A Rigorous Derivation of Electromagnetic Self-force

During the past century, there has been considerable discussion and analysis of the motion of a point charge, taking into account "self-force" effects due to the particle's own electromagnetic field. We analyze the issue of "particle motion" in classical electromagnetism in a rigorous and systematic way by considering a one-parameter family of solutions to the coupled Maxwell and matter equations corresponding to having a body whose charge-current density $J^a(\lambda)$ and stress-energy tensor $T_{ab} (\lambda)$ scale to zero size in an asymptotically self-similar manner about a worldline $\gamma$ as $\lambda \to 0$. In this limit, the charge, $q$, and total mass, $m$, of the body go to zero, and $q/m$ goes to a well defined limit. The Maxwell field $F_{ab}(\lambda)$ is assumed to be the retarded solution associated with $J^a(\lambda)$ plus a homogeneous solution (the "external field") that varies smoothly with $\lambda$. We prove that the worldline $\gamma$ must be a solution to the Lorentz force equations of motion in the external field $F_{ab}(\lambda=0)$. We then obtain self-force, dipole forces, and spin force as first order perturbative corrections to the center of mass motion of the body. We believe that this is the first rigorous derivation of the complete first order correction to Lorentz force motion. We also address the issue of obtaining a self-consistent perturbative equation of motion associated with our perturbative result, and argue that the self-force equations of motion that have previously been written down in conjunction with the "reduction of order" procedure should provide accurate equations of motion for a sufficiently small charged body with negligible dipole moments and spin. There is no corresponding justification for the non-reduced-order equations.Comment: 52 pages, minor correction

Black hole shadows, photon rings, and lensing rings

The presence of a bright "photon ring" surrounding a dark "black hole shadow" has been discussed as an important feature of the observational appearance of emission originating near a black hole. We clarify the meaning and relevance of these heuristics with analytic calculations and numerical toy models. The standard usage of the term "shadow" describes the appearance of a black hole illuminated from all directions, including from behind the observer. A backlit black hole casts a somewhat larger shadow. Neither "shadow" heuristic is particularly relevant to understanding the appearance of emission originating near the black hole, where the emission profile and gravitational redshift play the dominant roles in determining the observed size of the central dark area. A photon ring results from light rays that orbit around the black hole in the near-field region before escaping to infinity, where they arrive near a ring-shaped "critical curve" on the image plane. Although the brightness can become arbitrarily large near this critical curve in the case of optically thin emitting matter near the black hole, we show that the enhancement is only logarithmic, and hence is of no relevance to present observations. For optically thin emission from a geometrically thin or thick disk, photons that make only a fraction of an orbit will generically give rise to a much wider "lensing ring," which is a demagnified image of the back of the disk, superimposed on top of the direct emission. For nearly face-on viewing, the lensing ring is centered at a radius similar to 5% larger than the photon ring and, depending on the details of the emission, its width is similar to 0.5-1M (where M is the mass of the black hole). It can be relatively brighter by a factor of 2-3, as compared to the surrounding parts of the image, and thus could provide a significant feature in high-resolution images. Nevertheless, the characteristic features of the observed image are dominated by the location and properties of the emitting matter near the black hole. We comment on the recent M87* Event Horizon Telescope observations and mass measurement.NSF [PHY-1505124, PHY-1804216, PHY-1752809, PHY-1708081]; Kavli Institute for Cosmological Physics at the University of Chicago through an endowment from the Kavli Foundation; Marion and Stuart Rice AwardThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Thrombolyse der Arteria cerebri media

Zusammenfassung: In den ersten 3h nach Eintritt eines akuten ischämischen Hirninfarkts ist die intravenöse Thrombolyse (IVT) die evidenzbasierte Therapie (IVT 3-4,5h: "off-label use" mit Einverständnis des Patienten). Die intraarterielle Thrombolyse (IAT) führt in der A.cerebri media (ACM) allerdings häufiger zur Rekanalisation als die IVT. Daher ist die IAT in dafür ausgerüsteten Kliniken ergänzend oder alternativ zur IVT bis zu 6h nach Symptombeginn zu erwäge

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

Quality of life in survivors after cervical artery dissection

Background and purpose : Little data exists about longterm outcome, quality of life (QOL) and its predictors after spontaneous cervical artery dissections (sCAD). Methods : Clinical and radiological data of 114 patients with sCAD were collected prospectively. Six patients died within 3 months, the remaining 108 were contacted after a mean of 1498 days (range: 379-3455), 99 survivors (92 %) replied. QOL, assessed with the stroke-specific QOL scale (SSQOL), and functional abilities, measured with modified Rankin Scale (mRS) were compared, and predictors of QOL were analyzed. Subgroup analyses were performed for patients with ischemic stroke, those with isolated local symptoms or transient ischemic symptoms and those without significant disabilities (mRS 0-1) at follow-up. Results : Seventy-one of 99 patients (72 %) had no significant disability, but only 53 (54 %) reported a good QOL (SS-QOL ≥ 4). Compared to the self-rated premorbid QOL of all patients, SS-QOL was impaired after sCAD (p 0.5). High National Institute of Health Stroke Scale score on admission and higher age were independent predictors of impaired QOL (p < 0.05). Conclusion : QOL is impaired in almost half of long-term survivors after sCAD, even in patients with local or transient symptoms or without functional disability. Impairment of QOL is a surprisingly frequent long-term sequela after sCAD and deserves attention as an outcome measure in these patient