Spherically-symmetric solutions in general relativity using a tetrad-based approach

We present a tetrad-based method for solving the Einstein field equations for spherically-symmetric systems and compare it with the widely-used Lemaître–Tolman–Bondi (LTB) model. In particular, we focus on the issues of gauge ambiguity and the use of comoving versus ‘physical’ coordinate systems. We also clarify the correspondences between the two approaches, and illustrate their differences by applying them to the classic examples of the Schwarzschild and Friedmann–Lemaître–Robertson–Walker spacetimes. We demonstrate that the tetrad-based method does not suffer from the gauge freedoms inherent to the LTB model, naturally accommodates non-uniform pressure and has a more transparent physical interpretation. We further apply our tetrad-based method to a generalised form of ‘Swiss cheese’ model, which consists of an interior spherical region surrounded by a spherical shell of vacuum that is embedded in an exterior background universe. In general, we allow the fluid in the interior and exterior regions to support pressure, and do not demand that the interior region be compensated. We pay particular attention to the form of the solution in the intervening vacuum region and illustrate the validity of Birkhoff’s theorem at both the metric and tetrad level. We then reconsider critically the original theoretical arguments underlying the so-called \(R_{\mathrm{h}} = ct\) cosmological model, which has recently received considerable attention. These considerations in turn illustrate the interesting behaviour of a number of ‘horizons’ in general cosmological models.     

Review and suggested resolution of the problem of Schrodinger’s cat

This paper reviews and suggests a resolution of the problem of definite outcomes of measurement. This problem, also known as ‘Schrodinger’s cat’, has long posed an apparent paradox because the state resulting from a measurement appears to be a quantum superposition in which the detector is in two macroscopically distinct states (alive and dead in the case of the cat) simultaneously. Many alternative interpretations of the quantum mathematical formalism, and several alternative modifications of the theory, have been proposed to resolve this problem, but no consensus has formed supporting any one of them. Applying standard quantum theory to the measurement state, together with the analysis and results of decades of nonlocality experiments with pairs of entangled systems, this paper shows the entangled measurement state is not a paradoxical macroscopic superposition of states. It is instead a phase-dependent superposition of correlations between states of the subsystems. Thus Schrodinger’s cat is a non-paradoxical ‘macroscopic correlation’ in which one of the two correlated systems happens to be a detector. This insight resolves the problem of definite outcomes but it does not entirely resolve the measurement problem because the entangled state is still reversible.     

Frequency/temperature relationships of c.w. IMPATT diodes

Some measurements of the relationship between frequency and ambient temperature for c.w. IMPATT diodes are reported. Several diodes have been characterised between 9 and 13 GHz for various bias and coupling conditions. An interpretation of the results is presented on the basis of several simple models. Reasonable agreement with experiment is observed, considering the limitations of the models.     

Angle modulation of frequency locked Gunn oscillators

It is shown experimentally and theoretically that frequency modulation through the bias circuit of free-running Gunn oscillators at low modulation frequencies can be converted to an equivalent phase modulation by frequency locking. Judicious choice of locking bandwidth causes the low-frequency phase-modulation coefficient to be of the same order of magnitude as that measured at high modulation frequencies. The phase-modulation coefficient at high frequencies is unaltered by frequency locking.     

Note on the relationship between the domain-transit frequency and the cavity-controlled frequency of thin Gunn devices

Some measurements on thin Gunn devices mounted in cavities covering the range 7?20GHz are reported. For any particular device, it has been found that VBf is approximately constant, where VB is the bias voltage which gives maximum r.f. output at the frequency f. This observation has been related to the domain-transit frequency.     

Ambient-temperature effects in transferred-electron amplifiers

The effect of ambient temperature on the gain and centre frequency of transferred-electron reflection amplifiers is reported for devices with n+ or metal-alloy cathode contacts. The dependence of the centre frequency on temperature was much stronger than predicted theoretically, and, contrary to expectation, similar performance was obtained from both types of diode.     

A comparison of the Shannon and Kullback information measures

Two widely used information measures are compared. It is shown that the Kullback measure, unlike the Shannon measure, provides the basis for a consistent theory of information which extends to continuous sample spaces and to nonconstant prior distributions. It is shown that the Kullback measure is a generalization of the Shannon measure, and that the Kullback measure has more reasonable additivity properties than does the Shannon measure. The results lend support to Jaynes's entropy maximization procedure.     

Materials for capacitive carbon dioxide microsensors capable of operating at ambient temperatures

The responses of alkylamine functionalized organic bridged polysilsesquioxanes on chemicapacitive sensors to carbon dioxide (CO₂) are described operating at temperatures ranging from 15 to 50°C. These hybrid organic–inorganic network materials were synthesized by the sol–gel polymerization of a mixture of a matrix monomer and functional monomer at various ratios followed by aging and ink-jet deposition of the sol on each capacitive sensor. During exposure of the sensor to known concentrations of analyte, the material’s capacitance was measured. From these changes in capacitance, detection limits ranging from 40 to 100 ppm were calculated. Furthermore, a correlation was observed with increasing length of the alkyl chain in the amine monomer correlating with an increase in CO₂ sensitivity and a decrease in water sensitivity. These materials offer a new method for CO₂ detection for building control systems or other low-power applications using low operating temperatures.