Self-force via Green functions and worldline integration

A compact object moving in curved spacetime interacts with its own gravitational field. This leads to both dissipative and conservative corrections to the motion, which can be interpreted as a self-force acting on the object. The original formalism describing this self-force relied heavily on the Green function of the linear differential operator that governs gravitational perturbations. However, because the global calculation of Green functions in non-trivial black hole spacetimes has been an open problem until recently, alternative methods were established to calculate self-force effects using sophisticated regularization techniques that avoid the computation of the global Green function. We present a method for calculating the self-force that employs the global Green function and is therefore closely modeled after the original self-force expressions. Our quantitative method involves two stages: (i) numerical approximation of the retarded Green function in the background spacetime; (ii) evaluation of convolution integrals along the worldline of the object. This novel approach can be used along arbitrary worldlines, including those currently inaccessible to more established computational techniques. Furthermore, it yields geometrical insight into the contributions to self-interaction from curved geometry (back-scattering) and trapping of null geodesics. We demonstrate the method on the motion of a scalar charge in Schwarzschild spacetime. This toy model retains the physical history-dependence of the self-force but avoids gauge issues and allows us to focus on basic principles. We compute the self-field and self-force for many worldlines including accelerated circular orbits, eccentric orbits at the separatrix, and radial infall. This method, closely modeled after the original formalism, provides a promising complementary approach to the self-force problem.Comment: 18 pages, 9 figure

Gravitational self-torque and spin precession in compact binaries

We calculate the effect of self-interaction on the "geodetic" spin precession of a compact body in a strong-field orbit around a black hole. Specifically, we consider the spin precession angle $\psi$ per radian of orbital revolution for a particle carrying mass $\mu$ and spin $s \ll (G/c) \mu^2$ in a circular orbit around a Schwarzschild black hole of mass $M \gg \mu$. We compute $\psi$ through $O(\mu/M)$ in perturbation theory, i.e, including the correction $\delta\psi$ (obtained numerically) due to the torque exerted by the conservative piece of the gravitational self-field. Comparison with a post-Newtonian (PN) expression for $\delta\psi$, derived here through 3PN order, shows good agreement but also reveals strong-field features which are not captured by the latter approximation. Our results can inform semi-analytical models of the strong-field dynamics in astrophysical binaries, important for ongoing and future gravitational-wave searches.Comment: 5 pages, 1 table, 1 figure. Minor changes to match published versio

Metric perturbations of Kerr spacetime in Lorenz gauge: Circular equatorial orbits

We construct the metric perturbation in Lorenz gauge for a compact body on a circular equatorial orbit of a rotating black hole (Kerr) spacetime, using a newly-developed method of separation of variables. The metric perturbation is formed from a linear sum of differential operators acting on Teukolsky mode functions, and certain auxiliary scalars, which are solutions to ordinary differential equations in the frequency domain. For radiative modes, the solution is uniquely determined by the $s=\pm2$ Weyl scalars, the $s=0$ trace, and $s=0,1$ gauge scalars whose amplitudes are determined by imposing continuity conditions on the metric perturbation at the orbital radius. The static (zero-frequency) part of the metric perturbation, which is handled separately, also includes mass and angular momentum completion pieces. The metric perturbation is validated against the independent results of a 2+1D time domain code, and we demonstrate agreement at the expected level in all components, and the absence of gauge discontinuities. In principle, the new method can be used to determine the Lorenz-gauge metric perturbation at a sufficiently high precision to enable accurate second-order self-force calculations on Kerr spacetime in future. We conclude with a discussion of extensions of the method to eccentric and non-equatorial orbits.Comment: 88 pages, 14 figure

The relationship between imaging-based body composition analysis and the systemic inflammatory response in patients with cancer: a systematic review

Background and aim: Cancer is the second leading cause of death globally. Nutritional status (cachexia) and systemic inflammation play a significant role in predicting cancer outcome. The aim of the present review was to examine the relationship between imaging-based body composition and systemic inflammation in patients with cancer. Methods: MEDLINE, EMBASE, Cochrane Library and Google Scholar were searched up to 31 March 2019 for published articles using MESH terms cancer, body composition, systemic inflammation, Dual energy X-ray absorptiometry (DEXA), magnetic resonance imaging (MRI), ultrasound sonography (USS) and computed tomography (CT). Studies performed in adult patients with cancer describing the relationship between imaging-based body composition and measures of the systemic inflammatory response were included in this review. Results: The literature search retrieved 807 studies and 23 met the final eligibility criteria and consisted of prospective and retrospective cohort studies comprising 11,474 patients. CT was the most common imaging modality used (20 studies) and primary operable (16 studies) and colorectal cancer (10 studies) were the most commonly studied cancers. Low skeletal muscle index (SMI) and systemic inflammation were consistently associated; both had a prognostic value and this relationship between low SMI and systemic inflammation was confirmed in four longitudinal studies. There was also evidence that skeletal muscle density (SMD) and systemic inflammation were associated (9 studies). Discussion: The majority of studies examining the relationship between CT based body composition and systemic inflammation were in primary operable diseases and in patients with colorectal cancer. These studies showed that there was a consistent association between low skeletal muscle mass and the presence of a systemic inflammatory response. These findings have important implications for the definition of cancer cachexia and its treatment

Comparison of the prognostic value of ECOG-PS, MGPS and BMI/WL: Implications for a clinically important framework in the assessment and treatment of advanced cancer

BACKGROUND AND AIMS:The systemic inflammatory response is associated with the loss of lean tissue, anorexia, weakness, fatigue and reduced survival in patients with advanced cancer and therefore is important in the definition of cancer cachexia. The aim of the present study was to carry out a direct comparison of the prognostic value of Eastern Cooperative Oncology Group Performance Status (ECOG-PS), modified Glasgow Prognostic Score (mGPS) and Body Mass Index/Weight Loss Grade (BMI/WL grade) in patients with advanced cancer. METHOD:All data were collected prospectively across 18 sites in the UK and Ireland. Patient's age, sex, ECOG-PS, mGPS and BMI/WL grade were recorded, as were details of underlying disease including metastases. Survival data were analysed using univariate and multivariate Cox regression. RESULTS:A total of 730 patients were assessed. The majority of patients were male (53%), over 65 years of age (56%), had an ECOG-PS>0/1 (56%), mGPS≥1 (56%), BMI≥25 (51%), <2.5% weight loss (57%) and had metastatic disease (86%). On multivariate cox regression analysis ECOG-PS (HR 1.61 95%CI 1.42-1.83, p < 0.001), mGPS (HR 1.53, 95%CI 1.39-1.69, p < 0.001) and BMI/WL grade (HR 1.41, 95%CI 1.25-1.60, p < 0.001) remained independently associated with overall survival. In patients with a BMI/WL grade 0/1 both ECOG and mGPS remained independently associated with overall survival. CONCLUSION:The ECOG/mGPS framework may form the basis of risk stratification of survival in patients with advanced cancer

A comparison of CT-body composition measurements in non-cancer and cancer patients from a single UK centre

Objectives: Establish the prevalence of low skeletal muscle index and density in our population, by comparing age and sex matched cohorts of patients with and without cancer, using standardized methodology for CT-Body composition (CT-BC). Methods: A retrospective analysis of prospectively collected data. Patients admitted to our institution between 17th March 2020 - 1st May 2020, with confirmed coronavirus disease and imaging suitable for CT-BC (n=52), were age and sex matched with patients undergoing resection for colorectal cancer (n=52). Results: 104 patients were included in the final analysis. 43% (n=45) were male, 77% (n=80) were aged 65 years or older, 50% (n=50) were overweight (BMI ≥25) and 53% (n=55) were systemically inflamed (mGPS ≥1). The prevalence of a low SMI (56% vs. 65%) and low SMD (83% vs. 67%) was similar between cohorts. A low SMI and SMD were both associated with age (p<0.05 and p<0.01, respectively) on univariate analysis. On multivariate analysis, a low SMD was independently associated with age (OR 2.38 (1.34-4.22), p=0.003) and mGPS (OR 2.10 (1.20-3.68), p=0.01). Conclusions: In conclusion, the prevalence of a low SMI and low SMD was similar in non-cancer and cancer cohorts in our institution

Conserved Charges in the Principal Chiral Model on a Supergroup

The classical principal chiral model in 1+1 dimensions with target space a compact Lie supergroup is investigated. It is shown how to construct a local conserved charge given an invariant tensor of the Lie superalgebra. We calculate the super-Poisson brackets of these currents and argue that they are finitely generated. We show how to derive an infinite number of local charges in involution. We demonstrate that these charges Poisson commute with the non-local charges of the model