arXiv subjects
Publications and source records attributed to Denis Pollney.
Numerical relativity has faced the problem that standard 3+1 simulations of black hole spacetimes without singularity excision and with singularity avoiding lapse and vanishing shift fail after an evolution time of around 30-40M due to the so-called slice stretching. We discuss lapse and shift conditions for the non-excision case that effectively cure slice stretching and allow run times of 1000M and more.
We extend previous work on 3D black hole excision to the case of distorted black holes, with a variety of dynamic gauge conditions that are able to respond naturally to the spacetime dynamics. We show that the combination of excision and gauge conditions we use is able to drive highly distorted, rotating black holes to an almost static state at late times, with well behaved metric functions, without the need for any special initial conditions or analytically prescribed gauge functions. Further, we show for the first time that one can extract accurate waveforms from these simulations, with the full machinery of excision and dynamic gauge conditions. The evolutions can be carried out for long times, far exceeding the longevity and accuracy of even better resolved 2D codes. While traditional 2D codes show errors in quantities such as apparent horizon mass of over 100% by t = 100M, and crash by t = 150M, with our new techniques the same systems can be evolved for hundreds of M's in full 3D with errors of only a few percent.
We use the computer algebra system \textit{GRTensorII} to examine invariants polynomial in the Riemann tensor for class $B$ warped product spacetimes - those which can be decomposed into the coupled product of two 2-dimensional spaces, one Lorentzian and one Riemannian, subject to the separability of the coupling: $ds^2 = ds_{Σ_1}^2 (u,v) + C(x^γ)^2 ds_{Σ_2}^2 (θ,ϕ)$ with $C(x^γ)^2=r(u,v)^2 w(θ,ϕ)^2$ and $sig(Σ_1)=0, sig(Σ_2)=2ε(ε=\pm 1)$ for class $B_{1}$ spacetimes and $sig(Σ_1)=2ε, sig(Σ_2)=0$ for class $B_{2}$. Although very special, these spaces include many of interest, for example, all spherical, plane, and hyperbolic spacetimes. The first two Ricci invariants along with the Ricci scalar and the real component of the second Weyl invariant $J$ alone are shown to constitute the largest independent set of invariants to degree five for this class. Explicit syzygies are given for other invariants up to this degree. It is argued that this set constitutes the largest functionally independent set to any degree for this class, and some physical consequences of the syzygies are explored.
We examine the relative performance of algorithms for the calculation of curvature in spacetime. The classical coordinate component method is compared to two distinct versions of the Newman-Penrose tetrad approach for a variety of spacetimes, and distinct coordinates and tetrads for a given spacetime. Within the system GRTensorII, we find that there is no single preferred approach on the basis of speed. Rather, we find that the fastest algorithm is the one that minimizes the amount of time spent on simplification. This means that arguments concerning the theoretical superiority of an algorithm need not translate into superior performance when applied to a specific spacetime calculation. In all cases it is the global simplification strategy which is of paramount importance. An appropriate simplification strategy can change an untractable problem into one which can be solved essentially instantaneously.