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

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

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

Recent Decisions

Comments on recent decisions by William J. Harte, John A. Di Nardo, Donald A. Garrity, Nick J. Neiers, Arthur J. Perry, G. R. Blakey, Matthew T. Hogan, and John V. Reilly, Jr

Land use change through the lens of macroecology : insights from Azorean arthropods and the maximum entropy theory of ecology

Human activity and land management practices, in particular land use change, have resulted in the global loss of biodiversity. These types of disturbance affect the shape of macroecological patterns, and therefore analyzing these patterns can provide insights into how ecosystems are affected by land use change. We here use arthropod census data from 96 sites at Terceira Island in the Azores archipelago across four different land uses of increasing management intensity: native forest, exotic forest, semi-natural pasture and intensive pasture, to examine the effects of land use type on three macroecological patterns: the species abundance distribution, the metabolic rate distribution of individuals and the species–area relationship. The maximum entropy theory of ecology (METE) has successfully predicted these patterns across habitats and taxa in undisturbed ecosystems, and thus provides a null expectation for their shapes. Across these patterns, we find that the forest habitats are the best fit by METE predictions, while the semi-natural pasture is consistently the worst fit, and the intensive pasture is intermediately well fit. We show that the direction of failure of the METE predictions at the pasture sites is likely due to the hyper-dominance of introduced spider species present there. We hypothesize that the particularly poor fit for the semi-natural pasture is due to the mix of arthropod communities out of equilibrium, leading to greater heterogeneity in composition and complex dynamics that violate METE's assumption of static state variables. The comparative better fit for the intensive pasture plausibly results from more homogeneous arthropod communities that are well adapted to intensive management, and thus whose state variables are less in flux. Analyzing deviations from theoretical predictions across land use type provides useful information about how land use and disturbance affect ecosystems, and such comparisons could be useful across other habitats and taxa.Funding for this project was provided in part by grant DEB 1751380 from the US National Science Foundation, as well as by grants to PAVB FCT-UIDP/00329/2020-2024 (Thematic Line 1 – integrated ecological assessment of environmental change on biodiversity) and MACRISK – PTDC/BIA-CBI/0625/2021, through the FCT – Fundação para a Ciência e a Tecnologia. MB acknowledges the support of the Natural Sciences and Engineering Research Council of Canada (NSERC) (PGSD2-517114-2018). Data acquisition was provided by the projects: ‘Consequences of land use change on Azorean fauna and flora – the 2010 Target' (Ref: Direcção Regional de Ciência e Tecnologia M.2.1.2/I/003/2008) and ‘Direcção Regional dos Recursos Florestais' (‘Secretaria Regional da Agricultura e Pescas') through the Project ‘Reservas Florestais dos Açores: Cartografia e Inventariação dos Artrópodes Endémicos dos Açores' (PROJ. 17.01 – 080203).info:eu-repo/semantics/publishedVersio