On the well posedness of the Baumgarte-Shapiro-Shibata-Nakamura formulation of Einstein's field equations

We give a well posed initial value formulation of the Baumgarte-Shapiro-Shibata-Nakamura form of Einstein's equations with gauge conditions given by a Bona-Masso like slicing condition for the lapse and a frozen shift. This is achieved by introducing extra variables and recasting the evolution equations into a first order symmetric hyperbolic system. We also consider the presence of artificial boundaries and derive a set of boundary conditions that guarantee that the resulting initial-boundary value problem is well posed, though not necessarily compatible with the constraints. In the case of dynamical gauge conditions for the lapse and shift we obtain a class of evolution equations which are strongly hyperbolic and so yield well posed initial value formulations

Stable radiation-controlling boundary conditions for the generalized harmonic Einstein equations

This paper is concerned with the initial-boundary value problem for the Einstein equations in a first-order generalized harmonic formulation. We impose boundary conditions that preserve the constraints and control the incoming gravitational radiation by prescribing data for the incoming fields of the Weyl tensor. High-frequency perturbations about any given spacetime (including a shift vector with subluminal normal component) are analyzed using the Fourier-Laplace technique. We show that the system is boundary-stable. In addition, we develop a criterion that can be used to detect weak instabilities with polynomial time dependence, and we show that our system does not suffer from such instabilities. A numerical robust stability test supports our claim that the initial-boundary value problem is most likely to be well-posed even if nonzero initial and source data are included.Comment: 27 pages, 4 figures; more numerical results and references added, several minor amendments; version accepted for publication in Class. Quantum Gra

Well-Posed Initial-Boundary Evolution in General Relativity

Maximally dissipative boundary conditions are applied to the initial-boundary value problem for Einstein's equations in harmonic coordinates to show that it is well-posed for homogeneous boundary data and for boundary data that is small in a linearized sense. The method is implemented as a nonlinear evolution code which satisfies convergence tests in the nonlinear regime and is robustly stable in the weak field regime. A linearized version has been stably matched to a characteristic code to compute the gravitational waveform radiated to infinity.Comment: 5 pages, 6 figures; added another convergence plot to Fig. 2 + minor change

Testing outer boundary treatments for the Einstein equations

Various methods of treating outer boundaries in numerical relativity are compared using a simple test problem: a Schwarzschild black hole with an outgoing gravitational wave perturbation. Numerical solutions computed using different boundary treatments are compared to a `reference' numerical solution obtained by placing the outer boundary at a very large radius. For each boundary treatment, the full solutions including constraint violations and extracted gravitational waves are compared to those of the reference solution, thereby assessing the reflections caused by the artificial boundary. These tests use a first-order generalized harmonic formulation of the Einstein equations. Constraint-preserving boundary conditions for this system are reviewed, and an improved boundary condition on the gauge degrees of freedom is presented. Alternate boundary conditions evaluated here include freezing the incoming characteristic fields, Sommerfeld boundary conditions, and the constraint-preserving boundary conditions of Kreiss and Winicour. Rather different approaches to boundary treatments, such as sponge layers and spatial compactification, are also tested. Overall the best treatment found here combines boundary conditions that preserve the constraints, freeze the Newman-Penrose scalar Psi_0, and control gauge reflections.Comment: Modified to agree with version accepted for publication in Class. Quantum Gra

Promising use of filgotinib in patients affected by systemic sclerosis: Preliminary data from a case series of 5 patients

Objective: To assess the efficacy and safety of Filgotinib for the management of cutaneous, visceral and articular involvement in pat ients affected by systemic sclerosis. Methods: 5 patients affected by SSc referring to the Scleroderma Units of Modena and Reggio Emilia between October 2021 and February 2023, were enrolled. Patients received 200 mg of Filgotinib once daily for a period of 52 weeks. Skin, articular and visceral organ involvement were evaluated at the baseline and every 12 weeks after the start of the treatment. Results: A significant improvement of articular involvement was seen at 12th week. All patients confirmed a significant amelioration in articular involvement at 52th week, with a significant reduction in TJ, SDAI/CDAI, DAS28-CRP. PDUS performed after 24 and 52 weeks of treatment supported the remission. A significant decrease of mRSS, improvement of other skin manifestations and a stabilization of ILD, assessed through HRCT and PFTs, were noticed in patients with dcSSc. The 2 patients with dsSSC showed a clinical improvement assessed using the CRISS score. No drug-related side effects were recorded and neither patients discontinued the treatment. No deaths were reported. Conclusion: Filgotinib was safe, effective and well tolerated in the treatment of articular and visceral involvement in patients affected by SSc

Well-posedness of boundary layer equations for time-dependent flow of non-Newtonian fluids

We consider the flow of an upper convected Maxwell fluid in the limit of high Weissenberg and Reynolds number. In this limit, the no-slip condition cannot be imposed on the solutions. We derive equations for the resulting boundary layer and prove the well-posedness of these equations. A transformation to Lagrangian coordinates is crucial in the argument

Stability of general-relativistic accretion disks

Self-gravitating relativistic disks around black holes can form as transient structures in a number of astrophysical scenarios such as binary neutron star and black hole-neutron star coalescences, as well as the core-collapse of massive stars. We explore the stability of such disks against runaway and non-axisymmetric instabilities using three-dimensional hydrodynamics simulations in full general relativity using the THOR code. We model the disk matter using the ideal fluid approximation with a $\Gamma$-law equation of state with $\Gamma=4/3$. We explore three disk models around non-rotating black holes with disk-to-black hole mass ratios of 0.24, 0.17 and 0.11. Due to metric blending in our initial data, all of our initial models contain an initial axisymmetric perturbation which induces radial disk oscillations. Despite these oscillations, our models do not develop the runaway instability during the first several orbital periods. Instead, all of the models develop unstable non-axisymmetric modes on a dynamical timescale. We observe two distinct types of instabilities: the Papaloizou-Pringle and the so-called intermediate type instabilities. The development of the non-axisymmetric mode with azimuthal number m = 1 is accompanied by an outspiraling motion of the black hole, which significantly amplifies the growth rate of the m = 1 mode in some cases. Overall, our simulations show that the properties of the unstable non-axisymmetric modes in our disk models are qualitatively similar to those in Newtonian theory.Comment: 30 pages, 21 figure

The Cauchy Problem for the Einstein Equations

Various aspects of the Cauchy problem for the Einstein equations are surveyed, with the emphasis on local solutions of the evolution equations. Particular attention is payed to giving a clear explanation of conceptual issues which arise in this context. The question of producing reduced systems of equations which are hyperbolic is examined in detail and some new results on that subject are presented. Relevant background from the theory of partial differential equations is also explained at some lengthComment: 98 page

Ocean colour changes in the North Pacific since 1930

In this paper we present an analysis of historical ocean colour data from the North Pacific Ocean. This colour is described by the Forel-Ule colour index, a sea colour comparator scale that is composed of 21 tube colours that is routinely measured since the year 1890. The main objective of this research is to characterise colour changes of the North Pacific Ocean at a timescale of decades. Next to the seasonal colour changes, due to the yearly cycle of biological activity, this time series between 1930 and 1999 might contain information on global changes in climate conditions. From seasonal independent analyses of the long-term variations it was found that the greenest values, with mean Forel-Ule scale ((FU) ̅) of 4.1 were reached during the period of 1950-1954, with a second high ((FU) ̅ = 3) in the period 1980-1984. The bluest ocean was encountered during the years 1990-1994. The data indicate that after 1955 a remarkable long bluing took place till 1980