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

Classical and Quantum Integrability of 2D Dilaton Gravities in Euclidean space

Euclidean dilaton gravity in two dimensions is studied exploiting its representation as a complexified first order gravity model. All local classical solutions are obtained. A global discussion reveals that for a given model only a restricted class of topologies is consistent with the metric and the dilaton. A particular case of string motivated Liouville gravity is studied in detail. Path integral quantisation in generic Euclidean dilaton gravity is performed non-perturbatively by analogy to the Minkowskian case.Comment: 27 p., LaTeX, v2: included new refs. and a footnot

Abelian 2-form gauge theory: special features

It is shown that the four $(3 + 1)$-dimensional (4D) free Abelian 2-form gauge theory provides an example of (i) a class of field theoretical models for the Hodge theory, and (ii) a possible candidate for the quasi-topological field theory (q-TFT). Despite many striking similarities with some of the key topological features of the two $(1 + 1)$-dimensional (2D) free Abelian (and self-interacting non-Abelian) gauge theories, it turns out that the 4D free Abelian 2-form gauge theory is {\it not} an exact TFT. To corroborate this conclusion, some of the key issues are discussed. In particular, it is shown that the (anti-)BRST and (anti-)co-BRST invariant quantities of the 4D 2-form Abelian gauge theory obey the recursion relations that are reminiscent of the exact TFTs but the Lagrangian density of this theory is not found to be able to be expressed as the sum of (anti-)BRST and (anti-)co-BRST exact quantities as is the case with the {\it topological} 2D free Abelian (and self-interacting non-Abelian) gauge theories.Comment: LaTeX, 23 pages, journal ref. give

Generalized 2d dilaton gravity with matter fields

We extend the classical integrability of the CGHS model of 2d dilaton gravity [1] to a larger class of models, allowing the gravitational part of the action to depend more generally on the dilaton field and, simultaneously, adding fermion- and U(1)-gauge-fields to the scalar matter. On the other hand we provide the complete solution of the most general dilaton-dependent 2d gravity action coupled to chiral fermions. The latter analysis is generalized to a chiral fermion multiplet with a non-abelian gauge symmetry as well as to the (anti-)self-dual sector df = *df (df = -*df) of a scalar field f.Comment: 37 pages, Latex; typos and Eqs. (44,45) corrected; paragraph on p. 26, referring to a work of S. Solodukhin, reformulated; references adde

Long time black hole evaporation with bounded Hawking flux

The long time behavior of an evaporating Schwarzschild black hole is studied exploiting that it can be described by an effective theory in 2D, a particular dilaton gravity model. A crucial technical ingredient is Izawa's result on consistent deformations of 2D BF theory, while the most relevant physical assumption is boundedness of the asymptotic matter flux during the whole evaporation process. An attractor solution, the endpoint of the evaporation process, is found. Its metric is flat. However, the behavior of the dilaton field is nontrivial: it is argued that during the final flicker a first order phase transition occurs from a linear to a constant dilaton vacuum, thereby emitting a shock wave with a total energy of a fraction of the Planck mass. Another fraction of the Planck mass may reside in a cold remnant. [Note: More detailed abstract in the paper]Comment: 34 pages, 6 figures, v2: included new references and 2 new footnotes; v3: mayor revisions (extended intro, included pedagogical example, rearranged presentation, extended discussion on information paradox, updated references); v4: updated refs. (+ new ones), added comments, mostly on dilaton evaporation, rewrote abstract (short for arXiv, long for journal), moved pedagogic sec. to ap

Chebyshev's bias for composite numbers with restricted prime divisors

Let P(x,d,a) denote the number of primes p<=x with p=a(mod d). Chebyshev's bias is the phenomenon that `more often' P(x;d,n)>P(x;d,r) than the other way around, where n is a quadratic non-residue mod d and r is a quadratic residue mod d. If P(x;d,n)>=P(x;d,r) for every x up to some large number, then one expects that N(x;d,n)>=N(x;d,r) for every x. Here N(x;d,a) denotes the number of integers n<=x such that every prime divisor p of n satisfies p=a(mod d). In this paper we develop some tools to deal with this type of problem and apply them to show that, for example, N(x;4,3)>=N(x;4,1) for every x. In the process we express the so called second order Landau-Ramanujan constant as an infinite series and show that the same type of formula holds true for a much larger class of constants. In a sequel to this paper the methods developed here will be used and somewhat refined to resolve a conjecture from P. Schmutz Schaller to the extent that the hexagonal lattice is `better' than the square lattice (see p. 201 of Bull. Amer. Math. Soc. 35 (1998), 193-214).Comment: 26 page

Virtual black hole phenomenology from 2d dilaton theories

Equipped with the tools of (spherically reduced) dilaton gravity in first order formulation and with the results for the lowest order S-matrix for s-wave gravitational scattering (P. Fischer, D. Grumiller, W. Kummer, and D. Vassilevich, gr-qc/0105034) new properties of the ensuing cross-section are discussed. We find CPT invariance, despite of the non-local nature of our effective theory and discover pseudo-self-similarity in its kinematic sector. After presenting the Carter-Penrose diagram for the corresponding virtual black hole geometry we encounter distributional contributions to its Ricci-scalar and a vanishing Einstein-Hilbert action for that configuration. Finally, a comparison is done between our (Minkowskian) virtual black hole and Hawking's (Euclidean) virtual black hole bubbles.Comment: 17 pages, 13 figure

Volume 10, Number 9 - June 1930

Volume 10, Number 9 – June 1930. 62 pages including covers and advertisements. LaCroix, John Carthage (verse) Schaller, Harvey The Books Fell to the Floor Gillis, Clinton M. Hasbroucke & Co. Hickey, Carroll Valete (verse) Carlson, Edward Lodestar (verse) Daniels, Ralph Impressions of the Seniors Gorman, John P. Alumni Notes Daniels, Ralph Editorial Hickey, Carroll Exchange Quirk, Charles C. Chronicle Krieger, John E. Athletic