Null Cones in Lorentz-Covariant General Relativity

The oft-neglected issue of the causal structure in the flat spacetime approach to Einstein's theory of gravity is considered. Consistency requires that the flat metric's null cone be respected, but this does not happen automatically. After reviewing the history of this problem, we introduce a generalized eigenvector formalism to give a kinematic description of the relation between the two null cones, based on the Segre' classification of symmetric rank 2 tensors with respect to a Lorentzian metric. Then we propose a method to enforce special relativistic causality by using the naive gauge freedom to restrict the configuration space suitably. A set of new variables just covers this smaller configuration space and respects the flat metric's null cone automatically. In this smaller space, gauge transformations do not form a group, but only a groupoid. Respecting the flat metric's null cone ensures that the spacetime is globally hyperbolic, indicating that the Hawking black hole information loss paradox does not arise.Comment: groupoid nature of gauge transformations explained; shortened, new references, 102 page

Null Cones and Einstein's Equations in Minkowski Spacetime

If Einstein's equations are to describe a field theory of gravity in Minkowski spacetime, then causality requires that the effective curved metric must respect the flat background metric's null cone. The kinematical problem is solved using a generalized eigenvector formalism based on the Segr\'{e} classification of symmetric rank 2 tensors with respect to a Lorentzian metric. Securing the correct relationship between the two null cones dynamically plausibly is achieved using the naive gauge freedom. New variables tied to the generalized eigenvector formalism reduce the configuration space to the causality-respecting part. In this smaller space, gauge transformations do not form a group, but only a groupoid. The flat metric removes the difficulty of defining equal-time commutation relations in quantum gravity and guarantees global hyperbolicity

Light Cone Consistency in Bimetric General Relativity

General relativity can be formally derived as a flat spacetime theory, but the consistency of the resulting curved metric's light cone with the flat metric's null cone has not been adequately considered. If the two are inconsistent, then gravity is not just another field in flat spacetime after all. Here we discuss recent progress in describing the conditions for consistency and prospects for satisfying those conditions.Comment: contribution to the Proceedings of the 20th Texas Symposium on Relativistic Astrophysics; 3 pages, 1 figur

Study of Chromium-Frit-Type Coatings for High-Temperature Protection of Molybdenum

The achievement of more compact and efficient power plants for aircraft is dependent, among other factors, on the perfection of heat-resisting materials that are superior to those in current use. Molybdenum is one of the high-melting metals (melting point, 4750 F). It is fairly abundant and also can be worked into many of the shapes required in modern power plants. To permit its widespread use at elevated temperatures, however, some means must first be found to prevent its rapid oxidation. The application of a protective coating is one method that might be used to achieve this goal. In the present work, a number of chromium-frit-type coatings were studied. These were bonded to molybdenum specimens by firing in controlled atmospheres to temperatures in the range of 2400 to 2700 F

Moderate temperature rechargeable sodium batteries

Cells utilizing the organic electrolyte, NaI in triglyme, operated at approx. 130 C with Na(+) - intercalating cathodes. However, their rate and stability were inadequate. NaAlCl4 was found to be a highly useful electrolyte for cell operation at 165-190 C. Na(+) intercalating chalcogenides reacted with NaAlCl4 during cycling to form stable phases. Thus, VS2 became essentially VS2Cl, with reversible capacity of approx 2.8 e(-)/V, and a mid-discharge voltage of approx 2.5V and 100 deep discharge cycles were readily achieved. A positive electrode consisting of VCl3 and S plus NaAlCl4 was subjected to deep-discharge cycles 300 times and it demonstrated identity with the in-situ-formed BSxCly cathode. NiS2 and NiS which are not Na(+)-intercalating structures formed highly reversible electrodes in NaAlCl4. The indicated discharge mechanism implies a theoretical capacity 4e(-)/Ni for NiS2 and 2e(-)/Ni for NiS. The mid-discharge potentials are, respectively, 2.4V and 2.1V. A Na/NiS2 cell cycling at a C/5 rate has exceeded 500 deep discharge cycles with 2.5e(-)/Ni average utilization. A 4 A-hr nominal capacity prototype Na/NiS2 cell was tested at 190 C. It was voluntarily terminated after 80 cycles. Further development, particularly of cathode structure and hardware should produce a battery capable of at least 50-W-hr/lb and more than 1000 cycles

Hydroxyl radical oxidation of phospholipid-coated NaCl particles.

Biological organic compounds mixed with NaCl and other inorganic compounds in sea-salt aerosol particles react in air with oxidants such as ozone and hydroxyl (OH) radicals. Laboratory studies of model systems can provide insight into these reactions. We report here studies of the kinetics and mechanism of oxidation of unsaturated 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) on NaCl by gas phase OH in air at room temperature and 1 atm pressure using diffuse reflection infrared Fourier transform spectrometry (DRIFTS) and matrix-assisted laser desorption/ionization-time-of-flight-mass spectrometry (MALDI-TOF-MS) to identify possible structures of surface-bound reaction products. For comparison, some studies were also carried out on the saturated 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) on NaCl. The calculated concentration of hydroxyl radicals, generated by photolysis of isopropyl nitrite, was (1.6-6.4) × 10(8) radicals cm(-3). Surface-bound aldehydes, ketones, organic nitrates and nitrate ions were identified as products of these reactions and structures of potential products were proposed based on mechanistic considerations combined with the MALDI-TOF-MS and DRIFTS spectra. The loss rate of vinyl hydrogen, =C-H, at 3008 cm(-1) was used to obtain a lower limit for the rate constant (k1) for addition of OH to the double bond, k1 > (3 ± 1) × 10(-13) cm(3) molecule(-1) s(-1) (1s), corresponding to a reaction probability of γ(add) > (4 ± 1) × 10(-3) (1s). Assuming that abstraction from -CH2- groups in POPC is the same as for DPPC, the percentage of the reaction that occurs by addition is ~80%. This is similar to the percent addition predicted using structure-reactivity relationships for gas-phase reactions. Decreasing the amount of POPC relative to NaCl resulted in more nitrate ion formation and less relative loss of POPC, and increasing the OH concentration resulted in a more rapid loss of POPC and faster product formation. These studies suggest that under atmospheric conditions with an OH concentration of 5 × 10(6) radicals cm(-3), the lifetime of POPC with respect to OH is <6 days