Black Holes in a Non-Empty Universe express
A stick thrown into a pond sinks straight down. But if the pond's water is slowly rising, the stick will be delayed and sink somewhere unexpected. So it is with black holes: we usually assume they sit in a void, but the entire universe is gently stretching. This stretch, like the rising water, slightly alters the path of anything orbiting nearby.
The authors took a simple model: a black hole in an expanding universe. It turns out that because of the expansion, a star or a small black hole loses energy a bit faster. Its orbit becomes circular sooner, and then — plummet. The time until the fall shortens. If the expansion is very weak, as in the real cosmos, the effect is barely noticeable. But if a galaxy cluster is nearby, it acts similarly and can noticeably speed up the fall.
This matters for future space-based detectors. They will catch gravitational waves — the ripples in space from such falls. If expansion is ignored, you could miscount events and misinterpret the signal itself. The rising water in the pond changes not only the stick's fate but also the ripples on the surface.
Original abstract
as written by the authors arXiv:2602.17154
The inspiral of a compact object into a black hole is a key source of low - frequency gravitational waves for future space-based detectors like LISA. While models of this process have advanced considerably, they typically focus on asymptotically flat spacetimes. In this paper, we investigate how departures from asymptotic flatness, whether driven by cosmic expansion or large-scale galactic environments, alter adiabatic orbital evolution. Using the Schwarzschild - de Sitter (SdS) metric, we parametrize these deviations via an `SdS parameter' ($$\lambda$$) and analyze its impact on bound orbits. We calculate how $$\lambda$$ shifts the separatrix between bound and plunging states and modifies the relationship between a binary's energy, angular momentum, and orbital geometry. By applying a modified quadrupole formula in the weak-field limit, we investigate the effect of $$\lambda$$ on circularization, plunge times, and orbital trajectories. We show that a positive SdS parameter accelerates eccentricity decay and shortens inspiral timescales. We also generate adiabatic waveforms from inspirals evolving under radiation reaction, exhibiting an increase in amplitude and a cumulative phase advance induced by $$\lambda$$. While these effects are negligible if $$\lambda$$ is strictly cosmological, they become observationally relevant if the parameter serves as a proxy for astrophysical environments that induce $$\sim r^2$$ potential corrections. Our results suggest that such environmental coupling could meaningfully bias event rate estimates and waveform templates for space-based gravitational-wave astronomy.
The expansion of the universe is noticeable even over the distance from Earth to the Moon: it adds about 3 centimeters per year.
In the movie 'Interstellar,' the heroes fly to a black hole without thinking about cosmic expansion, but it could have thrown off their calculations.