Probing the vector charge of Sagittarius A* with pulsar timing

Abstract

Timing a pulsar orbiting around Sagittarius A* (Sgr A*) can provide uswith a unique opportunity of testing gravity theories. We investigate thedetectability of a vector charge carried by the Sgr A* black hole (BH) in thebumblebee gravity model with simulated future pulsar timing observations. Thespacetime of a bumblebee BH introduces characteristic changes to the orbitaldynamics of the pulsar and the light propagation of radio signals. Assuming atiming precision of 1 ms, our simulation shows that a 5-yr observation of apulsar with an orbital period Pb ∼ 0.5 yr and an orbitaleccentricity e ∼ 0.8 can probe a vector charge-to-mass ratio as small asQ/M ∼ 10-3, which is much more stringent than the current constraint fromthe Event Horizon Telescope (EHT) observations, and comparable to theprospective constraint from extreme mass-ratio inspirals with the LaserInterferometer Space Antenna (LISA).