General relativistic hydrodynamics in curvilinear coordinates

General relativistic hydrodynamics and magnetohydrodynamics: hyperbolic systems in relativistic astrophysics

Multiinstantons in Curvilinear Coordinates

The 'tHooft's 5N-parametric multiinstanton solution is generalized to curvilinear coordinates. Expressions can be simplified by the gauge transformation that makes η-symbols constant in the vierbein formalism. This generates the compensating addition to the gauge potential of pseudoparticles. Typical examples (4-spherical, 2 + 2-and 3 + 1-cylindrical coordinates) are studied and explicit formul...

Instantons in curvilinear coordinates

The multi-instanton solutions by ’tHooft and Jackiw, Nohl & Rebbi are generalized to curvilinear coordinates. Expressions can be notably simplified by the appropriate gauge transformation. This generates the compensating addition to the gauge potential of pseudoparticles. Singularities of the compensating connection are irrelevant for physics but affect gauge dependent quantities. The third con...

General relativistic hydrodynamics with a Roe solver

We present a numerical method to solve the equations of general relativistic hydrodynamics in a given external gravitational field. The method is based on a generalization of Roe’s approximate Riemann solver for the non relativistic Euler equations in Cartesian coordinates. The new method is applied to a set of standard test problems for general relativistic hydrodynamics, and is shown to perfo...

General relativistic hydrodynamics with special relativistic Riemann solvers

We present a general and practical procedure to solve the general relativistic hydrodynamic equations by using any of the special relativistic Riemann solvers recently developed for describing the evolution of special relativistic flows. Our proposal relies on a local change of coordinates in terms of which the spacetime metric is locally Minkowskian and permits accurate numerical calculations ...