At the centers of many galaxies lurk black holes — regions with gravity so strong that even light cannot escape. Stars often orbit them, and sometimes one of those stars is a pulsar, a cosmic lighthouse sending out strictly periodic radio pulses. When such a pulsar moves behind a black hole, its signals reach us with a delay. This isn't just a delay from a detour in space — the spinning black hole itself twists spacetime around it, like a spoon stirring thick honey, and drags the signal along.
The authors of the study used the STVG theory (scalar–tensor–vector gravity)—a variant of modified gravity that tries to explain galaxy rotation without invoking dark matter. In this theory, a black hole has an extra parameter α that controls the strength of gravitational vector forces. The scientists calculated how the signal delay depends on α and on the black hole's spin (a). They extended the known Laguna–Wolszczan formula, adding more subtle effects.
It turns out that different values of α can noticeably change pulse arrival times — from a few microseconds to fractions of a second. These are tiny shifts, but modern radio telescopes can detect them. All that's needed is to find a suitable pair: a pulsar and a black hole where the pulsar regularly passes behind the black hole. Then the delay becomes a natural laboratory for testing the laws of gravity.
as written by the authors arXiv:2606.25611
Modified gravity (MOG) theories are alternatives to general relativity (GR) that arose primarily from the need to explain the observed galactic flat rotation curves without invoking the elusive dark matter hypothesized by GR. A well known MOG is the Scalar-Tensor-Vector-Gravity (STVG) developed by Moffat, who has also found a spinning solution called the Kerr-MOG black hole (BH) characterized by the spin $$a$$ and MOG parameter $$\alpha$$, the latter determining the strength of the gravitational vector forces. We consider the static-MOG metric ($$a=0$$) to first understand how the nature of geometry drastically changes depending on different sectors of $$\alpha $$. Then we study the influence of $$\alpha $$ in each sector on a new astrophysical diagnostic caused by \textit{frame dragging}, viz., the difference $$\Delta t$$ in the times of arrival (TOA) at the observer of signals emanating from a variable pulsar (PSR) passing behind a Kerr-MOG lens in a PSR-BH binary system. The study generalizes the zeroth order Laguna-Wolszczan formula up to third PPN order in $$\left(1/r\right)$$ using thin-lens approximation, which reveals how $$\Delta t$$ is influenced both by $$a$$ and $$\alpha$$. The magnitude and sign of $$\alpha $$ indicate deviations from GR ($$\alpha =0$$) and future measurements may constrain $$\alpha$$ provided a suitable binary is identified.
Pulsars are ultra-dense remnants of exploded stars that spin hundreds of times per second. Their pulses are so stable they can rival atomic clocks.
In Carl Sagan's novel Contact, a signal from an extraterrestrial civilization arrives through a system of black holes, warping time and space.