Effective stress-energy tensors, self-force, and broken symmetry

Deriving the motion of a compact mass or charge can be complicated by the presence of large self-fields. Simplifications are known to arise when these fields are split into two parts in the so-called Detweiler-Whiting decomposition. One component satisfies vacuum field equations, while the other does not. The force and torque exerted by the (often ignored) inhomogeneous "S-type" portion is analyzed here for extended scalar charges in curved spacetimes. If the geometry is sufficiently smooth, it is found to introduce effective shifts in all multipole moments of the body's stress-energy tensor. This greatly expands the validity of statements that the homogeneous R field determines the self-force and self-torque up to renormalization effects. The forces and torques exerted by the S field directly measure the degree to which a spacetime fails to admit Killing vectors inside the body. A number of mathematical results related to the use of generalized Killing fields are therefore derived, and may be of wider interest. As an example of their application, the effective shift in the quadrupole moment of a charge's stress-energy tensor is explicitly computed to lowest nontrivial order.Comment: 22 pages, fixed typos and simplified discussio

Mechanics of extended masses in general relativity

The "external" or "bulk" motion of extended bodies is studied in general relativity. Compact material objects of essentially arbitrary shape, spin, internal composition, and velocity are allowed as long as there is no direct (non-gravitational) contact with other sources of stress-energy. Physically reasonable linear and angular momenta are proposed for such bodies and exact equations describing their evolution are derived. Changes in the momenta depend on a certain "effective metric" that is closely related to a non-perturbative generalization of the Detweiler-Whiting R-field originally introduced in the self-force literature. If the effective metric inside a self-gravitating body can be adequately approximated by an appropriate power series, the instantaneous gravitational force and torque exerted on it is shown to be identical to the force and torque exerted on an appropriate test body moving in the effective metric. This result holds to all multipole orders. The only instantaneous effect of a body's self-field is to finitely renormalize the "bare" multipole moments of its stress-energy tensor. The MiSaTaQuWa expression for the gravitational self-force is recovered as a simple application. A gravitational self-torque is obtained as well. Lastly, it is shown that the effective metric in which objects appear to move is approximately a solution to the vacuum Einstein equation if the physical metric is an approximate solution to Einstein's equation linearized about a vacuum background.Comment: 39 pages, 2 figures; fixed equation satisfied by the Green function used to construct the effective metri

Self-forces from generalized Killing fields

A non-perturbative formalism is developed that simplifies the understanding of self-forces and self-torques acting on extended scalar charges in curved spacetimes. Laws of motion are locally derived using momenta generated by a set of generalized Killing fields. Self-interactions that may be interpreted as arising from the details of a body's internal structure are shown to have very simple geometric and physical interpretations. Certain modifications to the usual definition for a center-of-mass are identified that significantly simplify the motions of charges with strong self-fields. A derivation is also provided for a generalized form of the Detweiler-Whiting axiom that pointlike charges should react only to the so-called regular component of their self-field. Standard results are shown to be recovered for sufficiently small charge distributions.Comment: 21 page

Multipole structure of current vectors in curved spacetime

A method is presented which allows the exact construction of conserved (i.e. divergence-free) current vectors from appropriate sets of multipole moments. Physically, such objects may be taken to represent the flux of particles or electric charge inside some classical extended body. Several applications are discussed. In particular, it is shown how to easily write down the class of all smooth and spatially-bounded currents with a given total charge. This implicitly provides restrictions on the moments arising from the smoothness of physically reasonable vector fields. We also show that requiring all of the moments to be constant in an appropriate sense is often impossible; likely limiting the applicability of the Ehlers-Rudolph-Dixon notion of quasirigid motion. A simple condition is also derived that allows currents to exist in two different spacetimes with identical sets of multipole moments (in a natural sense).Comment: 13 pages, minor changes, accepted to J. Math. Phy

Electromagnetic self-forces and generalized Killing fields

Building upon previous results in scalar field theory, a formalism is developed that uses generalized Killing fields to understand the behavior of extended charges interacting with their own electromagnetic fields. New notions of effective linear and angular momenta are identified, and their evolution equations are derived exactly in arbitrary (but fixed) curved spacetimes. A slightly modified form of the Detweiler-Whiting axiom that a charge's motion should only be influenced by the so-called "regular" component of its self-field is shown to follow very easily. It is exact in some interesting cases, and approximate in most others. Explicit equations describing the center-of-mass motion, spin angular momentum, and changes in mass of a small charge are also derived in a particular limit. The chosen approximations -- although standard -- incorporate dipole and spin forces that do not appear in the traditional Abraham-Lorentz-Dirac or Dewitt-Brehme equations. They have, however, been previously identified in the test body limit.Comment: 20 pages, minor typos correcte

Effects of exenatide and liraglutide on heart rate, blood pressure and body weight : systematic review and meta-analysis

Objectives: To synthesise current evidence for the effects of exenatide and liraglutide on heart rate, blood pressure and body weight. Design: Meta-analysis of available data from randomised controlled trials comparing Glucagon-like peptide-1 (GLP-1) analogues with placebo, active antidiabetic drug therapy or lifestyle intervention. Participants: Patients with type 2 diabetes. Outcome measures: Weighted mean differences between trial arms for changes in heart rate, blood pressure and body weight, after a minimum of 12-week follow-up. Results: 32 trials were included. Overall, GLP-1 agonists increased the heart rate by 1.86 beats/min (bpm) (95% CI 0.85 to 2.87) versus placebo and 1.90 bpm (1.30 to 2.50) versus active control. This effect was more evident for liraglutide and exenatide long-acting release than for exenatide twice daily. GLP-1 agonists decreased systolic blood pressure by −1.79 mm Hg (−2.94 to −0.64) and −2.39 mm Hg (−3.35 to −1.42) compared to placebo and active control, respectively. Reduction in diastolic blood pressure failed to reach statistical significance (−0.54 mm Hg (−1.15 to 0.07) vs placebo and −0.50 mm Hg (−1.24 to 0.24) vs active control). Body weight decreased by −3.31 kg (−4.05 to −2.57) compared to active control, but by only −1.22 kg (−1.51 to −0.93) compared to placebo. Conclusions: GLP-1 analogues are associated with a small increase in heart rate and modest reductions in body weight and blood pressure. Mechanisms underlying the rise in heart rate require further investigation

The World of UCL

From its foundation in 1826, UCL embraced a progressive and pioneering spirit. It was the first university in England to admit students regardless of religion and made higher education affordable and accessible to a much broader section of society. It was also effectively the first university to welcome women on equal terms with men. From the outset UCL showed a commitment to innovative ideas and new methods of teaching and research. This book charts the history of UCL from 1826 through to the present day, highlighting its many contributions to society in Britain and around the world. It covers the expansion of the university through the growth in student numbers and institutional mergers. It documents shifts in governance throughout the years and the changing social and economic context in which UCL operated, including challenging periods of reconstruction after two World Wars. Today UCL is one of the powerhouses of research and teaching, and a truly global university. It is currently seventh in the QS World University Rankings. This completely revised and updated edition features a new chapter based on interviews with key individuals at UCL. It comes at a time of ambitious development for UCL with the establishment of an entirely new campus in East London, UCL East, and Provost Michael Arthur’s ‘UCL 2034’ strategy which aims to secure the university’s long-term future and commits UCL to delivering global impact

On the multifractal statistics of the local order parameter at random critical points : application to wetting transitions with disorder

Disordered systems present multifractal properties at criticality. In particular, as discovered by Ludwig (A.W.W. Ludwig, Nucl. Phys. B 330, 639 (1990)) on the case of diluted two-dimensional Potts model, the moments $\bar{\rho^q(r)}$ of the local order parameter $\rho(r)$ scale with a set $x(q)$ of non-trivial exponents $x(q) \neq q x(1)$. In this paper, we revisit these ideas to incorporate more recent findings: (i) whenever a multifractal measure $w(r)$ normalized over space $\sum_r w(r)=1$ occurs in a random system, it is crucial to distinguish between the typical values and the disorder averaged values of the generalized moments $Y_q =\sum_r w^q(r)$, since they may scale with different generalized dimensions $D(q)$ and $\tilde D(q)$ (ii) as discovered by Wiseman and Domany (S. Wiseman and E. Domany, Phys Rev E {\bf 52}, 3469 (1995)), the presence of an infinite correlation length induces a lack of self-averaging at critical points for thermodynamic observables, in particular for the order parameter. After this general discussion valid for any random critical point, we apply these ideas to random polymer models that can be studied numerically for large sizes and good statistics over the samples. We study the bidimensional wetting or the Poland-Scheraga DNA model with loop exponent $c=1.5$ (marginal disorder) and $c=1.75$ (relevant disorder). Finally, we argue that the presence of finite Griffiths ordered clusters at criticality determines the asymptotic value $x(q \to \infty) =d$ and the minimal value $\alpha_{min}=D(q \to \infty)=d-x(1)$ of the typical multifractal spectrum $f(\alpha)$.Comment: 17 pages, 20 figure

Insulin mediated upregulation of the renin angiotensin system in human subcutaneous adipocytes is reduced by Rosiglitazone

Background: Obesity associated hypertension is likely to be due to multiple mechanisms. Identification of the renin-angiotensin system (RAS) within adipose tissue does, however, suggest a potential causal role for it in obesity-associated hypertension. Obese patients are often hyperinsulinaemic, but mechanisms underlying insulin upregulation of the RAS in adipose tissue are unclear. TNFα, an inducer of angiotensinogen in hepatocytes, is elevated in hyperinsulinaemic, obese individuals, and may provide a link in mediating insulin upregulation of the RAS in adipose tissue. Further, thiazolidinediones lower blood pressure in vivo and downregulation of the RAS in adipose tissue may contribute to this effect. We therefore examined the effect of rosiglitazone (RSG), on the insulin mediated upregulation of the RAS. Methods and Results: Sera were obtained from the arterial circulation and from venous blood draining subcutaneous abdominal adipose tissue. Isolated human abdominal subcutaneous adipocytes (n=12) were treated with insulin (1-1000nM) and insulin in combination with RSG (10nM), and RSG (10nM) alone to determine angiotensinogen expression, angiotensin II, bradykinin and TNFα secretion. Subcutaneous adipocytes were also treated with TNFα (10-100ng/mL) to examine the direct effect on angiotensinogen expression and angiotensin II secretion. The findings showed that the arterio-venous difference in angiotensin II levels was significant (↑23%; p<0.001). Insulin increased TNFα secretion in a concentration-dependent manner (p<0.01) whilst RSG (10nM) significantly reduced the insulin mediated rise in TNFα (p<0.001), as well as AGT and angiotensin II. TNFα also increased angiotensinogen and angiotensin II in isolated adipocytes. Conclusions: Our in vivo data suggest that human subcutaneous adipose tissue is a significant source of angiotensin II. This study also demonstrates a potential TNFα mediated mechanism through which insulin may stimulate the RAS and may contribute to explain obesity associated hypertension. RSG downregulates the RAS in subcutaneous adipose tissue and this effect may contribute to the long-term effect of RSG on blood pressure