On the steady states of the spherically symmetric Einstein-Vlasov system

Using both numerical and analytical tools we study various features of static, spherically symmetric solutions of the Einstein-Vlasov system. In particular, we investigate the possible shapes of their mass-energy density and find that they can be multi-peaked, we give numerical evidence and a partial proof for the conjecture that the Buchdahl inequality $\sup_{r > 0} 2 m(r)/r < 8/9$, $m(r)$ the quasi-local mass, holds for all such steady states--both isotropic {\em and} anisotropic--, and we give numerical evidence and a partial proof for the conjecture that for any given microscopic equation of state--both isotropic {\em and} anisotropic--the resulting one-parameter family of static solutions generates a spiral in the radius-mass diagram.Comment: 34 pages, 18 figures, LaTe

Sharp bounds on 2m/r for static spherical objects

Sharp bounds are obtained, under a variety of assumptions on the eigenvalues of the Einstein tensor, for the ratio of the Hawking mass to the areal radius in static, spherically symmetric space-times.Comment: We changed a footnote in which an earlier result of H\aa{}kan Andr\'{e}asson was not described correctl

A numerical investigation of the stability of steady states and critical phenomena for the spherically symmetric Einstein-Vlasov system

The stability features of steady states of the spherically symmetric Einstein-Vlasov system are investigated numerically. We find support for the conjecture by Zeldovich and Novikov that the binding energy maximum along a steady state sequence signals the onset of instability, a conjecture which we extend to and confirm for non-isotropic states. The sign of the binding energy of a solution turns out to be relevant for its time evolution in general. We relate the stability properties to the question of universality in critical collapse and find that for Vlasov matter universality does not seem to hold.Comment: 29 pages, 10 figure

Global existence for the spherically symmetric Einstein-Vlasov system with outgoing matter

We prove a new global existence result for the asymptotically flat, spherically symmetric Einstein-Vlasov system which describes in the framework of general relativity an ensemble of particles which interact by gravity. The data are such that initially all the particles are moving radially outward and that this property can be bootstrapped. The resulting non-vacuum spacetime is future geodesically complete.Comment: 16 page

Sharp bounds on the critical stability radius for relativistic charged spheres

In a recent paper by Giuliani and Rothman \cite{GR}, the problem of finding a lower bound on the radius $R$ of a charged sphere with mass M and charge Q<M is addressed. Such a bound is referred to as the critical stability radius. Equivalently, it can be formulated as the problem of finding an upper bound on M for given radius and charge. This problem has resulted in a number of papers in recent years but neither a transparent nor a general inequality similar to the case without charge, i.e., M\leq 4R/9, has been found. In this paper we derive the surprisingly transparent inequality $$\sqrt{M}\leq\frac{\sqrt{R}}{3}+\sqrt{\frac{R}{9}+\frac{Q^2}{3R}}.$$ The inequality is shown to hold for any solution which satisfies $p+2p_T\leq\rho,$ where $p\geq 0$ and $p_T$ are the radial- and tangential pressures respectively and $\rho\geq 0$ is the energy density. In addition we show that the inequality is sharp, in particular we show that sharpness is attained by infinitely thin shell solutions.Comment: 20 pages, 1 figur

On the area of the symmetry orbits in T2T^2 symmetric spacetimes with Vlasov matter

This paper treats the global existence question for a collection of general relativistic collisionless particles, all having the same mass. The spacetimes considered are globally hyperbolic, with Cauchy surface a 3-torus. Furthermore, the spacetimes considered are isometrically invariant under a two-dimensional group action, the orbits of which are spacelike 2-tori. It is known from previous work that the area of the group orbits serves as a global time coordinate. In the present work it is shown that the area takes on all positive values in the maximal Cauchy development.Comment: 27 pages, version 2 minor changes and correction

Existence of initial data satisfying the constraints for the spherically symmetric Einstein-Vlasov-Maxwell system

Using ODE techniques we prove the existence of large classes of initial data satisfying the constraints for the spherically symmetric Einstein-Vlasov-Maxwell system. These include data for which the ratio of total charge to total mass is arbitrarily large.Comment: 12 page

Optimal consumption, investment and housing with means-tested public pension in retirement

© 2017 Elsevier B.V. In this paper, we develop an expected utility model for retirement behaviour in the decumulation phase of Australian retirees with sequential family status subject to consumption, housing, investment, bequest, and government-provided means-tested Age Pension. We account for mortality risk and risky investment assets, and we introduce a “health” proxy to capture the decreasing level of consumption for older retirees. Then, we find the optimal housing at retirement, the optimal consumption and optimal risky asset allocation depending on age and wealth. The model is solved numerically as a stochastic control problem, and it is calibrated using the maximum likelihood method with empirical data of consumption and housing from the Australian Bureau of Statistics 2009–2010 Survey. The model fits the characteristics of the data well to explain the behaviour of Australian retirees. The key findings are as follows. First, the optimal policy is highly sensitive to means-tested Age Pension early in retirement, but this sensitivity fades with age. Second, the allocation to risky assets shows a complex relationship with the means-tested Age Pension. As a general rule, when wealth decreases, the proportion allocated to risky assets increases, because the Age Pension works as a buffer against investment losses. Third, couples can be more aggressive with risky allocations owing to their longer life expectancy compared with singles

Isolation and properties of PS II membrane fragments depleted of the non heme iron center

AbstractThe functional properties and the content of non heme iron and cytochrome b559 were investigated by measuring flash induced transient changes of the relative fluorescence quantum yield and applying Mössbauer spectroscopy. It was found that untreated PS II membrane fragments contain a heterogeneous population of two types of non heme iron centers and about 2 cytochrome b559 per PS II. Twofold treatment of these samples with a recently described ‘iron depletion’ procedure (MacMillan, F., Lendzian, F., Renger, G. and Lubitz, W. (1995) Biochemistry 34, 3144–8156) leads to a complete loss (below the detection limit of Mössbauer spectroscopy) of the non heme iron center while more than 50% of the PS II complexes retain the functional integrity for light induced formation of the ‘stable’ radical pair YZOX P680Pheo QA−.. This sample type deprived of virtually all non heme iron in PS II provides a most suitable material for magnetic resonance studies that require an elimination of the interaction between Fe2+ and nearby radicals