Accretion disk around the rotating Damour-Solodukhin wormhole

A new rotating generalization of the Damour-Solodukhin wormhole (RDSWH), called Kerr-like wormhole, has recently been proposed and investigated by Bueno \textit{et al} for echoes in the gravitational wave signal. We show a novel feature of the RDSWH, viz., that the kinematic properties such as the ISCO\ or marginally stable radius $r_{\text{ms}}$, efficiency $\epsilon$ and the disk potential $V_{\text{eff}}$ are \textit{independent} of $\lambda$ (which means they are identical to their KBH counterparts for any given spin). Differences however appear in the emissivity properties for higher values $0.1<\lambda\leq 1$ (say) and for the extreme spin $a_{\star}=0.998$. The kinematic and emissivity are generic properties as variations of the wormhole mass and the rate of accretion within the model preserve these properties. Specifically, the behavior of the luminosity peak is quite opposite to each other for the two objects, which could be useful from the viewpoint of observations. Apart from this, an estimate of the difference $\Delta_{\lambda}$ in the maxima of flux of radiation $F(r)$ shows non-zero values but is too tiny to be observable at present for $\lambda < 10^{-3}$ permitted by the strong lensing bound. The broad conclusion is that RDSWH\ are experimentally indistinguishable from KBH by accretion characteristics.Comment: 9 pages, 3 tables, 13 figure

Optimization of Adams-type difference formulas in Hilbert space W2(2,1)(0,1)W_2^{(2,1)}(0,1)

In this paper, we consider the problem of constructing new optimal explicit and implicit Adams-type difference formulas for finding an approximate solution to the Cauchy problem for an ordinary differential equation in a Hilbert space. In this work, I minimize the norm of the error functional of the difference formula with respect to the coefficients, we obtain a system of linear algebraic equations for the coefficients of the difference formulas. This system of equations is reduced to a system of equations in convolution and the system of equations is completely solved using a discrete analog of a differential operator $d^2/dx^2-1$. Here we present an algorithm for constructing optimal explicit and implicit difference formulas in a specific Hilbert space. In addition, comparing the Euler method with optimal explicit and implicit difference formulas, numerical experiments are given. Experiments show that the optimal formulas give a good approximation compared to the Euler method

Sagnac delay in the Kerr-dS space-time: Implications for Mach's principle

Relativistic twin paradox can have important implications for Mach's principle. It has been recently argued that the behavior of the time asynchrony (different aging of twins) between two flying clocks along closed loops can be attributed to the existence of an absolute spacetime, which makes Mach's principle unfeasible. In this paper, we shall revisit, and support, this argument from a different viewpoint using the Sagnac delay. This is possible since the above time asynchrony is known to be exactly the same as the Sagnac delay between two circumnavigating light rays re-uniting at the orbiting source/receiver. We shall calculate the effect of mass $M$ and cosmological constant $\Lambda$ on the delay in the general case of Kerr-de Sitter spacetime. It follows that, in the independent limits $M\rightarrow 0$, spin $a\rightarrow 0$ and $\Lambda\rightarrow 0$, while the Kerr-dS metric reduces to Minkowski metric, the clocks need not tick in consonance since there will still appear a non-zero observable Sagnac delay. While we do not measure spacetime itself, we do measure the Sagnac effect, which signifies an absolute substantive Minkowski spacetime instead of a void. We shall demonstrate a completely different limiting behavior of Sagnac delay, heretofore unknown, between the case of non-geodesic and geodesic source/observer motion.Comment: 15 pages. arXiv admin note: text overlap with arXiv:1709.0841

―KITAB AL-HIKMAH‖ AND ―HIKMAH‖ IN HAKIM TIRMIDHI‘S SCIENTIFIC HERITAGE

This article contains information about ―Kitab al-Hikma‖ by Hakim Tirmidhi and its structures. In addition, various ideas about ―Hikmah were analyzed

Can accretion properties distinguish between a naked singularity, wormhole and black hole?

We first advance a mathematical novelty that the three geometrically and topologically distinct objects mentioned in the title can be exactly obtained from the Jordan frame vacuum Brans I solution by a combination of coordinate transformations, trigonometric identities and complex Wick rotation. Next, we study their respective accretion properties using the Page-Thorne model which studies accretion properties exclusively for $r\geq r_{\text{ms}}$ (the minimally stable radius of particle orbits), while the radii of singularity/ throat/ horizon $r<r_{\text{ms}}$. Also, its Page-Thorne efficiency $\epsilon$ is found to increase with decreasing $r_{\text{ms}}$ and also yields $\epsilon=0.0572$ for Schwarzschild black hole (SBH). But in the singular limit $r\rightarrow r_{s}$ (radius of singularity), we have $\epsilon\rightarrow 1$ giving rise to $100 \%$ efficiency in agreement with the efficiency of the naked singularity constructed in [10]. We show that the differential accretion luminosity $\frac{d\mathcal{L}_{\infty}}{d\ln{r}}$ of Buchdahl naked singularity (BNS) is always substantially larger than that of SBH, while Eddington luminosity at infinity $L_{\text{Edd}}^{\infty}$ for BNS could be arbitrarily large at $r\rightarrow r_{s}$ due to the scalar field $\phi$ that is defined in $(r_{s}, \infty)$. It is concluded that BNS accretion profiles can still be higher than those of regular objects in the universe.Comment: 17 pages, 12 figure

Immunological indicators of complications of surgical bowel disease in children

The article is devoted to the development of immunological indicators of intestinal inflammation in children, which is of great importance for health authorities when organizing specialized pediatric and surgical services. The proposed method contributes to the early diagnosis and prevention of complications of inflammatory surgical bowel diseases in children, which is of great practical importance. The purpose of the study: To develop immunological indicators of complications of surgical bowel diseases in children. A retrospective analysis of 867 case histories of children who received inpatient treatment at the Department of Pediatric Surgery of the Bukhara branch of the Republican Scientific Center of Emergency Medical Care from 2019 to 2022 for surgical diseases of the gastrointestinal tract was carried out. The authors conducted an immunological study of 91 pediatric patients. All children underwent immunological blood tests: cellular and humoral immunity, cytokines (TNFα, IFNα, IL-8, MCP-1 and vascular endothelial growth factor VEGF-A) were studied. For the prevention of postoperative complications of CKD in children, it is recommended to determine IFNα in the blood serum in the period before surgery to solve the indications for immunocorrection. A noticeable positive relationship was established between IFNα and CD8 – r = 0.34, between IFNα and CD23 – r = 0.38, between IFNα and IgA – r = 0.39, between IFNα and PCT – r = 0.36. At the same time, PCT has a noticeable negative relationship with CD16 – r = -0.31 and with CD8 – r = -0.31 against the background of a noticeable positive relationship with IgG – r = 0.32 and IFNα – r = 0.36. It was found that IFNα is a more informative indicator of the effectiveness of the immune response, and PCT is an indicator of the effectiveness of antibacterial therapy in surgical bowel diseases in childre

INITIAL LENGTH SCALE ESTIMATE FOR WAVEGUIDES WITH SOME RANDOM SINGULAR POTENTIALS

Abstract. In this work we consider three examples of random singular perturbations in multi-dimensional models of waveguides. These perturbations are described by a large potential supported on a set of a small measure, by a compactly supported fast oscillating potential, and by a delta-potential. In all cases we prove initial length scale estimate