Explicit Global Coordinates for Schwarzschild and Reissner-Nordstroem

We construct coordinate systems that cover all of the Reissner-Nordstroem solution with m>|q| and m=|q|, respectively. This is possible by means of elementary analytical functions. The limit of vanishing charge q provides an alternative to Kruskal which, to our mind, is more explicit and simpler. The main tool for finding these global charts is the description of highly symmetrical metrics by two-dimensional actions. Careful gauge fixing yields global representatives of the two-dimensional theory that can be rewritten easily as the corresponding four-dimensional line elements.Comment: 12 pages, 3 Postscript figures, sign error in Eq. (37) and below corrected, references and Note added; to appear in Class. Quantum Gra

Analytical study of the fracture of liquid- filled tanks impacted by hypervelocity particles

Shock waves in water and stress waves in tank walls of water-filled fuel tanks impacted by hypervelocity particle

Classical and Quantum Gravity in 1+1 Dimensions, Part III: Solutions of Arbitrary Topology

All global solutions of arbitrary topology of the most general 1+1 dimensional dilaton gravity models are obtained. We show that for a generic model there are globally smooth solutions on any non-compact 2-surface. The solution space is parametrized explicitly and the geometrical significance of continuous and discrete labels is elucidated. As a corollary we gain insight into the (in general non-trivial) topology of the reduced phase space. The classification covers basically all 2D metrics of Lorentzian signature with a (local) Killing symmetry.Comment: 39 pages, 22 figures, uses AMSTeX, extended version of former chapter 7 (Gravitational Kinks) now available as gr-qc/9707053, problem with figure 6 fixe

Symmetries in two-dimensional dilaton gravity with matter

The symmetries of generic 2D dilaton models of gravity with (and without) matter are studied in some detail. It is shown that $\delta_2$, one of the symmetries of the matterless models, can be generalized to the case where matter fields of any kind are present. The general (classical) solution for some of these models, in particular those coupled to chiral matter, which generalizes the Vaidya solution of Einstein Gravity, is also given.Comment: Minor changes have been made; the references have been updated and some added; 11 pages. To appear in Phys. Rev.

On the Canonical Reduction of Spherically Symmetric Gravity

In a thorough paper Kuchar has examined the canonical reduction of the most general action functional describing the geometrodynamics of the maximally extended Schwarzschild geometry. This reduction yields the true degrees of freedom for (vacuum) spherically symmetric general relativity. The essential technical ingredient in Kuchar's analysis is a canonical transformation to a certain chart on the gravitational phase space which features the Schwarzschild mass parameter $M_{S}$, expressed in terms of what are essentially Arnowitt-Deser-Misner variables, as a canonical coordinate. In this paper we discuss the geometric interpretation of Kuchar's canonical transformation in terms of the theory of quasilocal energy-momentum in general relativity given by Brown and York. We find Kuchar's transformation to be a ``sphere-dependent boost to the rest frame," where the ``rest frame'' is defined by vanishing quasilocal momentum. Furthermore, our formalism is general enough to cover the case of (vacuum) two-dimensional dilaton gravity. Therefore, besides reviewing Kucha\v{r}'s original work for Schwarzschild black holes from the framework of hyperbolic geometry, we present new results concerning the canonical reduction of Witten-black-hole geometrodynamics.Comment: Revtex, 35 pages, no figure

Topological Field Theories and Geometry of Batalin-Vilkovisky Algebras

The algebraic and geometric structures of deformations are analyzed concerning topological field theories of Schwarz type by means of the Batalin-Vilkovisky formalism. Deformations of the Chern-Simons-BF theory in three dimensions induces the Courant algebroid structure on the target space as a sigma model. Deformations of BF theories in $n$ dimensions are also analyzed. Two dimensional deformed BF theory induces the Poisson structure and three dimensional deformed BF theory induces the Courant algebroid structure on the target space as a sigma model. The deformations of BF theories in $n$ dimensions induce the structures of Batalin-Vilkovisky algebras on the target space.Comment: 25 page

The Becklin-Neugebauer Object as a Runaway B Star, Ejected 4000 years ago from the theta^1C system

We attempt to explain the properties of the Becklin-Neugebauer (BN) object as a runaway B star, as originally proposed by Plambeck et al. (1995). This is one of the best-studied bright infrared sources, located in the Orion Nebula Cluster -- an important testing ground for massive star formation theories. From radio observations of BN's proper motion, we trace its trajectory back to Trapezium star theta^1C, the most massive (45 Msun) in the cluster and a relatively tight (17 AU) visual binary with a B star secondary. This origin would be the most recent known runaway B star ejection event, occurring only \~4000 yr ago and providing a unique test of models of ejection from multiple systems of massive stars. Although highly obscured, we can constrain BN's mass (~7 Msun) from both its bolometric luminosity and the recoil of theta^1C. Interaction of a runaway B star with dense ambient gas should produce a compact wind bow shock. We suggest that X-ray emission from this shocked gas may have been seen by Chandra: the offset from the radio position is ~300 AU in the direction of BN's motion. Given this model, we constrain the ambient density, wind mass-loss rate and wind velocity. BN made closest approach to the massive protostar, source ``I'', 500 yr ago. This may have triggered enhanced accretion and thus outflow, consistent with previous interpretations of the outflow being a recent (~10^3 yr) "explosive" event.Comment: 6 pages, accepted to ApJ Letter

Type Ia Supernova Scenarios and the Hubble Sequence

The dependence of the Type Ia supernova (SN Ia) rate on galaxy type is examined for three currently proposed scenarios: merging of a Chandrasekhar--mass CO white dwarf (WD) with a CO WD companion, explosion of a sub--Chandrasekhar mass CO WD induced by accretion of material from a He star companion, and explosion of a sub--Chandrasekhar CO WD in a symbiotic system. The variation of the SNe Ia rate and explosion characteristics with time is derived, and its correlation with parent population age and galaxy redshift is discussed. Among current scenarios, CO + He star systems should be absent from E galaxies. Explosion of CO WDs in symbiotic systems could account for the SNe Ia rate in these galaxies. The same might be true for the CO + CO WD scenario, depending on the value of the common envelope parameter. A testable prediction of the sub--Chandrasekhar WD model is that the average brightness and kinetic energy of the SN Ia events should increase with redshift for a given Hubble type. Also for this scenario, going along the Hubble sequence from E to Sc galaxies SNe Ia events should be brighter on average and should show larger mean velocities of the ejecta. The observational correlations strongly suggest that the characteristics of the SNe Ia explosion are linked to parent population age. The scenario in which WDs with masses below the Chandrasekhar mass explode appears the most promising one to explain the observed variation of the SN Ia rate with galaxy type together with the luminosity--expansion velocity trend.Comment: 16 pages uuencoded compressed Postscript, 2 figures included. ApJ Letters, in pres

The Expected Rate of Gamma-Ray Burst Afterglows In Supernova Searches

We predict the rate at which Gamma-Ray Burst (GRB) afterglows should be detected in supernova searches as a function of limiting flux. Although GRB afterglows are rarer than supernovae, they are detectable at greater distances because of their higher intrinsic luminosity. Assuming that GRBs trace the cosmic star formation history and that every GRB gives rise to a bright afterglow, we find that the average detection rate of supernovae and afterglows should be comparable at limiting magnitudes brighter than K=18. The actual rate of afterglows is expected to be somewhat lower since only a fraction of all gamma-ray selected GRBs were observed to have associated afterglows. However, the rate could also be higher if the initial gamma-ray emission from GRB sources is more beamed than their late afterglow emission. Hence, current and future supernova searches can place strong constraints on the afterglow appearance fraction and the initial beaming angle of GRB sources.Comment: 13 pages, submitted to ApJ

The BHK Color Diagram: a New Tool to Study Young Stellar Populations

A new method to derive age differences between the various super star clusters observed in starburst galaxies using the two color diagram (B-H) vs (H-K) is presented. This method offers a quick and easy way to differentiate very young and intermediate age stellar populations even if data on extinction are unavailable. In this case, discrimination of regions younger and older than 4 Myr is feasible. With the availability of data on extinction, the time resolution can be improved significantly. The application of the method to the starbursting system Arp 299 is presented. The validity of the method is confirmed by comparing the equivalent width of the H-alpha line with the chronological map of the northern part of NGC 3690.Comment: 32 pages, 7 figures, 1 table, AJ accepte