Similarities Between Classical Timelike Geodesics in a Naked Reissner-Nordstrom Singularity Background and the Behaviour of Electrons in Quantum Theory

It is generally assumed that naked singularities must be physically excluded, as they could otherwise introduce unpredictable influences in their future null cones. Considering geodesics for a naked Reissner-Nordstrom singularity, it is found that the singularity is effectively clothed by its repulsive nature. Regarding electron as naked singularity, the size of the clothed singularity (electron) turns out to be classical electro-magnetic radius of the electron, to an observer falling freely from infinity, initially at rest. The size shrinks for an observer falling freely from infinity, with a positive initial velocity. For geodetic parameters corresponding to negative energy there are trapped geodesics. The similarity of this picture with that arising in the Quantum Theory is discussed.Comment: 8 pages, 6 figure

On the definition of matter collineations

It is shown that when the stress-energy tensor of a spacetime is diagonal and is written in the mixed form, its collineations admit infinite dimensional Lie algebras except possibly in the case when the tensor depends on all the spacetime coordinates. The result can be extended for more general second rank tensors

Drop size in a liquid pulsed sieve-plate extraction column

Peer reviewedPublisher PD

Asymptotic Behaviour of the Proper Length and Volume of the Schwarzschild Singularity

Though popular presentations give the Schwarzschild singularity as a point it is known that it is spacelike and not timelike. Thus it has a "length" and is not a "point". In fact, its length must necessarily be infinite. It has been proved that the proper length of the Qadir-Wheeler suture model goes to infinity [1], while its proper volume shrinks to zero, and the asymptotic behaviour of the length and volume have been calculated. That model consists of two Friedmann sections connected by a Schwarzschild "suture". The question arises whether a similar analysis could provide the asymptotic behaviour of the Schwarzschild black hole near the singularity. It is proved here that, unlike the behaviour for the suture model, for the Schwarzschild essential singularity $\Delta s$ $\thicksim$ $K^{1/3}\ln K$ and $V\thicksim$ $K^{-1}\ln K$, where $K$ is the mean extrinsic curvature, or the York time.Comment: 13 pages, 1 figur

The Relativistic Generalization of the Gravitational Force for Arbitrary Spacetimes

It has been suggested that re-expressing relativity in terms of forces could provide fresh insights. The formalism developed for this purpose only applied to static, or conformally static, space-times. Here we extend it to arbitrary space-times. It is hoped that this formalism may lead to a workable definition of mass and energy in relativity.Comment: 16 page

Weyl collineations that are not curvature collineations

Though the Weyl tensor is a linear combination of the curvature tensor, Ricci tensor and Ricci scalar, it does not have all and only the Lie symmetries of these tensors since it is possible, in principle, that "asymmetries cancel". Here we investigate if, when and how the symmetries can be different. It is found that we can obtain a metric with a finite dimensional Lie algebra of Weyl symmetries that properly contains the Lie algebra of curvature symmetries. There is no example found for the converse requirement. It is speculated that there may be a fundamental reason for this lack of "duality".Comment: 9 page

Response of face-selective brain regions to trustworthiness and gender of faces

Neuropsychological and neuroimaging studies have demonstrated a role for the amygdala in processing the perceived trustworthiness of faces, but it remains uncertain whether its responses are linear (with the greatest response to the least trustworthy-looking faces), or quadratic (with increased fMRI signal for the dimension extremes). It is also unclear whether the trustworthiness of the stimuli is crucial or if the same response pattern can be found for faces varying along other dimensions. In addition, the responses to perceived trustworthiness of face-selective regions other than the amygdala are seldom reported. The present study addressed these issues using a novel set of stimuli created through computer image-manipulation both to maximise the presence of naturally occurring cues that underpin trustworthiness judgments and to allow systematic manipulation of these cues. With a block-design fMRI paradigm, we investigated neural responses to computer-manipulated trustworthiness in the amygdala and core face-selective regions in the occipital and temporal lobes. We asked whether the activation pattern is specific for differences in trustworthiness or whether it would also track variation along an orthogonal male–female gender dimension. The main findings were quadratic responses to changes in both trustworthiness and gender in all regions. These results are consistent with the idea that face-responsive brain regions are sensitive to face distinctiveness as well as the social meaning of the face features

Dynamic Simulation Methods for Evaluating Motor Vehicle and Roadway Design and Resolving Policy Issues

This study had three objectives: (1) to develop a comprehensive truck simulation that executes rapidly, has a modular program construction to allow variation of vehicle characteristics, and is able to realistically predict vehicle motion and the tire-road surface interaction forces; (2) to develop a model of doweled portland cement concrete pavement that can be used to determine slab deflection and stress at predetermined nodes, and that allows for the variation of traditional thickness design factors; and (3) to implement these two models on a work station with suitable menu driven modules so that both existing and proposed pavements can be evaluated with respect to design life, given specific characteristics of the heavy vehicles that will be using the facility. This report summarizes the work that has been performed during the first year of the study. Briefly, the following has been accomplished: A two dimensional model of a typical 3-S2 tractor-trailer combination was created. A finite element structural analysis program, ANSYS, was used to model the pavement. Computer runs have been performed varying the parameters defining both vehicle and road elements. The resulting time specific displacements for each node are plotted, and the displacement basin is generated for defined vehicles. Relative damage to the pavement can then be estimated. A damage function resulting from load replications must be assumed that will be reflected by further pavement deterioration. Comparison with actual damage on Interstate 80 will eventually allow verification of these procedures

Is a Two-Day Cardiopulmonary Exercise Test a Valid Tool for The Diagnosis of Post-Exertional Malaise in Long COVID?

A two-day cardiopulmonary exercise testing (CPET) protocol (maximal ramp-incremental cycle test repeated 24hr apart) in myalgic encephalomyelitis/chronic fatigue syndrome (ME/CFS) patients has suggested that day-2 performance is decreased relative to day-1. This difference has been attributed to post-exertional malaise (PEM), suggesting the two-day CPET as a protocol to investigate PEM in Long COVID (LC) patients. PURPOSE: We aimed to investigate any effects of PEM on exercise performance and cardiorespiratory and perceptual responses to a two-day CPET in LC patients to determine whether the day-1 CPET would impair performance, cardiorespiratory responses or perceptions of exercise at day-2. METHODS: Fifteen LC patients with one or more symptoms persisting for more than three months after their initial infection [n=7 females; n=1 hospitalized; mean(SD); age 53(11) yrs; body mass index 32.2(8.5) kg/m2; time between COVID-19 onset and CPET 13(7) months; forced expiratory volume in 1 second 89(15) %pred; forced vital capacity 92(14) %pred; diffusing capacity of the lungs for carbon monoxide 92(15) %pred; total lung capacity 86(12) %pred] were studied. Prior to any exercise testing, PEM was assessed relative to the past six months using the modified DePaul Symptom Questionnaire (mDSQ) (0-4 symptoms frequency and severity scores). Each performed a two-day CPET protocol; ramp was 10-20 W/min, with the same ramp rate used for the day-1 and day-2 CPET. Peak oxygen uptake, peak work rate, and gas exchange threshold were measured using standard techniques. Ratings of perceived dyspnea and leg effort during cycling were recorded at peak exercise using the modified Borg’s Scale (0-10). One-sample t-tests were used to assess significance of test-retest mean difference. RESULTS: The mDSQ indicated the presence of PEM symptoms in 80% of participants. However, no significant differences between day-1 and day-2 CPET were found in any of the variables assessed. CONCLUSION: The absence of any difference in cardiorespiratory and perceptual responses in 2-day CPET testing, despite patient reported presence of PEM symptoms, suggests that the two-day CPET protocol may not be a valid tool for the diagnosis of PEM in LC patients