High-powered gravitational news

Abstract

We describe the computation of the Bondi news for gravitational radiation. We have implemented a computer code for this problem. We discuss the theory behind it as well as the results of validation tests. Our approach uses the compactified null cone formalism, with the computational domain extending to future null infinity and with a worldtube as inner boundary. We calculate the appropriate full Einstein equations in computational eth form in (a) the interior of the computational domain and (b) on the inner boundary. At future null infinity, we transform the computed data into standard Bondi coordinates and so are able to express the news in terms of its standard N + and N × polarization components. The resulting code is stable and secondorder convergent. It runs successfully even in the highly nonlinear case, and has been tested with the news as high as 400, which represents a gravitational radiation power of about 10 13 M ⊙ /sec.

General relativistic null-cone evolutions with a high-order scheme

“…(66)). This is a significant improvement in efficiency over the original 2nd-order scheme developed in [12] including its advancements [15,3]. We also note that when further increasing the radial and time resolution, the error falls below ∼ 10 −12 and we observe an expected drop in convergence order due to nonlinear effects.…”

“…(19a) through Eq. (21) were first presented in [12]. We repeat them here, but with a mis-print in Eq.…”

“…A prominent result was the first stable dynamical evolution of a black hole spacetime in three spatial dimensions achieved by the Pittsburgh group [11,12]. Since then, the Pittsburgh null code (or PITTNullCode) has become the main building block for current implementations of characteristic extraction used in numerical relativity simulations [1,2,3,4,5], and is now part of the publicly available Einstein Toolkit [13].…”

“…Over the years, there have been several improvements to the original algorithm as implemented in [11,12]. Stereographic coordinates were replaced by more uniform angular grids [15,16].…”

“…The evolution equations are written in the Bondi form, following the prescription of [12]. Time and outward radial integrations are performed by method-of-lines schemes.…”