Gauge Problem in the Gravitational Self-Force II. First Post Newtonian Force under Regge-Wheeler Gauge

We discuss the gravitational self-force on a particle in a black hole space-time. For a point particle, the full (bare) self-force diverges. It is known that the metric perturbation induced by a particle can be divided into two parts, the direct part (or the S part) and the tail part (or the R part), in the harmonic gauge, and the regularized self-force is derived from the R part which is regular and satisfies the source-free perturbed Einstein equations. In this paper, we consider a gauge transformation from the harmonic gauge to the Regge-Wheeler gauge in which the full metric perturbation can be calculated, and present a method to derive the regularized self-force for a particle in circular orbit around a Schwarzschild black hole in the Regge-Wheeler gauge. As a first application of this method, we then calculate the self-force to first post-Newtonian order. We find the correction to the total mass of the system due to the presence of the particle is correctly reproduced in the force at the Newtonian order.Comment: Revtex4, 43 pages, no figure. Version to be published in PR

Radiative multipole moments of integer-spin fields in curved spacetime

Radiative multipole moments of scalar, electromagnetic, and linearized gravitational fields in Schwarzschild spacetime are computed to third order in v in a weak-field, slow-motion approximation, where v is a characteristic velocity associated with the motion of the source. To zeroth order in v, a radiative moment of order l is given by the corresponding source moment differentiated l times with respect to retarded time. At second order in v, additional terms appear inside the spatial integrals. These are near-zone corrections which depend on the detailed behavior of the source. At third order in v, the correction terms occur outside the spatial integrals, so that they do not depend on the detailed behavior of the source. These are wave-propagation corrections which are heuristically understood as arising from the scattering of the radiation by the spacetime curvature surrounding the source. Our calculations show that the wave-propagation corrections take a universal form which is independent of multipole order and field type. We also show that in general relativity, temporal and spatial curvatures contribute equally to the wave-propagation corrections.Comment: 34 pages, ReVTe

Self-force: Computational Strategies

Building on substantial foundational progress in understanding the effect of a small body's self-field on its own motion, the past 15 years has seen the emergence of several strategies for explicitly computing self-field corrections to the equations of motion of a small, point-like charge. These approaches broadly fall into three categories: (i) mode-sum regularization, (ii) effective source approaches and (iii) worldline convolution methods. This paper reviews the various approaches and gives details of how each one is implemented in practice, highlighting some of the key features in each case.Comment: Synchronized with final published version. Review to appear in "Equations of Motion in Relativistic Gravity", published as part of the Springer "Fundamental Theories of Physics" series. D. Puetzfeld et al. (eds.), Equations of Motion in Relativistic Gravity, Fundamental Theories of Physics 179, Springer, 201

Incidentally found abdominal para-aortic and inferior mesenteric root lymph node metastases of prostatic adenocarcinoma in a surgical case with sigmoid colon cancer

We report a rare case of incidentally found metastatic adenocarcinoma in the abdominal para-aortic and inferior mesenteric root lymph nodes originating from the prostate, at the time of surgery in a patient with sigmoid colon cancer. A man in his mid-seventies was scheduled to undergo laparoscopic-assisted sigmoidectomy and regional lymph node dissection. At the beginning of laparoscopic surgery, a caterpillar-like swelling of abdominal para-aortic lymph nodes was found; the diagnosis using frozen sections was a metastatic adenocarcinoma showing cribriform and solid growth patterns different from typical colorectal cancer. The surgical procedure was changed to an abdominal sigmoidectomy with widely extended lymph node dissection, including inferior mesenteric root lymph nodes and sampling of abdominal para-aortic lymph nodes. The resected sigmoid colon cancer was a papillary/tubular adenocarcinoma invading the muscularis with no lymph node metastasis (pT2N0M0/pStage IIA). Additionally, the presence of a metastatic adenocarcinoma showing cribriform and solid growth patterns different from the primary sigmoid colon cancer was confirmed in the abdominal para-aortic and inferior mesenteric root lymph nodes. The metastatic adenocarcinoma cells were positive for prostate-specific antigen (PSA) and negative for CDX2, indicating that the tumor was from the prostate. A total of ten prostatic core needle biopsy specimens also contained a usual (acinar) adenocarcinoma, with a Gleason score of 4 + 5 = 9. Androgen blockade was performed; the serum PSA level was reduced to 0.06 nanograms per microliter in the subsequent five months. Regardless of radiologic images, examination of serum PSA level is recommended before surgery in male surgical colorectal cancer patients more than 60 years old

Hemoglobin‐platelet index as a prognostic factor in patients with peripheral T‐cell lymphoma

Abstract Peripheral T‐cell lymphoma (PTCL) is a heterogeneous group of aggressive lymphomas with a poor prognosis. The International Prognostic Index (IPI) and the Prognostic Index for PTCL‐unspecified (PIT) is used to predict the prognosis of PTCL. The hemoglobin‐platelet index (HPI), based on anemia and thrombocytopenia status, is associated with the prognosis of diffuse large B‐cell lymphoma. However, its significance in terms of predicting the prognosis of PTCL has not been fully investigated. We herein retrospectively analyzed 100 patients with newly diagnosed PTCL in our department. At a median follow‐up of 3.2 years, the median progression‐free survival (PFS) and overall survival (OS) was 0.72 (95% confidence interval [CI]: 0.56–1.2) years and 2.0 (95% CI: 1.5–4.7) years, respectively. Multivariate analysis revealed that elevated lactic dehydrogenase (LDH) and hypoalbuminemia were independent adverse variables for PFS. The HPI showed significant predictive value for both PFS and OS. As a new prognostic model comprising the HPI, LDH, and albumin, the LA‐HPI allowed the stratification of patients into four distinct risk subgroups: low risk (zero risk factors), low‐intermediate risk (one risk factors), high‐intermediate risk (two or three risk factors), or high risk (four risk factors). The PFS and OS differed significantly among the patients by the LA‐HPI score. The LA‐HPI demonstrated better predictive performance compared to the IPI, PIT, and HPI. Our data demonstrated the prognostic utility of the HPI in patients with PTCL. The LA‐HPI, incorporating four readily obtainable parameters, exhibited superior performance compared to traditional indices