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Item Crenshaw transcripts 2023(0023-08-24) Crenshaw, Kenyatta; Elby, AndrewItem Vapor Pressures of Saturated Aqueous Salt Solutions of Selected Inorganic Salts(1965) Acheson, Donald Theodore; Mason, Edward A.; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md)The vapor pressure of saturated aqueous salt solutions as functions of temperature have been measured for lithium bromide, lithium iodide, sodium bromide, potassium hydroxide, cesium fluoride, and zinc bromide. The temperature range is about plus s 0 c. to 70°c., with this range extended from minus 10°c. to plus 105°c. for lithium bromide and restricted to plus s 0 c. to 35°c. for sodium bromide. Vapor pressures, water 0 activities, and heats of vaporization and solution are tabulated at 5 C. intervals except in the vicinities of changes of hydration of the solid phase, where pressures and activities are plotted with sufficient frequency to show details. The experimental uncertainty in pressure is + 10 x 10-3 millibars and that in the heat of solution is+ 2 percent.Item The Stability of the Schwarzschild Metric(1968) Vishveshwara, C. V.; Misner, Charles W.; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md)The stability of the Schwarzschild exterior metric against small perturbations is investigated. The exterior extending from the Schwarzschild radius r =2m to spatial infinity is visualized as having been produced by a spherically symmetric mass distribution that collapsed into the Schwarzschild horizon in the remote past. As a preamble to the stability analysis, the phenomenon of spherically symmetric gravitational collapse is discussed under the conditions of zero pressure, absence of rotation and adiabatic flow. This is followed by a brief study of the Kruskal coordinates in which the apparent singularity at r = 2m is no longer present; the process of spherical collapse and the consequent production of the Schwarzschild empty space geometry down to the Schwarzschild horizon are depicted on the Kruskal diagram. The perturbations superposed on the Schwarzschild background metric are the same as those given by Regge and Wheeler consisting of odd and even parity classes, and with the time dependence exp(-ikt), where k is the frequency. An analysis of the Einstein field equations computed to first order in the perturbations away from the Schwarzschild background metric shows that when the frequency is made purely imaginary, the solutions that vanish at large values of r, conforming to the requirement of asymptotic flatness, will diverge near the Schwarzschild surface in the Kruskal coordinates even at the initial instant t = 0. Since the background metric itself is finite at this surface, the above behaviour of the perturbation clearly contradicts the basic assumption that the perturbations are small compared to .the background metric. Thus perturbations with imaginary frequencies that grow exponentially with time are physically unacceptable and hence the metric is stable. In the case of the odd perturbations, the above proof of stability is made rigorous by showing that the radial functions for real values of k form a complete set, by superposition of which any well behaved initial perturbation can be represented so that the time development of such a perturbation is non-divergent, since each of the component modes is purely oscillatory in time. A similar rigorous extension of the proof of stability has not been possible in the case of the even perturbations because the frequency (or k2) does not appear linearly in the differential equation. A study of stationary perturbations (k = 0) shows that the only nontrivial stationary perturbation that can exist is that due to the rotation of the source which is given by the odd perturbation with the angular momentum £ = 1. Finally, complex frequencies are introduced under the boundary conditions of only outgoing waves at infinity and purely incoming waves at the Schwarzschild surface. The physical significance of this situation is discussed and its connection with phenomena such as radiation damping and resonance scattering, and with the idea of causality is pointed out.Item Almost Symmetric Spaces and Gravitational Radiation(1967) Matzner, Richard Alfred; Misner, Charles W.; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md)Item Gravitational Radiation in the Limit of High Frequency(1967) Isaacson, Richard Allen; Misner, Charles W.; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md)This dissertation deals with a technique for obtaining approximate radiative solutions to the Einstein equations of general relativity in situations where the gravitational fields of interest are quite strong. In the first chapter, we review the history of the problem and discuss previous work along related lines. In the second chapter, we assume the radiation to be of high frequency and expand the field equations in powers of the small wavelength this supplies. This assumption provides an approximation scheme valid for all orders of 1/r, for arbitrary velocities up to that of light, and for arbitrary intensities of the gravitational field. To lowest order we obtain a gauge invariant linear wave equation for gravitational radiation, which is a covariant generalization of that for massless spin-two fields in flat space, This wave equation is then solved by the W.K.B. approximation to show that gravitational waves travel on null geodesics with amplitude and frequency modified by gravitational fields in exactly the same way as are those of light waves, and with their polarization parallel transported along the geodesics, again as is the case for light. The metric containing high frequency gravitational waves is shown to be type N to lowest order, and some limits to the methods used are discussed. In the third chapter we go beyond the linear terms in the high frequency expansion, and consider the lowest order non-linear terms. They are shown to provide a natural, gauge invariant, averaged effective stress tensor for the energy localized in the high frequency radiation. By assuming the W.K.B. form for the field, this tensor is found to have the same structure as that for an electromagnetic null field. A Poynting vector is used to investigate the flow of energy and momentum in the gravitational wave field, and it is seen that high frequency waves propagate along null hypersurfaces and are not backscattered off by the curvature of space. Expressions for the total energy and momentum carried by the field to flat null infinity are given in terms of coordinate independent integrals valid within regions of strong field strength. The formalism is applied to the case of spherical gravitational waves where a news function is obtained, and where the source is found to lose exactly the energy and momentum contained in the radiation field.Item Infinite Red-Shifts in General Relativity(Cornell University Press, 1967) Misner, Charles W; Beckedorff, David LThe Oppenheimer-Snyder description of continued gravitational collapse is reformulated as a matching together of two familiar solutions of the Einstein gravitational equations. From one solution, the Friedmann cosmology with zero-pressure matter, one selects the interior of a sphere whose points move on timelike geodesics. From the other solution one selects the exterior of such a sphere in the vacuum Schwarzschild solution. For the expected choice of parameters (sphere circumference, interior density, exterior mass) these can be fit together smoothly enough to satisfy the Einstein equations. The matching conditions are that the first and second fundamental forms at the joining 3-surface agree. The description of this collapsing ball of matter survives its passage through Finkelstein's (1958) smooth unidirectional membrane€ at r=2M and is most conveniently presented using the Kruskal coordinates for the Schwarzschild solution. This project was proposed and designed by Misner (choice of solutions and matching requirements), but the execution and first written presentation were carried out by Beckedorff and provided his Princeton senior thesis in April 1962. ( http://www.physics.umd.edu/grt/cwm/Beckedorff1962.pdf ) In this 1963 presentation Misner emphasizes that the properties of matter at high densities are irrelevant to the question of whether such a collapse can occur for sufficiently massive objects. The detailed computations by Beckedorff are here linked in an appended file.