Gravitational reaction force on a particle in the Schwarzschild background

We formulate a new method to calculate the gravitational reaction force on a particle of mass $\mu$ orbiting a massive black hole of mass $M$. In this formalism, the tail part of the retarded Green function, which is responsible for the reaction force, is calculated at the level of the Teukolsky equation. Our method naturally allows a systematic post-Minkowskian (PM) expansion of the tail part at short distances. As a first step, we consider the case of a Schwarzschild black hole and explicitly calculate the first post-Newtonian (1PN) tail part of the Green function. There are, however, a couple of issues to be resolved before explicitly evaluating the reaction force by applying the present method. We discuss possible resolutions of these issues.Comment: 15 pages, no figure, submitted to Prog. Theor. Phy

A new analytical method for self-force regularization II. Testing the efficiency for circular orbits

In a previous paper, based on the black hole perturbation approach, we formulated a new analytical method for regularizing the self-force acting on a particle of small mass $\mu$ orbiting a Schwarzschild black hole of mass $M$, where $\mu\ll M$. In our method, we divide the self-force into the $\tilde S$-part and $\tilde R$-part. All the singular behaviors are contained in the $\tilde S$-part, and hence the $\tilde R$-part is guaranteed to be regular. In this paper, focusing on the case of a scalar-charged particle for simplicity, we investigate the precision of both the regularized $\tilde S$-part and the $\tilde R$-part required for the construction of sufficiently accurate waveforms for almost circular inspiral orbits. For the regularized $\tilde S$-part, we calculate it for circular orbits to 18 post-Newtonian (PN) order and investigate the convergence of the post-Newtonian expansion. We also study the convergence of the remaining $\tilde{R}$-part in the spherical harmonic expansion. We find that a sufficiently accurate Green function can be obtained by keeping the terms up to $\ell=13$.Comment: 21pages, 12 figure

Wnt-4 and Ets-1 signaling pathways for regeneration after acute renal failure

Ischemic acute renal failure (ARF) is the most common form of ARF in the adult population. The molecular mechanisms of tubular regeneration after ischemic renal injury remain largely unknown. An understanding of the mechanisms that lead to renal cell proliferation and regeneration will be necessary for the exploration of novel therapeutic strategies for the treatment of ARF. It has been suggested that regeneration processes may recapitulate developmental processes in order to restore organ or tissue function. The adult tubular epithelial cells have a potent ability of regenerate after cellular damage. We examined functional role of two developmental genes, Wnt-4 and Ets-1, in renal tubular regeneration in ARF. The Wnt-β-catenin pathway plays key roles in embryogenesis. Wnt-4 is known to be expressed in the mesonephric duct in the embryonic development. To clarify the significance of the Wnt-4-β-catenin pathway in ARF, we used a rat ARF model in vivo and LLC-PK1 cells as an in vitro model. After clamping left rat renal artery for 1 hour, we examined whole kidney homogenate and total RNA extracted at 3, 6, 12, 24, 48, and 72 hours after reperfusion by Western blot analysis and real-time reverse transcription-polymerase chain reaction (RT-PCR). Wnt-4 mRNA and protein expression were strongly increased at 3 to 12 hours and 6 to 24 hours after ischemia, respectively. In immunohistologic examination, Wnt-4 was expressed in the proximal tubules and coexpressed with aquaporin 1 and proliferating cell nuclear antigen (PCNA). Cyclin D1 and cyclin A were expressed at 12 to 48 hours after reperfusion. Furthermore, overexpression of Wnt-4 and β-catenin promoted the cell cycle and increased the promoter activity and protein expression of cyclin D1 and cyclin A in LLC-PK1 cells. These data suggest that the Wnt-4-β-catenin pathway plays a key role in the cell cycle progression of renal tubules in ARF. The Ets family of transcription factors is defined by a conserved DNA-binding Ets domain that forms a winged helix-turn-helix structure motif. The Ets family is involved in a diverse array of biologic functions, including cellular growth, migration, and differentiation. To clarify the significance of Ets-1 in ARF, we used a rat ARF model in vivo and LLC-PK1 cells as an in vitro model. Ets-1 mRNA and protein expression were strongly increased at 3 to 12 hours and 6 to 24 hours after the ischemia, respectively. In the immunohistologic examination, Ets-1 was expressed in the proximal tubules and coexpressed with PCNA. Furthermore, overexpression of Ets-1 promoted the cell cycle and increased the promoter activity and protein expression of cyclin D1 in LLC-PK1 cells. Ets-1 promoter activity increased between 3 hours and 6 hours in hypoxia, and hypoxia also induced changes in the Ets-1 protein level in LLC-PK1 cells. Taken together, these data suggest that Ets-1 plays a key role in the cell cycle progression of renal tubules in ARF. Our data suggest that Wnt-4-β-catenin and Ets-1 pathways regulate the transcription of cyclin D1 and control the regeneration of renal tubules in ARF. These developmental genes may play key roles in dedifferentiation and regeneration of the renal tubular cells after ARF