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

Strong lensing, plane gravitational waves and transient flashes

Plane-symmetric gravitational waves are considered as gravitational lenses. Numbers of images, frequency shifts, mutual angles, and image distortion parameters are computed exactly in essentially all non-singular plane wave spacetimes. For a fixed observation event in a particular plane wave spacetime, the number of images is found to be the same for almost every source. This number can be any positive integer, including infinity. Wavepackets of finite width are discussed in detail as well as waves which maintain a constant amplitude for all time. Short wavepackets are found to generically produce up to two images of each source which appear (separately) only some time after the wave has passed. They are initially infinitely bright, infinitely blueshifted images of the infinitely distant past. Later, these images become dim and acquire a rapidly-increasing redshift. For sufficiently weak wavepackets, one such "flash" almost always exists. The appearance of a second flash requires that the Ricci tensor inside the wave exceed a certain threshold. This might occur if a gravitational plane wave is sourced by, e.g., a sufficiently strong electromagnetic plane wave

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

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

Investigating the neuroimmunomodulatory effects of 40Hz light flicker treatment in 5xFAD model of Alzheimer’s Disease

AD is a chronic neurodegenerative condition affecting the aging population. Recently there has been global concern due to the rising prevalence of the disease and increasing financial burden of care. Despite the increasing prevalence of Alzheimer’s Disease (AD) there are currently no non-invasive treatments available for patients, with all available therapies only targeting the symptoms of disease and not the cause. Recently, a potential new form of treatment for AD has been gaining interest due to its non-invasive properties. Several studies have found that flickering a light at a 40Hz frequency was capable of reducing the disease pathology and improve memory retention in mouse models of AD via an unknown mechanism. We sought to unveil some of the mechanisms of this potential therapy. Using previously published methods we investigated the ability of 40Hz flickering light to reduce amyloid-β (Aβ) in the brains of 5xFAD mice- a transgenic mouse model of AD. We first used 9-month-old animals and treated for 1 hour a day for either 5 consecutive days or 15 days. In these 9-month-old animals we observed no significant changes in Aβ pathology (either plaque area or number) within the visual cortex (VC). We then changed the format of our treatment and reduced the ages of our animals to 4-5 months and revised our treatment equipment. At this reduced age we observed a significant reduction in total Aβ area alongside changes in gene expression in the VC for genes associated with the Aβ processing pathway, such as endogenous mouse APP and γ-secretase protein PSEN1. We then examined if the 40Hz light-flicker exhibited sex-dependent responses as previous studies have not examined sex-based differences. We observed that while some genes showed consistent changes between the sexes (PSEN1 & mAPP) some genes exhibited significant differences between male and female 5xFAD mice (BACE1 & Cst7), suggesting that the response was sex-dependent. Thus, 40Hz light flicker treatment reduced expression of Aβ in 4- 5-month-old 5xFAD mice as well as inducing significant changes in gene expression within the VC.AD is a chronic neurodegenerative condition affecting the aging population. Recently there has been global concern due to the rising prevalence of the disease and increasing financial burden of care. Despite the increasing prevalence of Alzheimer’s Disease (AD) there are currently no non-invasive treatments available for patients, with all available therapies only targeting the symptoms of disease and not the cause. Recently, a potential new form of treatment for AD has been gaining interest due to its non-invasive properties. Several studies have found that flickering a light at a 40Hz frequency was capable of reducing the disease pathology and improve memory retention in mouse models of AD via an unknown mechanism. We sought to unveil some of the mechanisms of this potential therapy. Using previously published methods we investigated the ability of 40Hz flickering light to reduce amyloid-β (Aβ) in the brains of 5xFAD mice- a transgenic mouse model of AD. We first used 9-month-old animals and treated for 1 hour a day for either 5 consecutive days or 15 days. In these 9-month-old animals we observed no significant changes in Aβ pathology (either plaque area or number) within the visual cortex (VC). We then changed the format of our treatment and reduced the ages of our animals to 4-5 months and revised our treatment equipment. At this reduced age we observed a significant reduction in total Aβ area alongside changes in gene expression in the VC for genes associated with the Aβ processing pathway, such as endogenous mouse APP and γ-secretase protein PSEN1. We then examined if the 40Hz light-flicker exhibited sex-dependent responses as previous studies have not examined sex-based differences. We observed that while some genes showed consistent changes between the sexes (PSEN1 & mAPP) some genes exhibited significant differences between male and female 5xFAD mice (BACE1 & Cst7), suggesting that the response was sex-dependent. Thus, 40Hz light flicker treatment reduced expression of Aβ in 4- 5-month-old 5xFAD mice as well as inducing significant changes in gene expression within the VC

Palaeontological site conservation and the law in Britain

The legal situation regarding palaeontological site conservation in Britain is unclear. There is no modern review of the law. Five main areas of concern are identified. Most exsisting laws do not specifically consider the needs of palaeontological conservation. Legislation empowers the Nature Conservancy Council upon policy decisions. The NCC is primarily concerned with nationally important sites, and responsibility for recording other sites therefore falls upon voluntary National Scheme for Geological Site Documentation. Local authorities have potentially useful powers. Site occupiers are disadvantaged by the damage caused by, and to some extent the liability due to visitiors, but they can forbid access to almost all sites on private land. The ownership of in situ fossils may be presumed to go with the mineral rights in the land, and collecting them without permission may involve criminal damage and theft. Loose fossils may in some cases be legally collected without express permission. If the landowner has not exerted rights of controil of access or ownership. This is potentially important for coastal exposures. The compulsary public ownership of fossils is not likely to be a successful strategy in geological conservation. Resources are on the whole better spent in education and popularization than on compulsion

Acoustic measurement differences on trees and logs from hardwoods in wet and dry condition

peer-reviewedAcoustic velocities measured on standing trees using time-of-flight (TOF) devices have been found to be between 7% and 36% higher for softwoods than those in logs using resonance techniques based on longitudinal frequencies. This effect was explained in three different ways: (1) TOF devices on standing trees measure outerwood containing more mature wood while resonance methods assess the whole crosssection, (2) the variation in the velocity is due to loading conditions in standing trees, while logs are free of loads and (3) the acoustic waves are dilatational waves in the case of TOF measurements on standing trees and one-dimensional longitudinal waves in the case of resonance on logs. This is an important topic considering the fact that resonance methods are considered more accurate for predicting mechanical properties and it has been proposed that correction factors should be applied on TOF measurements. In the present work, four hardwoods from Irish forests were studied and, on average, TOF velocities measured in the forest above fibre saturation point (FSP) were 19.8% higher than those from resonance measurements taken on logs immediately after felling. However, this difference reduced to 5.4% when the measurements were repeated at a moisture content (MC) of about 18% in the laboratory. Therefore, there is a MC effect on the velocity differences. Furthermore, higher differences were systematically found in older specimens in wet condition. However, this age effect was small in most cases