Free hyperboloidal evolution in axisymmetry
PT-CERN Call 2021/2
Edgar Gasperin Garcia
Instituto Superior Técnico (Universidade de Lisboa)
CENTRA - Center for astrophysics and gravitation
Intimately related to other areas of astrophysics and cosmology is the recently born field of gravitational wave (GW) astronomy. Crucial in the analysis of GW data is the input from numerical simulations in the form of waveform templates, which in turn carry the information from the physics in the strong-field regime described by General Relativity (GR) via numerical simulations, from which the wave signals are extracted. As detector sensitivity increases, it needs to be matched by an improvement in the accuracy of the templates. One very promising and elegant way to get rid of finite-radius-extraction error is to numerically evolve the physical system of interest (e.g. a black hole binary) on hyperboloidal slices: spacelike slices that reach future null infinity, which corresponds to the endpoints of future-directed null geodesics and where global quantities of spacetimes such as energy or radiation are unambiguously defined. Conformal compactification, based on an idea by Nobel-laureate Penrose , is a suitable approach to the hyperboloidal initial value problem, further developed by Friedrich . Formal divergences in the equations make numerical implementations of this problem challenging, but previous successful implementations encourage us to follow this promising path. The aim of this project is to generalise the existing free-evolution hyperboloidal spherically symmetric code  to axisymmetry, and so i) get closer to a full 3D hyperboloidal infrastructure to simulate binary coalescences and extract GW signals, and ii) couple the axisymmetric Einstein equations to physical content, such as scalar fields, the Maxwell equations and the Yang-Mills fields, to study their phenomenology in a scenario more general than spherical symmetry, and among them consider specially the candidates to fundamental fields. Additionally, the code can also be adapted to describe an Anti-deSitter (AdS) spacetime, and used to study collapse in axisymmetry.