Conserved quantities and the formation of black holes in the Brans-Dicke theory of gravitation

In Part I, we construct a symmetric stress-energy-momentum pseudo-tensor for the gravitational fields of Brans-Dicke theory, and use this to establish rigorously conserved integral expressions for energy-momentum Pⁱ and angular momentum J^ik. Application of the two-dimensional surface integrals to the exact static spherical vacuum solution of Brans leads to an identification of our conserved mass with the active gravitational mass. Application to the distant fields of an arbitrary stationary source reveals that Pⁱ and J^ik have the same physical interpretation as in general relativity. For gravitational waves whose wavelength is small on the scale of the background radius of curvature, averaging over several wavelengths in the Brill-Hartle-Isaacson manner produces a stress-energy-momentum tensor for gravitational radiation which may be used to calculate the changes in Pⁱ and J^ik of their source.

In Part II, we develop strong evidence in favor of a conjecture by Penrose--that, in the Brans-Dicke theory, relativistic gravitational collapse in three dimensions produce black holes identical to those of general relativity. After pointing out that any black hole solution of general relativity also satisfies Brans-Dicke theory, we establish the Schwarzschild and Kerr geometries as the only possible spherical and axially symmetric black hole exteriors, respectively. Also, we show that a Schwarzschild geometry is necessarily formed in the collapse of an uncharged sphere.

Appendices discuss relationships among relativistic gravity theories and an example of a theory in which black holes do not exist.

Diurnal periodicity of activity in the spawning perch P. fluviatilis L. [Translation from: Kalamies 1972(7) 3, 1972]

Diurnal periodicity of spawning in the perch so far are rather meagre and found to be partly contrary to experiences of perch anglers. Therefore a study was made on the spawning during a 5-day period in the spring of 1971 in the Kuusamo area. Observations were made during the main spawning season, between 4- 9 June 1971. The perch were often measured, weighed and then released back into the water. The differences between spawning and non-spawning perch were studied as well as the time of roe discharge in a 24 hour period. Activity and environmental factors such as light intensity were also taken into consideration.

Diurnal periodicity of winter activity in the perch, Perca fluviatilis L. [Translation from: Kalamies 1973(1) 3.]

Since 1967 data have been collected on the distribution of fish caught in a 24 hour period during the winter angling season. The present study on activity periods is based on data from nearly 2000 perch collected between 1967 and 1971. The distribution of number of fish caught during 24 hrs during December - May was studied. Of the total, the most productive period was found to be between 0600 - l600 hrs., with the peak period occurring between 0800 - 1000 hrs. The present data together show that during the darkest months of the year, the perch is only active in the mid-day period. Throughout the whole winter fishing season, activity only occurs during the time between surise and sunset.

Seasonal variation in the diurnal periodicity of activity of the perch, Perca fluviatilis L. [Translation from: Kalamies 1973(3) 3.]

The most common catch of the amateur angler is the perch and it is the diurnal periodicity of activity (& catchability) which is examined in this study based on earlier articles and manuscripts by the authors. Of all environmental factors, variation in light and temperature are the chief reasons in establishing the times of activity periods. Winter, summer and autumn activity was studied. The spawning perch was found to be more active than the non-spawning perch. The time of day in which the fish may be active is dependant on its ability to sense changes in the external environment. Its adaptation to light is the reason for day-activity in the winter, and also accounts for the fact that hardly any activity occurs between sunset and sunrise when this period exceeds 6 hours.

1. Ultrasonic studies of binary liquid structure in the critical region. Theory and experiment for the 2,6-lutidine/water system. 2. Hartree-Fock calculations of electric polarizabilities of some simple atoms and molecules, and their practicality. 3. Calculation of vibrational transition probabilities in collinear atom-diatom and diatom-diatom collisions with Lennard-Jones interaction

Part 1. Many interesting visual and mechanical phenomena occur in the critical region of fluids, both for the gas-liquid and liquid-liquid transitions. The precise thermodynamic and transport behavior here has some broad consequences for the molecular theory of liquids. Previous studies in this laboratory on a liquid-liquid critical mixture via ultrasonics supported a basically classical analysis of fluid behavior by M. Fixman (e. g., the free energy is assumed analytic in intensive variables in the thermodynamics)--at least when the fluid is not too close to critical. A breakdown in classical concepts is evidenced close to critical, in some well-defined ways. We have studied herein a liquid-liquid critical system of complementary nature (possessing a lower critical mixing or consolute temperature) to all previous mixtures, to look for new qualitative critical behavior. We did not find such new behavior in the ultrasonic absorption ascribable to the critical fluctuations, but we did find extra absorption due to chemical processes (yet these are related to the mixing behavior generating the lower consolute point). We rederived, corrected, and extended Fixman's analysis to interpret our experimental results in these more complex circumstances. The entire account of theory and experiment is prefaced by an extensive introduction recounting the general status of liquid state theory. The introduction provides a context for our present work, and also points out problems deserving attention. Interest in these problems was stimulated by this work but also by work in Part 3.

Part 2. Among variational theories of electronic structure, the Hartree-Fock theory has proved particularly valuable for a practical understanding of such properties as chemical binding, electric multipole moments, and X-ray scattering intensity. It also provides the most tractable method of calculating first-order properties under external or internal one-electron perturbations, either developed explicitly in orders of perturbation theory or in the fully self-consistent method. The accuracy and consistency of first-order properties are poorer than those of zero-order properties, but this is most often due to the use of explicit approximations in solving the perturbed equations, or to inadequacy of the variational basis in size or composition. We have calculated the electric polarizabilities of H₂, He, Li, Be, LiH, and N₂ by Hartree-Fock theory, using exact perturbation theory or the fully self-consistent method, as dictated by convenience. By careful studies on total basis set composition, we obtained good approximations to limiting Hartree-Fock values of polarizabilities with bases of reasonable size. The values for all species, and for each direction in the molecular cases, are within 8% of experiment, or of best theoretical values in the absence of the former. Our results support the use of unadorned Hartree-Pock theory for static polarizabilities needed in interpreting electron-molecule scattering data, collision-induced light scattering experiments, and other phenomena involving experimentally inaccessible polarizabilities.

Part 3. Numerical integration of the close-coupled scattering equations has been carried out to obtain vibrational transition probabilities for some models of the electronically adiabatic H₂-H₂ collision. All the models use a Lennard-Jones interaction potential between nearest atoms in the collision partners. We have analyzed the results for some insight into the vibrational excitation process in its dependence on the energy of collision, the nature of the vibrational binding potential, and other factors. We conclude also that replacement of earlier, simpler models of the interaction potential by the Lennard-Jones form adds very little realism for all the complication it introduces. A brief introduction precedes the presentation of our work and places it in the context of attempts to understand the collisional activation process in chemical reactions as well as some other chemical dynamics.

DIFFERENTIAL GEOMETRICAL METHODS IN THE STUDY OF OPTICAL-TRANSMISSION (SCALAR THEORY) .1. STATIC TRANSMISSION CASE

Static optical transmission is restudied by postulation of the optical path as the proper element in a three-dimensional Riemannian manifold (no torsion); this postulation can be applied to describe the light-medium interactive system. On the basis of the postulation, the behaviors of light transmitting through the medium with refractive index n are investigated, the investigation covering the realms of both geometrical optics and wave optics. The wave equation of light in static transmission is studied modally, the postulation being employed to derive the exact form of the optical field equation in a medium (in which the light is viewed as a single-component field). Correspondingly, the relationships concerning the conservation of optical fluid and the dynamic properties are given, and some simple applications of the theories mentioned are presented.

DIFFERENTIAL GEOMETRICAL METHODS IN THE STUDY OF OPTICAL-TRANSMISSION (SCALAR THEORY) .2. TIME-DEPENDENT TRANSMISSION THEORY

By generalization of the methods presented in Part I of the study [J. Opt. Soc. Am. A 12, 600 (1994)] to the four-dimensional (4D) Riemannian manifold case, the time-dependent behavior of light transmitting in a medium is investigated theoretically by the geodesic equation and curvature in a 4D manifold. In addition, the field equation is restudied, and the 4D conserved current of the optical fluid and its conservation equation are derived and applied to deduce the time-dependent general refractive index. On this basis the forces acting on the fluid are dynamically analyzed and the self-consistency analysis is given.

Holmium laser in-band pumped by a thulium laser in the same host of YAlO<inf>3inf>

We report on the room-temperature continuous-wave (CW) operation of a Ho:YAlO3 laser that is resonantly end pumped at 1.94 mu m by a diode-pumped thulium-doped laser in the same host. Through the use of a 1 at % Ho3+-doped 20-mm-long YAlO3 crystal (b cut), the Ho:YAlO3 laser generated 1 W of linearly polarized (E//c) output at 2118 nm and 0.55 W of E//a output at 2128.5 nm for an incident pump power of 5 W, with an output coupler transmission of 14 and 3%, respectively. An optical-to-optical conversion efficiency of 20% and a slope efficiency of 33% were achieved at 2118 nm corresponding to an incident pump power.