Numerically generated axisymmetric black hole spacetimes: Numerical methods and code tests

Evolution of distorted rotating black holes. I. Methods and tests

“…This problem could be removed if we use (η, φ) → (−η, −φ) instead of η → −η, resulting in consistent evolution equations on both sides of the throat. We point out that this condition is consistent with the Kerr initial data, and is the generalization of the technique of evolving Schwarzschild with a symmetric lapse [10].…”

“…In this first paper in this series we present details of a numerical code designed to evolve rotating black hole initial data sets, such as Kerr, Bowen and York [3], and a new class of data sets we have developed [8]. With such a code we can now study the dynamics of highly distorted, rotating black holes, paralleling recent work of the NCSA group on non-rotating holes [9,10]. The first studies of the physics of these evolving systems are presented in a companion paper [11], referred to henceforth as Paper II, and a complete study of the initial data sets will be discussed in Ref.…”

“…Note also that if a = 0 then q 0 = 0 and we recover the Schwarzschild 3-metric. This metric is now in the form used in the previous NCSA black hole studies [5,9,10,19,20]. Another solution we study is related to the original solution of Bowen and York [3].…”

“…Building on previous work [9,10], we construct our spacetimes to be inversion symmetric through the black hole "throat". This Einstein-Rosen bridge [16] construction has two geometrically identical sheets connected smoothly at the throat, located at η = 0.…”

“…[9,10] in defining the variables used in our code. Additional metric and extrinsic curvature variables must be introduced to allow for the odd-parity modes present now that the system allows for rotation.…”