Firm Heterogeneity and the Geography of International Trade

A key distinction which has emerged from heterogeneous firm models of international trade is that of exporting at the intensive and extensive margins. Empirically however, the two are often conflated, leading to biased estimates of the impact of falling trade costs. This paper exploits detailed firm level data, which includes information on the destination of exports to investigate causal links between enterprise productivity and the number of markets a firm serves as well as the relative size of those markets. Our focus is Sweden’s Food and Beverage sector, which is not only highly open, but has been subject to policy induced changes in trade costs (as well as falling natural barriers) over our sample period. We have data on almost 10,000 firm / time / destination observations across 6 years and 138 destinations. Our results confirm that conflating adjustment at the internal and external margins does bias trade resistance effects. Combining detailed firm specific information with data on destination characteristics confirms the importance of a range of country specific characteristics (including exchange rate risk) and facilitates the estimation of both distance and market size elasticities, from firm level data.trade costs, firm characteristics, destination characteristics, market size, distance

Regular coordinate systems for Schwarzschild and other spherical spacetimes

The continuation of the Schwarzschild metric across the event horizon is almost always (in textbooks) carried out using the Kruskal-Szekeres coordinates, in terms of which the areal radius r is defined only implicitly. We argue that from a pedagogical point of view, using these coordinates comes with several drawbacks, and we advocate the use of simpler, but equally effective, coordinate systems. One such system, introduced by Painleve and Gullstrand in the 1920's, is especially simple and pedagogically powerful; it is, however, still poorly known today. One of our purposes here is therefore to popularize these coordinates. Our other purpose is to provide generalizations to the Painleve-Gullstrand coordinates, first within the specific context of Schwarzschild spacetime, and then in the context of more general spherical spacetimes.Comment: 5 pages, 2 figures, ReVTeX; minor changes were made, new references were include

Spherically Symmetric Black Hole Formation in Painlev\'e-Gullstrand Coordinates

We perform a numerical study of black hole formation from the spherically symmetric collapse of a massless scalar field. The calculations are done in Painlev\'e-Gullstrand (PG) coordinates that extend across apparent horizons and allow the numerical evolution to proceed until the onset of singularity formation. We generate spacetime maps of the collapse and illustrate the evolution of apparent horizons and trapping surfaces for various initial data. We also study the critical behaviour and find the expected Choptuik scaling with universal values for the critical exponent and echoing period consistent with the accepted values of $\gamma=0.374$ and $\Delta = 3.44$, respectively. The subcritical curvature scaling exhibits the expected oscillatory behaviour but the form of the periodic oscillations in the supercritical mass scaling relation, while universal with respect to initial PG data, is non-standard: it is non-sinusoidal with large amplitude cusps.Comment: 12 pages, 7 figure

Acoustic analogues of black hole singularities

We search for acoustic analogues of a spherical symmetric black hole with a pointlike source. We show that the gravitational system has a dynamical counterpart in the constrained, steady motion of a fluid with a planar source. The equations governing the dynamics of the gravitational system can be exactly mapped in those governing the motion of the fluid. The different meaning that singularities and sources have in fluid dynamics and in general relativity is also discussed. Whereas in the latter a pointlike source is always associated with a (curvature) singularity in the former the presence of sources does not necessarily imply divergences of the fields.Comment: 9 pages, no figure

A Secret Tunnel Through The Horizon

Hawking radiation is often intuitively visualized as particles that have tunneled across the horizon. Yet, at first sight, it is not apparent where the barrier is. Here I show that the barrier depends on the tunneling particle itself. The key is to implement energy conservation, so that the black hole contracts during the process of radiation. A direct consequence is that the radiation spectrum cannot be strictly thermal. The correction to the thermal spectrum is of precisely the form that one would expect from an underlying unitary quantum theory. This may have profound implications for the black hole information puzzle.Comment: First prize in the Gravity Research Foundation Essay Competition. 7 pages, LaTe

Cauchy-perturbative matching revisited: tests in spherical symmetry

During the last few years progress has been made on several fronts making it possible to revisit Cauchy-perturbative matching (CPM) in numerical relativity in a more robust and accurate way. This paper is the first in a series where we plan to analyze CPM in the light of these new results. Here we start by testing high-order summation-by-parts operators, penalty boundaries and contraint-preserving boundary conditions applied to CPM in a setting that is simple enough to study all the ingredients in great detail: Einstein's equations in spherical symmetry, describing a black hole coupled to a massless scalar field. We show that with the techniques described above, the errors introduced by Cauchy-perturbative matching are very small, and that very long term and accurate CPM evolutions can be achieved. Our tests include the accretion and ring-down phase of a Schwarzschild black hole with CPM, where we find that the discrete evolution introduces, with a low spatial resolution of \Delta r = M/10, an error of 0.3% after an evolution time of 1,000,000 M. For a black hole of solar mass, this corresponds to approximately 5 s, and is therefore at the lower end of timescales discussed e.g. in the collapsar model of gamma-ray burst engines. (abridged)Comment: 14 pages, 20 figure

Einstein's Real "Biggest Blunder"

Albert Einstein's real "biggest blunder" was not the 1917 introduction into his gravitational field equations of a cosmological constant term \Lambda, rather was his failure in 1916 to distinguish between the entirely different concepts of active gravitational mass and passive gravitational mass. Had he made the distinction, and followed David Hilbert's lead in deriving field equations from a variational principle, he might have discovered a true (not a cut and paste) Einstein-Rosen bridge and a cosmological model that would have allowed him to predict, long before such phenomena were imagined by others, inflation, a big bounce (not a big bang), an accelerating expansion of the universe, dark matter, and the existence of cosmic voids, walls, filaments, and nodes.Comment: 4 pages, LaTeX, 11 references, Honorable Mention in 2012 Gravity Research Foundation Essay Award

Embedding spherical spacelike slices in a Schwarzschild solution

Given a spherical spacelike three-geometry, there exists a very simple algebraic condition which tells us whether, and in which, Schwarzschild solution this geometry can be smoothly embedded. One can use this result to show that any given Schwarzschild solution covers a significant subset of spherical superspace and these subsets form a sequence of nested domains as the Schwarzschild mass increases. This also demonstrates that spherical data offer an immediate counter example to the thick sandwich `theorem'

New Cosmological Solutions in Massive Gravity

We find new, simple cosmological solutions with flat, open, and closed spatial geometries, contrary to the previous wisdom that only the open model is allowed. The metric and the St\"{u}ckelberg fields are given explicitly, showing nontrivial configurations of the St\"{u}ckelberg in the usual Friedmann-Lema\^{i}tre-Robertson-Walker coordinates. The solutions exhibit self-acceleration, while being free from ghost instabilities. Our solutions can accommodate inhomogeneous dust collapse represented by the Lema\^{i}tre-Tolman-Bondi metric as well. Thus, our results can be used not only to describe homogeneous and isotropic cosmology but also to study gravitational collapse in massive gravity.Comment: 5 page

Generalized Painlev\'e-Gullstrand metrics

An obstruction to the implementation of spatially flat Painleve-Gullstrand(PG) slicings is demonstrated, and explicitly discussed for Reissner-Nordstrom and Schwarzschild-anti-deSitter spacetimes. Generalizations of PG slicings which are not spatially flat but which remain regular at the horizons are introduced. These metrics can be obtained from standard spherically symmetric metrics by physical Lorentz boosts. With these generalized PG metrics, problematic contributions to the imaginary part of the action in the Parikh-Wilczek derivation of Hawking radiation due to the obstruction can be avoided.Comment: Typos corrected, additional footnote