Birkhoff's theorem in the f(T) gravity

Generalized from the so-called teleparallel gravity which is exactly equivalent to general relativity, the $f(T)$ gravity has been proposed as an alternative gravity model to account for the dark energy phenomena. In this letter we prove that the external vacuum gravitational field for a spherically symmetric distribution of source matter in the $f(T)$ gravity framework must be static and the conclusion is independent of the radial distribution and spherically symmetric motion of the source matter that is, whether it is in motion or static. As a consequence, the Birkhoff's theorem is valid in the general $f(T)$ theory. We also discuss its application in the de Sitter space-time evolution phase as preferred to by the nowadays dark energy observations.Comment: 5p

Worldwide experience with a totally subcutaneous implantable defibrillator: Early results from the EFFORTLESS S-ICD registry

Aims The totally subcutaneous implantable-defibrillator (S-ICD) is a new alternative to the conventional transveno

Extended Birkhoff's Theorem in the f(T) Gravity

The f(T) theory, a generally modified teleparallel gravity, has been proposed as an alternative gravity model to account for the dark energy phenomena. Following our previous work [Xin-he Meng and Ying-bin Wang, EPJC(2011), arXiv:1107.0629v1], we prove that the Birkhoff's theorem holds in a more general context, specifically with the off diagonal tetrad case, in this communication letter. Then, we discuss respectively the results of the external vacuum and internal gravitational field in the f(T) gravity framework, as well as the extended meaning of this theorem. We also investigate the validity of the Birkhoff's theorem in the frame of f(T) gravity via conformal transformation by regarding the Brans-Dicke-like scalar as effective matter, and study the equivalence between both Einstein frame and Jordan frame.Comment: 7 pages, 1 figure, submitted to EPJ-C. arXiv admin note: substantial text overlap with arXiv:1107.062

Effects of a programme of vigorous physical activity during secondary school physical education on academic performance, fitness, cognition, mental health and the brain of adolescents (Fit to Study): Study protocol for a cluster randomised trial

Background. Early adolescence is a period of dynamic neurobiological change. Converging lines of research suggest that regular physical activity (PA) and improved aerobic fitness have the potential to stimulate positive brain changes, improve cognitive function and boost academic attainment in this age group, but high-quality studies are needed to substantiate these findings. The primary aim of the Fit to Study trial is to investigate whether short infusions of vigorous PA (VPA) delivered during secondary school physical education (PE) can improve attainment in maths, as described in a protocol published by NatCen Social Research. The present protocol concerns the trial’s secondary outcome measures, which are variables thought to moderate or mediate the relationship between PA and attainment, including the effect of the intervention on cardiorespiratory fitness, cognitive performance, mental health and brain structure and function. Method. The Fit to Study project is a cluster-randomised controlled trial that includes Year 8 pupils (aged 12–13) from secondary state schools in South/Mid-England. Schools were randomised into an intervention condition in which PE teachers delivered an additional 10 min of VPA per PE lesson for one academic year, or a ‘PE as usual’ control condition. Intervention and control groups were stratified according to whether schools were single-sex or co-educational. Assessments take place at baseline (end of Year 7, aged 11–12) and after 12 months (Year 8). Secondary outcomes are cardiorespiratory fitness, objective PA during PE, cognitive performance and mental health. The study also includes exploratory measures of daytime sleepiness, attitudes towards daily PA and PE enjoyment. A sub-set of pupils from a sub-set of schools will also take part in a brain imaging sub-study, which is embedded in the trial. Discussion. The Fit to Study trial could advance our understanding of the complex relationships between PA and aerobic fitness, the brain, cognitive performance, mental health and academic attainment during adolescence. Further, it will add to our understanding of whether school PE is an effective setting to increase VPA and fitness, which could inform future PA interventions and education policy

Birkhoff's Theorem in f(T) Gravity up to the Perturbative Order

f(T) gravity, a generally modified teleparallel gravity, has become very popular in recent times as it is able to reproduce the unification of inflation and late-time acceleration without the need of a dark energy component or an inflation field. In this present work, we investigate specifically the range of validity of Birkhoff's theorem with the general tetrad field via perturbative approach. At zero order, Birkhoff's theorem is valid and the solution is the well known Schwarzschild-(A)dS metric. Then considering the special case of the diagonal tetrad field, we present a new spherically symmetric solution in the frame of f(T) gravity up to the perturbative order. The results with the diagonal tetrad field satisfy the physical equivalence between the Jordan and the so-called Einstein frames, which are realized via conformal transformation, at least up to the first perturbative order.Comment: 8 pages, no figure. Final version, accepted for publication in EPJ