Analytical solutions for black-hole critical behaviour

Dynamical Einstein cluster is a spherical self-gravitating system of counterrotating particles, which may expand, oscillate and collapse. This system exhibits critical behaviour in its collapse at the threshold of black hole formation. It appears when the specific angular momentum of particles is tuned finely to the critical value. We find the unique exact self-similar solution at the threshold. This solution begins with a regular surface, involves timelike naked singularity formation and asymptotically approaches a static self-similar cluster.Comment: 4 pages, 3 figures, accepted for publication in General Relativity and Gravitation, typos correcte

Rebounce and Black hole formation in a Gravitational Collapse Model with Vanishing Radial Pressure

We examine spherical gravitational collapse of a matter model with vanishing radial pressure and non-zero tangential pressure. It is seen analytically that the collapsing cloud either forms a black hole or disperses depending on values of the initial parameters which are initial density, tangential pressure and velocity profile of the cloud. A threshold of black hole formation is observed near which a scaling relation is obtained for the mass of black hole, assuming initial profiles to be smooth. The similarities in the behaviour of this model at the onset of black hole formation with that of numerical critical behaviour in other collapse models are indicated.Comment: 15 pages, To be published in Gen.Rel.Gra

Bondian frames to couple matter with radiation

A study is presented for the non linear evolution of a self gravitating distribution of matter coupled to a massless scalar field. The characteristic formulation for numerical relativity is used to follow the evolution by a sequence of light cones open to the future. Bondian frames are used to endow physical meaning to the matter variables and to the massless scalar field. Asymptotic approaches to the origin and to infinity are achieved; at the boundary surface interior and exterior solutions are matched guaranteeing the Darmois--Lichnerowicz conditions. To show how the scheme works some numerical models are discussed. We exemplify evolving scalar waves on the following fixed backgrounds: A) an atmosphere between the boundary surface of an incompressible mixtured fluid and infinity; B) a polytropic distribution matched to a Schwarzschild exterior; C) a Schwarzschild- Schwarzschild spacetime. The conservation of energy, the Newman--Penrose constant preservation and other expected features are observed.Comment: 20 pages, 6 figures; to appear in General Relativity and Gravitatio

On the Singularity Structure and Stability of Plane Waves

We describe various aspects of plane wave backgrounds. In particular, we make explicit a simple criterion for singularity by establishing a relation between Brinkmann metric entries and diffeomorphism-invariant curvature information. We also address the stability of plane wave backgrounds by analyzing the fluctuations of generic scalar modes. We focus our attention on cases where after fixing the light-cone gauge the resulting world sheet fields appear to have negative "mass terms". We nevertheless argue that these backgrounds may be stable.Comment: 21 pages, 1 figur

Solar Wakes of Dark Matter Flows

We analyze the effect of the Sun's gravitational field on a flow of cold dark matter (CDM) through the solar system in the limit where the velocity dispersion of the flow vanishes. The exact density and velocity distributions are derived in the case where the Sun is a point mass. The results are extended to the more realistic case where the Sun has a finite size spherically symmetric mass distribution. We find that regions of infinite density, called caustics, appear. One such region is a line caustic on the axis of symmetry, downstream from the Sun, where the flow trajectories cross. Another is a cone-shaped caustic surface near the trajectories of maximum scattering angle. The trajectories forming the conical caustic pass through the Sun's interior and probe the solar mass distribution, raising the possibility that the solar mass distribution may some day be measured by a dark matter detector on Earth. We generalize our results to the case of flows with continuous velocity distributions, such as that predicted by the isothermal model of the Milky Way halo.Comment: 30 pages, 8 figure

String Cosmology: The Pre-Big Bang Scenario

A review is attempted of physical motivations, theoretical and phenomenological aspects, as well as outstanding problems, of the pre-big bang scenario in string cosmology.Comment: 46 pages, 8 Figures, Latex, Lectures delivered in Les Houches, July 199

The Similarity Hypothesis in General Relativity

Self-similar models are important in general relativity and other fundamental theories. In this paper we shall discuss the ``similarity hypothesis'', which asserts that under a variety of physical circumstances solutions of these theories will naturally evolve to a self-similar form. We will find there is good evidence for this in the context of both spatially homogenous and inhomogeneous cosmological models, although in some cases the self-similar model is only an intermediate attractor. There are also a wide variety of situations, including critical pheneomena, in which spherically symmetric models tend towards self-similarity. However, this does not happen in all cases and it is it is important to understand the prerequisites for the conjecture.Comment: to be submitted to Gen. Rel. Gra

Cognitive reserve moderates the association between cerebral blood flow and language performance in older adults with mild cognitive impairment

Higher cognitive reserve (CR) may offer protection from cognitive changes associated with reduced cerebral blood flow (CBF). We investigated CR as a moderator of the effect of CBF on cognition in older adults with mild cognitive impairment (MCI; N = 46) and those who are cognitively unimpaired (CU; N = 101). Participants underwent arterial spin labeling MRI, which was used to quantify CBF in 4 a priori regions. Estimated verbal intelligence quotient (VIQ) served as a proxy for CR. Multiple linear regressions examined whether VIQ moderated associations between CBF and cognition and whether this differed by cognitive status. Outcomes included memory and language performance. There were 3-way interactions (CBF*VIQ*cognitive status) on category fluency when examining hippocampal, superior frontal, and inferior frontal CBF. Follow-up analyses revealed that, within the MCI but not CU group, there were CBF*VIQ interactions on fluency in all a priori regions examined, where there were stronger, positive associations between CBF and fluency at higher VIQ. Conclusion: In MCI, higher CR plays a role in strengthening CBF-fluency associations. © 2023 The AuthorsOpen access articleThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Comparing neuropsychological, typical, and ADNI criteria for the diagnosis of mild cognitive impairment in Vietnam-era veterans

Objective: Neuropsychological criteria for mild cognitive impairment (MCI) more accurately predict progression to Alzheimer’s disease (AD) and are more strongly associated with AD biomarkers and neuroimaging profiles than ADNI criteria. However, research to date has been conducted in relatively healthy samples with few comorbidities. Given that history of traumatic brain injury (TBI) and post-traumatic stress disorder (PTSD) are risk factors for AD and common in Veterans, we compared neuropsychological, typical (Petersen/Winblad), and ADNI criteria for MCI in Vietnam-era Veterans with histories of TBI or PTSD. Method: 267 Veterans (mean age = 69.8) from the DOD-ADNI study were evaluated for MCI using neuropsychological, typical, and ADNI criteria. Linear regressions adjusting for age and education assessed associations between MCI status and AD biomarker levels (cerebrospinal fluid [CSF] p-tau181, t-tau, and Aβ42) by diagnostic criteria. Logistic regressions adjusting for age and education assessed the effects of TBI severity and PTSD symptom severity simultaneously on MCI classification by each criteria. Results: Agreement between criteria was poor. Neuropsychological criteria identified more Veterans with MCI than typical or ADNI criteria, and were associated with higher CSF p-tau181 and t-tau. Typical and ADNI criteria were not associated with CSF biomarkers. PTSD symptom severity predicted MCI diagnosis by neuropsychological and ADNI criteria. History of moderate/severe TBI predicted MCI by typical and ADNI criteria. Conclusions: MCI diagnosis using sensitive neuropsychological criteria is more strongly associated with AD biomarkers than conventional diagnostic methods. MCI diagnostics in Veterans would benefit from incorporation of comprehensive neuropsychological methods and consideration of the impact of PTSD. © U.S. Department of Veterans Affairs, 2024.Immediate accessThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]