Exact relativistic treatment of stationary counter-rotating dust disks III. Physical Properties

This is the third in a series of papers on the construction of explicit solutions to the stationary axisymmetric Einstein equations which can be interpreted as counter-rotating disks of dust. We discuss the physical properties of a class of solutions to the Einstein equations for disks with constant angular velocity and constant relative density which was constructed in the first part. The metric for these spacetimes is given in terms of theta functions on a Riemann surface of genus 2. It is parameterized by two physical parameters, the central redshift and the relative density of the two counter-rotating streams in the disk. We discuss the dependence of the metric on these parameters using a combination of analytical and numerical methods. Interesting limiting cases are the Maclaurin disk in the Newtonian limit, the static limit which gives a solution of the Morgan and Morgan class and the limit of a disk without counter-rotation. We study the mass and the angular momentum of the spacetime. At the disk we discuss the energy-momentum tensor, i.e. the angular velocities of the dust streams and the energy density of the disk. The solutions have ergospheres in strongly relativistic situations. The ultrarelativistic limit of the solution in which the central redshift diverges is discussed in detail: In the case of two counter-rotating dust components in the disk, the solutions describe a disk with diverging central density but finite mass. In the case of a disk made up of one component, the exterior of the disks can be interpreted as the extreme Kerr solution.Comment: 30 pages, 20 figures; to appear in Phys. Rev.

Biscayne aquifer in Dade and Broward Counties, Florida

The Biscayne Aquifer is the principal source of water for the heavily populated area in the vicinity of West Palm Beach and Miami. The publication of this data is timely and will assist in the intelligent development of the water resources of the area.(PDF has 64 pages

An assessment and validation study of nuclear reactors for low power space applications

The feasibility and safety of six conceptual small, low power nuclear reactor designs was evaluated. Feasibility evaluations included the determination of sufficient reactivity margins for seven years of full power operation and safe shutdown as well as handling during pre-launch assembly phases. Safety evaluations were concerned with the potential for maintaining subcritical conditions in the event of launch or transportation accidents. These included water immersion accident scenarios both with and without water flooding the core. Results show that most of the concepts can potentially meet the feasibility and safety requirements; however, due to the preliminary nature of the designs considered, more detailed designs will be necessary to enable these concepts to fully meet the safety requirements

Systematic study of high-pTp_T hadron and photon production with the PHENIX experiment

The suppression of hadrons with large transverse momentum ($p_{\rm T}$) in central Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 200 GeV compared to a binary scaled p+p reference is one of the major discoveries at RHIC. To understand the nature of this suppression PHENIX has performed detailed studies of the energy and system-size dependence of the suppression pattern, including the first RHIC measurement near SPS energies. An additional source of information is provided by direct photons. Since they escape the medium basically unaffected they can provide a high $p_{\rm T}$ baseline for hard-scattering processes. An overview of hadron production at high $p_{\rm T}$ in different colliding systems and at energies from $\sqrt{s_{\rm NN}} = 22.4 - 200$ GeV will be given. In addition, the latest direct photon measurements by the PHENIX experiment shall be discussed.Comment: 6 pages, 3 figures, Proceeding for the Conference Strangeness in Quark Matter, Levoca, Slovakia, June 24-29, 200

Exact relativistic treatment of stationary counter-rotating dust disks I: Boundary value problems and solutions

This is the first in a series of papers on the construction of explicit solutions to the stationary axisymmetric Einstein equations which describe counter-rotating disks of dust. These disks can serve as models for certain galaxies and accretion disks in astrophysics. We review the Newtonian theory for disks using Riemann-Hilbert methods which can be extended to some extent to the relativistic case where they lead to modular functions on Riemann surfaces. In the case of compact surfaces these are Korotkin's finite gap solutions which we will discuss in this paper. On the axis we establish for general genus relations between the metric functions and hence the multipoles which are enforced by the underlying hyperelliptic Riemann surface. Generalizing these results to the whole spacetime we are able in principle to study the classes of boundary value problems which can be solved on a given Riemann surface. We investigate the cases of genus 1 and 2 of the Riemann surface in detail and construct the explicit solution for a family of disks with constant angular velocity and constant relative energy density which was announced in a previous Physical Review Letter.Comment: 32 pages, 1 figure, to appear in Phys. Rev.

Harrison transformation of hyperelliptic solutions and charged dust disks

We use a Harrison transformation on solutions to the stationary axisymmetric Einstein equations to generate solutions of the Einstein-Maxwell equations. The case of hyperelliptic solutions to the Ernst equation is studied in detail. Analytic expressions for the metric and the multipole moments are obtained. As an example we consider the transformation of a family of counter-rotating dust disks. The resulting solutions can be interpreted as disks with currents and matter with a purely azimuthal pressure or as two streams of freely moving charged particles. We discuss interesting limiting cases as the extreme limit where the charge becomes identical to the mass, and the ultrarelativistic limit where the central redshift diverges.Comment: 20 pages, 9 figure

Boundary value problems for the stationary axisymmetric Einstein equations: a disk rotating around a black hole

We solve a class of boundary value problems for the stationary axisymmetric Einstein equations corresponding to a disk of dust rotating uniformly around a central black hole. The solutions are given explicitly in terms of theta functions on a family of hyperelliptic Riemann surfaces of genus 4. In the absence of a disk, they reduce to the Kerr black hole. In the absence of a black hole, they reduce to the Neugebauer-Meinel disk.Comment: 46 page