Isotropic Coordinates for Generalized Schwarzschild-like Solutions

Abstract

We consider a broad class of static, spherically symmetric generalized Schwarzschild-like solutions with multiple non-interacting anisotropic fluid sources and derive the coordinate transformation from Schwarzschild-like (curvature) to isotropic coordinates with conformally flat spatial slices. The isotropic form removes spatial-sector coordinate pathologies at the horizon, clarifies geometric quantities (e.g., ADM mass and curvature invariants), and enables the construction of well-posed initial data on t=const hypersurfaces, suitable for the Hamiltonian and conformal formulations of numerical relativity and for perturbation theory. The backgrounds in isotropic coordinates we develop make it straightforward to separate environmental effects from intrinsic strong-gravity signals and meet the growing interest in non-vacuum black hole phenomenology across scattering, lensing, and waveform modeling.

References in corpus (26)

• The Confrontation between General Relativity and Experiment
• The Dynamics of General Relativity
• Accurate Evolutions of Orbiting Black-Hole Binaries Without Excision
• Effective one-body approach to general relativistic two-body dynamics
• Gravitational wave extraction from an inspiraling configuration of merging black holes
• On the Numerical Integration of Einstein's Field Equations
• Testing the nature of dark compact objects: a status report
• Quintessence and black holes
• Black holes, gravitational waves and fundamental physics: a roadmap
• Can environmental effects spoil precision gravitational-wave astrophysics?
• The Einstein Toolkit: A Community Computational Infrastructure for Relativistic Astrophysics
• A simple construction of initial data for multiple black holes
• A single-domain spectral method for black hole puncture data
• Colliding Black Holes: The Close Limit
• Initial Data for Numerical Relativity
• A new probe of dark matter properties: gravitational waves from an intermediate mass black hole embedded in a dark matter mini-spike
• Quasinormal modes of a black hole surrounded by quintessence
• The Kiselev black hole is neither perfect fluid, nor is it quintessence
• Disks, spikes, and clouds: distinguishing environmental effects on BBH gravitational waveforms
• An Introduction to the Einstein Toolkit
• Lagrange Inversion
• Strong Gravitational Lensing by Kiselev Black Hole
• Decomposition of total stress-energy for the generalised Kiselev black hole
• Charged shells and elementary particles
• Lagrange Inversion Formula by Induction
• Schwarzschild-de Sitter Spacetimes, McVittie Coordinates, and Trumpet Geometries