Leibnizian, Galilean and Newtonian structures of spacetime

The following three geometrical structures on a manifold are studied in detail: (1) Leibnizian: a non-vanishing 1-form $\Omega$ plus a Riemannian metric \h on its annhilator vector bundle. In particular, the possible dimensions of the automorphism group of a Leibnizian G-structure are characterized. (2) Galilean: Leibnizian structure endowed with an affine connection $\nabla$ (gauge field) which parallelizes $\Omega$ and \h. Fixed any vector field of observers Z ($\Omega (Z) = 1$), an explicit Koszul--type formula which reconstruct bijectively all the possible $\nabla$'s from the gravitational ${\cal G} = \nabla_Z Z$ and vorticity $\omega = rot Z/2$ fields (plus eventually the torsion) is provided. (3) Newtonian: Galilean structure with \h flat and a field of observers Z which is inertial (its flow preserves the Leibnizian structure and $\omega = 0$). Classical concepts in Newtonian theory are revisited and discussed.Comment: Minor errata corrected, to appear in J. Math. Phys.; 22 pages including a table, Late

Decision Support for Redesigning Wastewater Treatment Technologies

This paper offers a methodology for structuring the design space for innovative process engineering technology development. The methodology is exemplified in the evaluation of a wide variety of treatment technologies for source-separated domestic wastewater within the scope of the Reinvent the Toilet Challenge. It offers a methodology for narrowing down the decision-making field based on a strict interpretation of treatment objectives for undiluted urine and dry feces and macroenvironmental factors (STEEPLED analysis) which influence decision criteria. Such an evaluation identifies promising paths for technology development such as focusing on space-saving processes or the need for more innovation in low-cost, energy-efficient urine treatment methods. Critical macroenvironmental factors, such as housing density, transportation infrastructure, and climate conditions were found to affect technology decisions regarding reactor volume, weight of outputs, energy consumption, atmospheric emissions, investment cost, and net revenue. The analysis also identified a number of qualitative factors that should be carefully weighed when pursuing technology development; such as availability of O&M resources, health and safety goals, and other ethical issues. Use of this methodology allows for coevolution of innovative technology within context constraints; however, for full-scale technology choices in the field, only very mature technologies can be evaluated

Mass of Colored Black Holes

New results pertaining to colored static black hole solutions to the Einstein-Yang-Mills equations are obtained. The isolated horizons framework is used to define the concept of Hamiltonian Horizon Mass of the black hole. An unexpected relation between the ADM and Horizon masses of the black hole solution with the ADM mass of the corresponding Bartnik-McKinnon soliton is found. These results can be generalized to other non-linear theories and they suggest a general testing bed for the instability of the corresponding hairy black holes.Comment: 8 pages, no figures, Revtex file. Minor changes made to clarify some formulas. References updated. Final version to appear in PRD/15

Slowly Rotating Non-Abelian Black Holes

It is shown that the well-known non-Abelian static SU(2) black hole solutions have rotating generalizations, provided that the hypothesis of linearization stability is accepted. Surprisingly, this rotating branch has an asymptotically Abelian gauge field with an electric charge that cannot vanish, although the non-rotating limit is uncharged. We argue that this may be related to our second finding, namely that there are no globally regular slowly rotating excitations of the particle-like Bartnik-McKinnon solutions.Comment: 8 pages, LaTe

Particle-Like Solutions of the Einstein-Dirac Equations

The coupled Einstein-Dirac equations for a static, spherically symmetric system of two fermions in a singlet spinor state are derived. Using numerical methods, we construct an infinite number of soliton-like solutions of these equations. The stability of the solutions is analyzed. For weak coupling (i.e., small rest mass of the fermions), all the solutions are linearly stable (with respect to spherically symmetric perturbations), whereas for stronger coupling, both stable and unstable solutions exist. For the physical interpretation, we discuss how the energy of the fermions and the (ADM) mass behave as functions of the rest mass of the fermions. Although gravitation is not renormalizable, our solutions of the Einstein-Dirac equations are regular and well-behaved even for strong coupling.Comment: 31 pages, LaTeX, 21 PostScript figures, some references adde

Black holes have no short hair

We show that in all theories in which black hole hair has been discovered, the region with non-trivial structure of the non-linear matter fields must extend beyond 3/2 the horizon radius, independently of all other parameters present in the theory. We argue that this is a universal lower bound that applies in every theory where hair is present. This {\it no short hair conjecture} is then put forward as a more modest alternative to the original {\it no hair conjecture}, the validity of which now seems doubtful.Comment: Published in Physical Review Letters, 13 pages in Late

Non-commuting coordinates, exotic particles, & anomalous anyons in the Hall effect

Our previous ``exotic'' particle, together with the more recent anomalous anyon model (which has arbitrary gyromagnetic factor $g$) are reviewed. The non-relativistic limit of the anyon generalizes the exotic particle which has $g=0$ to any $g$.When put into planar electric and magnetic fields, the Hall effect becomes mandatory for all $g\neq2$, when the field takes some critical value.Comment: A new reference added. Talk given by P. Horvathy at the International Workshop "Nonlinear Physics: Theory and Experiment. III. July'04, Gallipoli (Lecce, Italy). To be published in Theor. Math. Phys. Latex 9 pages, no figure

A Mass Formula for EYM Solitons

The Isolated Horizon formalism, together with a simple phenomenological model for colored black holes was recently used to predict a formula for the ADM mass of the solitons of the EYM system in terms of horizon properties of black holes {\it for all} values of the horizon area. In this note, this formula is tested numerically --up to a large value of the area-- for spherically symmetric solutions and shown to yield the known masses of the solitonsComment: 8 pages, 1 table, no figures. Revtex file. Revised file. Added reference

Internal Structure of Einstein-Yang-Mills Black Holes

It is shown that a generic black hole solution of the SU(2) Einstein-Yang-Mills equations develops a new type of an infinitely oscillating behavior near the singularity. Only for certain discrete values of the event horizon radius exceptional solutions exist, possessing an inner structure of the Schwarzschild or Reissner-Nordstrom type.Comment: 4.5 LaTeX pages, 8 eps figures, uses RevTeX, boxedeps.tex. 4 more typos fixed, a footnote adde

A simple theorem to generate exact black hole solutions

Under certain conditions imposed on the energy-momentum tensor, a theorem that characterizes a two-parameter family of static and spherically symmetric solutions to Einstein's field equations (black holes), is proved. A discussion on the asymptotics, regularity, and the energy conditions is provided. Examples that include the best known exact solutions within these symmetries are considered. A trivial extension of the theorem includes the cosmological constant {\it ab-initio}, providing then a three-parameter family of solutions.Comment: 14 pages; RevTex; no figures; typos corrected; references adde