A new study by researchers at the University of Amsterdam shows how gravitational waves from black holes can be used to reveal the presence of dark matter and help determine its properties. The key is a new model, based on Einstein’s theory of general relativity, that tracks in detail how a black hole interacts with the surrounding matter.

Researchers Rodrigo Vicente, Theophanes K. Karydas and Gianfranco Bertone from the UvA Institute of Physics (IoP) and the GRAPPA centre of excellence for Gravitation and Astroparticle Physics Amsterdam have published their results in the journal Physical Review Letters. In their paper, they introduce an improved way to model how dark matter around black holes affects the gravitational waves these systems emit.

Extreme mass-ratio inspirals

The work focuses on so-called extreme mass-ratio inspirals, or EMRIs: systems in which a relatively small, compact object - for example a black hole formed in the collapse of a single star - orbits and slowly spirals into a much more massive black hole, typically found at the centre of a galaxy. As it spirals inward, the smaller object emits a long gravitational-wave signal.

Future space missions such as the European Space Agency’s LISA space antenna, planned for launch in 2035, are expected to record these signals for months or even years, tracking hundreds of thousands to millions of orbital cycles. If modelled accurately, these “cosmic fingerprints” can reveal how matter - especially the mysterious dark matter that is thought to make up most of the matter in the Universe - is distributed in the immediate surroundings of massive black holes.

A relativistic point of view

Before missions like LISA begin taking data, it is crucial to predict in detail what kinds of signals we should expect and how to extract as much information as possible from them. Until now, most studies have relied on simplified descriptions of how the environment affects EMRIs. The new paper by the IoP/GRAPPA physicists closes this gap for a broad class of environments. It provides the first fully relativistic framework – meaning that it uses Einstein’s theory of gravity in full, instead of simpler approximations based on Newtonian gravity – to describe how the surroundings of a massive black hole modify an EMRI’s orbit and the resulting gravitational waves.

The study focuses in particular on dense concentrations of dark matter - often called “spikes” or “mounds” - that may form around massive black holes. By embedding their new relativistic description into state-of-the-art waveform models, the authors show how such structures would leave a measurable imprint on the signals recorded by future detectors. This work represents a fundamental step in a long-term programme that aims to use gravitational waves to map the distribution of dark matter in the Universe and shed light on its fundamental nature.