Background: Cross-sectional survey of ocular biometry and visual function in healthy eyes across the life span of a German population aged 20 to 69 years (n = 218). Subject number in percent per age category reflected the percentage within the respective age band of the population of Leipzig, Germany. Methods: Measurements obtained: subjective and objective refraction, best-corrected visual acuity, accommodation, contrast sensitivity, topography and pachymetry with Scheimpflug camera, axial length with non-contact partial coherence interferometry, and spectral-domain optical coherence tomography of the retina. Pearson correlation coefficients with corresponding p-values were given to present interrelationships between stature, biometric and refractive parameters or their associations with age. Two-sample T-tests were used to calculate gender differences. The area under the logarithmic contrast sensitivity function (AULCSF) was calculated for the analysis of contrast sensitivity as a single figure across a range of spatial frequencies. Results: The results of axial length (AL), anterior chamber depth (ACD) and anterior chamber volume (ACV) differed as a function of the age of the participants (rho (p value): AL −0.19 (0.006), ACD −0.56 (< 0.001), ACV-0.52 (< 0.001)). Longer eyes had deeper ACD (AL:ACD 0.62 (< 0.001), greater ACV (AL:ACV 0.65 (< 0.001) and steeper corneal radii (AL:R1ant; R2ant; R1post; R2post 0.40; 0.35; 0.36; 0.36 (all with (< 0.001)). Spherical equivalent was associated with age (towards hyperopia: 0.34 (< 0.001)), AL (−0.66 (< 0.001)), ACD (−0.52 (< 0.001)) and ACV (−0.46 (< 0.001)). Accommodation was found lower for older subjects (negative association with age, r = −0.82 (< 0.001)) and contrast sensitivity presented with smaller values for older ages (AULCSF −0.38, (< 0.001)), no change of retinal thickness with age. 58 % of the study cohort presented with a change of refractive correction above ±0.50 D in one or both eyes (64 % of these were habitual spectacle wearers), need for improvement was present in the young age-group and for older subjects with increasing age. Conclusion: Biometrical data of healthy German eyes, stratified by age, gender and refractive status, enabled cross-comparison of all parameters, providing an important reference database for future patient-based research and specific in-depth investigations of biometric data in epidemiological research. Trial registration: ClinicalTrials.gov # NCT01173614 July 28, 2010

Background: Cross-sectional survey of ocular biometry and visual function in healthy eyes across the life span of a German population aged 20 to 69 years (n = 218). Subject number in percent per age category reflected the percentage within the respective age band of the population of Leipzig, Germany. Methods: Measurements obtained: subjective and objective refraction, best-corrected visual acuity, accommodation, contrast sensitivity, topography and pachymetry with Scheimpflug camera, axial length with non-contact partial coherence interferometry, and spectral-domain optical coherence tomography of the retina. Pearson correlation coefficients with corresponding p-values were given to present interrelationships between stature, biometric and refractive parameters or their associations with age. Two-sample T-tests were used to calculate gender differences. The area under the logarithmic contrast sensitivity function (AULCSF) was calculated for the analysis of contrast sensitivity as a single figure across a range of spatial frequencies. Results: The results of axial length (AL), anterior chamber depth (ACD) and anterior chamber volume (ACV) differed as a function of the age of the participants (rho (p value): AL −0.19 (0.006), ACD −0.56 (< 0.001), ACV-0.52 (< 0.001)). Longer eyes had deeper ACD (AL:ACD 0.62 (< 0.001), greater ACV (AL:ACV 0.65 (< 0.001) and steeper corneal radii (AL:R1ant; R2ant; R1post; R2post 0.40; 0.35; 0.36; 0.36 (all with (< 0.001)). Spherical equivalent was associated with age (towards hyperopia: 0.34 (< 0.001)), AL (−0.66 (< 0.001)), ACD (−0.52 (< 0.001)) and ACV (−0.46 (< 0.001)). Accommodation was found lower for older subjects (negative association with age, r = −0.82 (< 0.001)) and contrast sensitivity presented with smaller values for older ages (AULCSF −0.38, (< 0.001)), no change of retinal thickness with age. 58 % of the study cohort presented with a change of refractive correction above ±0.50 D in one or both eyes (64 % of these were habitual spectacle wearers), need for improvement was present in the young age-group and for older subjects with increasing age. Conclusion: Biometrical data of healthy German eyes, stratified by age, gender and refractive status, enabled cross-comparison of all parameters, providing an important reference database for future patient-based research and specific in-depth investigations of biometric data in epidemiological research. Trial registration: ClinicalTrials.gov # NCT01173614 July 28, 2010

Some branches of quantum gravity demand the existence of higher dimensions and the addition of higher curvature terms to the gravitational Lagrangian in the form of the Lovelock polynomials. In this thesis we investigate some of the classical properties of Lovelock gravity. We first derive the Hamiltonian for Lovelock gravity and find that it takes the same form as in general relativity when written in terms of the Misner-Sharp mass function. We then minimally couple the action to matter fields to find Hamilton’s equations of motion. These are gauge fixed to be in the Painleve-Gullstrand co–ordinates and are well suited to numerical studies of black hole formation. We then use these equations of motion for the massless scalar field to study the formation of general relativistic black holes in four to eight dimensions and Einstein-Gauss-Bonnet black holes in five and six dimensions. We study Choptuik scaling, a phenomenon which relates the initial conditions of a matter distribution to the final observables of small black holes. In both higher dimensional general relativity and Einstein-Gauss-Bonnet gravity we confirm the existence of cusps in the mass scaling relation which had previously only been observed in four dimensional general relativity. In the general relativistic case we then calculate the critical exponents for four to eight dimensions and find agreement with previous calculations by Bland et al but not Sorkin et al who both worked in null co–ordinates. For the Einstein-Gauss-Bonnet case we find that the self-similar behaviour seen in the general relativistic case is destroyed. We find that it is replaced by some other form of scaling structure. In five dimensions we find that the period of the critical solution at the origin is proportional to roughly the cube root of the Gauss-Bonnet parameter and that there is evidence for a minimum black hole radius. In six dimensions we see evidence for a new type of scaling. We also show, from the equations of motion, that there is reason to expect qualitative differences between five and higher dimensions.

Some branches of quantum gravity demand the existence of higher dimensions and the addition of higher curvature terms to the gravitational Lagrangian in the form of the Lovelock polynomials. In this thesis we investigate some of the classical properties of Lovelock gravity. We first derive the Hamiltonian for Lovelock gravity and find that it takes the same form as in general relativity when written in terms of the Misner-Sharp mass function. We then minimally couple the action to matter fields to find Hamilton’s equations of motion. These are gauge fixed to be in the Painleve-Gullstrand co–ordinates and are well suited to numerical studies of black hole formation. We then use these equations of motion for the massless scalar field to study the formation of general relativistic black holes in four to eight dimensions and Einstein-Gauss-Bonnet black holes in five and six dimensions. We study Choptuik scaling, a phenomenon which relates the initial conditions of a matter distribution to the final observables of small black holes. In both higher dimensional general relativity and Einstein-Gauss-Bonnet gravity we confirm the existence of cusps in the mass scaling relation which had previously only been observed in four dimensional general relativity. In the general relativistic case we then calculate the critical exponents for four to eight dimensions and find agreement with previous calculations by Bland et al but not Sorkin et al who both worked in null co–ordinates. For the Einstein-Gauss-Bonnet case we find that the self-similar behaviour seen in the general relativistic case is destroyed. We find that it is replaced by some other form of scaling structure. In five dimensions we find that the period of the critical solution at the origin is proportional to roughly the cube root of the Gauss-Bonnet parameter and that there is evidence for a minimum black hole radius. In six dimensions we see evidence for a new type of scaling. We also show, from the equations of motion, that there is reason to expect qualitative differences between five and higher dimensions.

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