There is presented a particularly simple transformation of the Schwarzschild metric into new coordinates, whereby the "spherical singularity" is removed and the maximal singularity-free extension is clearly exhibited.

Maximal Extension of Schwarzschild Metric

Initial data are the starting point for any numerical simulation. In the case of numerical relativity, Einstein's equations constrain our choices of these initial data. We will examine several of the formalisms used for specifying Cauchy initial data in the 3 + 1 decomposition of Einstein's equations. We will then explore how these formalisms have been used in constructing initial data for spacetimes containing black holes and neutron stars. In the topics discussed, emphasis is placed on those issues that are important for obtaining astrophysically realistic initial data for compact binary coalescence.

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Initial Data for Numerical Relativity

Numerical relativity and compact binaries

Using York's method, the author discusses techniques for numerically constructing GR initial data on a Cauchy surface representing spacetimes containing arbitrary numbers of black holes, each with arbitrary mass, position, (linear) momentum and spin (angular momentum). The initial data slices discussed are maximal and 3-conformally flat. The author restricts the discussion to axisymmetric asymptotically flat vacuum (outside the black holes) slices, although these restrictions are not essential.

/pdf/coordinates-and-boundary-conditions-for-the-general-3oj4m8jgvf.pdf

Coordinates and boundary conditions for the general relativistic initial data problem

We perform general-relativistic simulations of charged black holes targeting GW150914 We show that the inspiral is most efficient for detecting black hole charge through gravitational waves and that GW150914 is compatible with having charge-to-mass ratio as high as 03 Our work applies to electric and magnetic charge and to theories with black holes endowed with U(1) (hidden or dark) charges Using our results, we place an upper bound on the deviation from general relativity in the dynamical strong-filed regime of Moffat's modified gravity

General Relativistic Simulations of the Quasicircular Inspiral and Merger of Charged Black Holes: GW150914 and Fundamental Physics Implications

The momentum constraint of the initial-value problem of general relativity is addressed. The undressed extrinsic curvature of a general compact momentum source is presented in terms of multipole moment integrals.

Jeffrey M. Bowen

Papers

General solution for flat-space longitudinal momentum

Inversion symmetric initial data for N charged black holes

Graphic displays of gravitational initial data