Perturbative hyperboloidal extraction of gravitational waves in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>3</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math> numerical relativity

We present a framework to propagate to null infinity gravitational waves computed at timelike world tubes in the interior of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mn>3</a:mn><a:mo>+</a:mo><a:mn>1</a:mn></a:mrow></a:math> (Cauchy) numerical relativity simulations. In our method, numerical relativity data are used as the inner inflowing boundary of a perturbative time-domain Regge-Wheeler-Zerilli simulation in hyperboloidal coordinates that reaches null infinity. We showcase waveforms from <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mo stretchy="false">(</c:mo><c:mn>3</c:mn><c:mo>+</c:mo><c:mn>1</c:mn><c:mo stretchy="false">)</c:mo><c:mi mathvariant="normal">D</c:mi></c:mrow></c:math> simulations of gravitational collapse of rotating neutron stars, binary black hole mergers and scattering, and binary neutron star mergers and compare them to other extrapolation methods. Our perturbative hyperboloidal extraction provides a simple yet efficient procedure to compute gravitational waves with data quality comparable to the Cauchy-characteristic extraction for several practical applications. Nonlinear effects in the wave propagation are not captured by our method, but the present work is a stepping stone toward more sophisticated hyperboloidal schemes for gravitational-wave extraction.