Comment on Ricci Collineations of Static Spherically Symmetric Spacetimes

We present a counter example to a theorem given by Amir {\em et al.} J. Math. Phys. {\bf 35}, 3005 (1994). We also comment on a misleading statements of the same reference.Comment: 4 pages,LaTex fil

Ricci Collineations for Non-Degenerate, Diagonal and Spherically Symmetric Ricci Tensors

The expression of the vector field generator of a Ricci Collineation for diagonal, spherically symmetric and non-degenerate Ricci tensors is obtained. The resulting expressions show that the time and radial first derivatives of the components of the Ricci tensor can be used to classify the collineation, leading to 64 families. Some examples illustrate how to obtain the collineation vector

Ricci Collineations of the Bianchi Type II, VIII, and IX Space-times

Ricci and contracted Ricci collineations of the Bianchi type II, VIII, and IX space-times, associated with the vector fields of the form (i) one component of $\xi^a(x^b)$ is different from zero and (ii) two components of $\xi^a(x^b)$ are different from zero, for $a,b=1,2,3,4$, are presented. In subcase (i.b), which is $\xi^a= (0,\xi^2(x^a),0,0)$, some known solutions are found, and in subcase (i.d), which is $\xi^a =(0,0,0,\xi^4(x^a))$, choosing $S(t)=const.\times R(t)$, the Bianchi type II, VIII, and IX space-times is reduced to the Robertson-Walker metric.Comment: 12 Pages, LaTeX, 1 Table, no figure

Classification of Spherically Symmetric Static Spacetimes according to their Matter Collineations

The spherically symmetric static spacetimes are classified according to their matter collineations. These are studied when the energy-momentum tensor is degenerate and also when it is non-degenerate. We have found a case where the energy-momentum tensor is degenerate but the group of matter collineations is finite. For the non-degenerate case, we obtain either {\it four}, {\it five}, {\it six} or {\it ten} independent matter collineations in which four are isometries and the rest are proper. We conclude that the matter collineations coincide with the Ricci collineations but the constraint equations are different which on solving can provide physically interesting cosmological solutions.Comment: 15 pages, no figure, Late

Ricci Collineations for type B warped space-times

We present the general structure of proper Ricci Collineations (RC) for type B warped space-times. Within this framework, we give a detailed description of the most general proper RC for spherically symmetric metrics. As examples, static spherically symmetric and Friedmann-Robertson-Walker space-times are considered.Comment: 18 pages, Latex, To appear in GR

Assessment of Night Vision Problems in Patients with Congenital Stationary Night Blindness

Congenital Stationary Night Blindness (CSNB) is a retinal disorder caused by a signal transmission defect between photoreceptors and bipolar cells. CSNB can be subdivided in CSNB2 (rod signal transmission reduced) and CSNB1 (rod signal transmission absent). The present study is the first in which night vision problems are assessed in CSNB patients in a systematic way, with the purpose of improving rehabilitation for these patients. We assessed the night vision problems of 13 CSNB2 patients and 9 CSNB1 patients by means of a questionnaire on low luminance situations. We furthermore investigated their dark adapted visual functions by the Goldmann Weekers dark adaptation curve, a dark adapted static visual field, and a two-dimensional version of the ‘‘Light Lab’’. In the latter test, a digital image of a living room with objects was projected on a screen. While increasing the luminance of the image, we asked the patients to report on detection and recognition of objects. The questionnaire showed that the CSNB2 patients hardly experienced any night vision problems, while all CSNB1 patients experienced some problems although they generally did not describe them as severe. The three scotopic tests showed minimally to moderately decreased dark adapted visual functions in the CSNB2 patients, with differences between patients. In contrast, the dark adapted visual functions of the CSNB1 patients were more severely affected, but showed almost no differences between patients. The results from the ‘‘2D Light Lab’’ showed that all CSNB1 patients were blind at low intensities (equal to starlight), but quickly regained vision at higher intensities (full moonlight). Just above their dark adapted thresholds both CSNB1 and CSNB2 patients had normal visual fields. From the results we conclude that night vision problems in CSNB, in contrast to what the name suggests, are not conspicuous and generally not disabling

Linear regression between the intensity at which 50% of the objects were detected (i50_d) or recognized (i50_r) and the visual acuity.

<p>The lines resemble the simple linear regression fits. A: The Pearson correlation coefficient for i50_d and the visual acuity was <i>R</i> = 0.84, p<0.01 for the CSNB2 patients, and <i>R</i> = 0.41, p>0.05 for the CSNB1 patients. B: The Pearson correlation coefficient for i50_r and the visual acuity was <i>R</i> = 0.92, p<0.01 for the CSNB2 patients, and <i>R</i> = 0.86, p<0.01 for the CSNB1 patients.</p

Statistical analyses of slope_d, slope_r, i50_d, i50_r, and the difference between i50_d and i50_r (i50_r–i50_d) between control subjects, CSNB2, and CSNB1 patients.

<p>Analyses were performed through One-Way ANOVA tests (overall effect) and Bonferroni corrected Post Hoc tests for pairwise multiple comparisons.</p>**<p><i>p</i>-value <0.001.</p>*<p><i>p</i>-value <0.05.</p><p>n.s. not significantly different.</p

Results of Parts 4 to 7 of the questionnaire.

<p>Top: answers of CSNB2 patients. Bottom: answers of CSNB1 patients. The black horizontal lines indicate the medians. The grey vertical lines extend from the first quartile to the third quartile and thus indicate the range of the mid 50% ranked answers. A black dot is used when the mid 50% ranked date contained one answer only.</p

Scotopic visual field results of the normal subjects, the CSNB2 patients, and the CSNB1 patients.

<p>A: The threshold found at each location of the scotopic visual field, plotted per subject. The open markers represent the average threshold found in that subject. The dashed lines indicate the measuring range, which was 28 to 75 dB in control subjects and CSNB2 patients, and 0 to 47 dB in CSNB1 patients. We found slightly elevated thresholds in CSNB2 patients compared to the thresholds of normal subjects. The thresholds were more elevated in the CSNB1 patients. B: The averaged thresholds of four locations at 7°, 45°, 60° and 75° on the horizontal axes per subject. Thresholds were slightly elevated towards the far end of the visual field in control subjects. We found an equal decline in the control subjects, the CSNB2 and the CSNB1 patients.</p