Relativistic propagation and frame dragging time delay in the timing of a pulsar orbiting the supermassive black hole SgrA*

Abstract

Timing a pulsar in a close orbit around the supermassive black hole SgrA* at the center of the Milky Way would open the window for an accurate determination of the black hole parameters and for new tests of General Relativity and alternative modified gravity theories. An important relativistic effect which has to be taken into account in the timing model is the propagation delay of the pulses in the gravitational field of the black hole. Due to the extreme mass ratio of the pulsar and the supermassive back hole we use the test particle limit to derive an exact analytical formula for the propagation delay in a Kerr spacetime and deduce a relativistic formula for the frame dragging effect on the arrival time. As an illustration, we treat an edge-on orbit in which the frame dragging effect is expected to be maximal. We compare our formula for the propagation time delay with Post-Newtonian approaches, and in particular with the frame dragging terms derived in previous works by Wex & Kopeikin and Rafikov & Lai. Our approach correctly identifies the asymmetry of the frame dragging delay with respect to superior conjunction, avoids singularities in the time delay, and indicates that in the Post-Newtonian approach frame dragging effects are generally slightly overestimated.

14 pages, 9 figures

References in corpus (14)

• First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way
• The Five-Hundred-Meter Aperture Spherical Radio Telescope (FAST) Project
• First Sagittarius A* Event Horizon Telescope Results. VI: Testing the Black Hole Metric
• Tempo2, a new pulsar timing package. II: The timing model and precision estimates
• Detection of the Schwarzschild precession in the orbit of the star S2 near the Galactic centre massive black hole
• Motion of spinning test bodies in Kerr spacetime
• An upper limit on the spin of SgrA${}^{\ast }$ based on stellar orbits in its vicinity
• Approximating light rays in the Schwarzschild field
• Searching for pulsars in the Galactic Centre at 3 and 2 mm
• Photon Emission from Circular Equatorial Kerr Orbiters
• Observations of Radio Magnetars with the Deep Space Network
• Analytical solution methods for geodesic motion
• Orbital spin dynamics of a millisecond pulsar around a massive black hole with an general mass quadrupole
• Radio timing in a millisecond pulsar-extreme/intermediate mass ratio binary system

Cited by in corpus (8)

• Photon Ring Astrometry for Superradiant Clouds
• Strong deflection of massive particles in spherically symmetric spacetimes
• Multi-scale Constraints on Scalar-Field couplings to Matter: The Geodetic and Frame-Dragging Effects
• Testing space-time geometries and theories of gravity at the Galactic Center with pulsar's time delay
• Kerr-scalaron metric and astronomical consequences near the Galactic Center black hole
• Is it possible to distinguish between different black hole solutions using the Shapiro time delay?
• Some applications of the Shapiro time delay
• Timing Gravity with Pulsars in the Strong Field