Darwin-Riemann Problems in General Relativity

Semi-Riemann Geometry and General Relativity

Generalized Riemann Spaces and General Relativity.

spectrum of K, and fixed t > 0. As a consequence, u(-, t) lies in the range of (K tI), and by Theorem 3 of Paper I, after a replacement on a set of measure zero, u(-, t) lies in C"T(D). If Eg(x) is the smooth representative of its equivalence class in L2' r(D), for any Borel set A in El lying in the interval XI < a, by Theorem 3 of Paper I, IE(A)g(x)I = I(K, I)-j(K R I)jE(A)g(x)I < C(oaI + I I)...

Numerical Problems in General Relativity

The construction of gravitational wave observatories is one of the greatest scientific efforts of our time. As a result, there is presently a strong need to numerically simulate the emission of gravitation radiation from massive astronomical events such as black hole collisions. This entails the numerical solution of the Einstein field equations. We briefly describe the field equations in their...

Solving the Darwin problem in the first post-Newtonian approximation of general relativity

We analytically calculate the equilibrium sequence of the corotating binary stars of incompressible fluid in the first post-Newtonian(PN) approximation of general relativity. By calculating the total energy and total angular momentum of the system as a function of the orbital separation, we investigate the innermost stable circular orbit for corotating binary(we call it ISCCO). It is found that...

A general framework for solving Riemann-Hilbert problems numerically

A new, numerical framework for the approximation of solutions to matrix-valued Riemann–Hilbert problems is developed, based on a recent method for the homogeneous Painlevé II Riemann–Hilbert problem. We demonstrate its effectiveness by computing solutions to other Painlevé transcendents. An implementation in Mathematica is made available online.