LazyTB: Extended LTB-solutions with Multiple Interacting Fluids
Abstract
We present a low entry barrier numerical code LazyTB that solves the Einstein equations in the ADM-formulation for a general spherically symmetric problem with an arbitrary number of fluids with user defined equations of state and optional interactions between the fluids mediated by drag-vectors. We present the ADM equations in terms of carefully chosen dimensionless variables that avoid some numerical instabilities by analytic cancellation of potentially diverging terms. We demonstrate the code by applying it to a number of examples including the standard LTB model, a model with radiation and dark matter, a polytropic dark energy model with a non-vanishing sound speed and a model with coupled interacting dark matter and dark energy. We also implement a suite of diagnostic tools, including ray-tracing algorithms, that allow extracting physical observables such as luminosity distances for observers at arbitrary locations from the simulations. The code is built to be easy to extend also beyond the late-universe applications considered in the examples of this paper. LazyTB is available at https://github.com/ollijvaisanen/LazyTB.
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BibTeX
@misc{kainulainen2026lazytb,
title = {{LazyTB: Extended LTB-solutions with Multiple Interacting Fluids}},
author = {Kimmo Kainulainen and Enrico D. Schiappacasse and Linda Tenhu and Olli Väisänen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09625},
eprint = {2610.09625},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09625},
}
RIS
TY - UNPB
TI - LazyTB: Extended LTB-solutions with Multiple Interacting Fluids
AU - Kimmo Kainulainen
AU - Enrico D. Schiappacasse
AU - Linda Tenhu
AU - Olli Väisänen
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.09625
UR - https://arxiv.org/abs/2610.09625
AB - We present a low entry barrier numerical code LazyTB that solves the Einstein equations in the ADM-formulation for a general spherically symmetric problem with an arbitrary number of fluids with user defined equations of state and optional interactions between the fluids mediated by drag-vectors. We present the ADM equations in terms of carefully chosen dimensionless variables that avoid some numerical instabilities by analytic cancellation of potentially diverging terms. We demonstrate the code by applying it to a number of examples including the standard LTB model, a model with radiation and dark matter, a polytropic dark energy model with a non-vanishing sound speed and a model with coupled interacting dark matter and dark energy. We also implement a suite of diagnostic tools, including ray-tracing algorithms, that allow extracting physical observables such as luminosity distances for observers at arbitrary locations from the simulations. The code is built to be easy to extend also beyond the late-universe applications considered in the examples of this paper. LazyTB is available at https://github.com/ollijvaisanen/LazyTB.
ER -