are inextricably linked with the dynamical equations satisfied by the Lorentzian geometry: entropy is proportional to area (plus corrections) if and only if the dynamical equations are the Einstein equations (plus corrections). It is quite possible to have Hawking radiation occur in physical situations in which the laws of black hole mechanics do not apply, and in situations in which the notion of black hole entropy does not even make any sense. This observation has important implications for any derivation of black hole entropy that seeks to deduce black hole entropy from the Hawking radiation.Comment: Uses ReV_TeX 3.0; Five pages in two-column forma

Relativistic Acoustic Geometry

Sound wave propagation in a relativistic perfect fluid with a non-homogeneous isentropic flow is studied in terms of acoustic geometry. The sound wave equation turns out to be equivalent to the equation of motion for a massless scalar field propagating in a curved space-time geometry. The geometry is described by the acoustic metric tensor that depends locally on the equation of state and the four-velocity of the fluid. For a relativistic supersonic flow in curved space-time the ergosphere and acoustic horizon may be defined in a way analogous the non-relativistic case. A general-relativistic expression for the acoustic analog of surface gravity has been found.Comment: 14 pages, LaTe

Mechanics of universal horizons

Modified gravity models such as Ho\v{r}ava-Lifshitz gravity or Einstein-{\ae}ther theory violate local Lorentz invariance and therefore destroy the notion of a universal light cone. Despite this, in the infrared limit both models above possess static, spherically symmetric solutions with "universal horizons" - hypersurfaces that are causal boundaries between an interior region and asymptotic spatial infinity. In other words, there still exist black hole solutions. We construct a Smarr formula (the relationship between the total energy of the spacetime and the area of the horizon) for such a horizon in Einstein-{\ae}ther theory. We further show that a slightly modified first law of black hole mechanics still holds with the relevant area now a cross-section of the universal horizon. We construct new analytic solutions for certain Einstein-{\ae}ther Lagrangians and illustrate how our results work in these exact cases. Our results suggest that holography may be extended to these theories despite the very different causal structure as long as the universal horizon remains the unique causal boundary when matter fields are added.Comment: Minor clarifications. References update