On Testing the Kerr Metric of the Massive Black Hole in the Galactic Center via Stellar Orbital Motion: Full General Relativistic Treatment

Abstract

The S-stars in the Galactic center (GC) are anticipated to provide unique dynamical constraint on the spin of the GC massive black hole (MBH). In this paper, we develop a fast full general relativistic method to simultaneously constrain the MBH mass, spin, and spin direction by considering both the motion of a star and the propagation of photons from the star to a distant observer. Assuming some example stars, we demonstrate that the spin-induced effects on the projected trajectory and redshift curve of a star depend on both the value and the direction of the spin. The maximum effects over a full orbit can differ by a factor upto more than one order of magnitude for cases with significantly different spin directions. Adopting the Markov Chain Monte Carlo fitting technique, we illustrate that the spin of the GC MBH is likely to be well constrained by using the motion of S0-2/S2 over a period of ~45yr if it is close to one and the astrometric and spectroscopic precisions (sigma_p,sigma_Z) can be as high as (10muas, 1km/s). In the mean time, the distance from the sun to the GC and the MBH mass can also be constrained to an unprecedented accuracy (0.01%-0.1%). If there exists a star with semimajor axis significantly smaller than that of S0-2/S2 and eccentricity larger than that of S0-2/S2, the MBH spin can be constrained with high accuracy over a period of <~10yr for (sigma_p,sigma_Z) ~ (10muas,1km/s), even if the spin is only moderately large (>~0.2).

29 pages, 17 figures

References in corpus (5)

• A Metric for Rapidly Spinning Black Holes Suitable for Strong-Field Tests of the No-Hair Theorem
• Testing the general relativistic ''no-hair'' theorems using the galactic center black hole SgrA*
• Gravitational bending of light by planetary multipoles and its measurement with microarcsecond astronomical interferometers
• On post-Newtonian orbits and the Galactic-center stars
• Clocks around Sgr A*

Cited by in corpus (45)

• Fundamental Physics with the Square Kilometre Array
• Testing black hole candidates with electromagnetic radiation
• Testing General Relativity with stellar orbits around the supermassive black hole in our Galactic center
• Testing General Relativity with the Event Horizon Telescope
• Sgr A* and General Relativity
• X-ray Quasi-periodic Eruptions driven by Star-Disc Collisions : Application to GSN069 and Probing the Spin of Massive Black Holes
• Testing the No-Hair Theorem with Observations of Black Holes in the Electromagnetic Spectrum
• Investigating the Relativistic Motion of the Stars Near the Supermassive Black Hole in the Galactic Center
• General relativistic effects on the orbit of the S2 star with GRAVITY
• Scalar field effects on the orbit of S2 star
• Constraining the range of Yukawa gravity interaction from S2 star orbits III: improvement expectations for graviton mass bounds
• The dark mass signature in the orbit of S2
• Exploring dark matter spike distribution around the Galactic centre with stellar orbits
• Accurate characterization of the stellar and orbital parameters of the exoplanetary system WASP-33 b from orbital dynamics
• What stellar orbit is needed to measure the spin of the Galactic center black hole from astrometric data?
• Prospects for constraining the spin of the massive black hole at the Galactic center via the relativistic motion of a surrounding star
• The black hole at the Galactic Center: observations and models
• Probing the spinning of the massive black hole in the Galactic Center via pulsar timing: A Full Relativistic Treatment
• The Galactic Center as a laboratory for theories of gravity and dark matter
• Post-Keplerian effects on radial velocity in binary systems and the possibility of measuring General Relativity with the S2 star in 2018
• Second-order time delay by a radially moving Kerr-Newman black hole
• On the Newtonian and Spin-induced Perturbations felt by the Stars Orbiting around the Massive Black Hole in the Galactic Center
• GRay2: A General Purpose Geodesic Integrator for Kerr Spacetimes
• The short-period S-stars S4711, S62, S4714 and the Lense-Thirring effect due to the spin of Sgr A${}^{\ast }$
• On the post-Keplerian corrections to the orbital periods of a two-body system and their application to the Galactic Center
• Multi-scale Constraints on Scalar-Field couplings to Matter: The Geodetic and Frame-Dragging Effects
• PPN motion of the S-stars around Sgr A*
• Computation of the general relativistic perihelion precession and of light deflection via the Laplace-Adomian Decomposition Method
• Testing the Black Hole No-hair Theorem with Galactic Center Stellar Orbits
• Kerr-Newman black hole lensing of relativistic massive particles in the weak field limit
• The impact of gravitational lensing in the reconstruction of stellar orbits around Sgr A*
• Is it possible to measure the Lense-Thirring orbital shifts of the short-period S-star S4716 orbiting Sgr A${}^{\ast }$?
• The Secular Periodic Evolution of X-ray Quasi-periodic Eruptions Driven by Star-disc Collisions
• Constraining a disformal Schwarzschild black hole in DHOST theories with the orbit of the S2 star
• Orbital precession of stars in the Galactic center
• Kerr-scalaron metric and astronomical consequences near the Galactic Center black hole
• Kerr-Schild Form of the Exact Metric for a Constantly Moving Kerr Black Hole and Null Gravitational Deflection
• Radial Velocity Measurements of an Orbiting Star Around Sgr A*
• Dynamical Measurement of Supermassive Black Hole Masses: QPE Timing Method
• Self-consistent Solutions of Evolving Nuclear Star Clusters with Two-Dimensional Monte-Carlo Dynamical Simulations
• Dark Matter reconstruction from stellar orbits in the Galactic Centre
• Limiting the Yukawa Gravity through the Black Hole Shadows of Sgr A* and M87*
• Extracting the Possible Intrinsic Relation between Radiative Efficiency and Mass of QSOs: a Maximum Likelihood Method and its Application to the SDSS DR7 QSOs
• Testing the Non-circularity of the Spacetime around Sagittarius A* with Orbiting Pulsars
• On the reconstruction of motion of a binary star moving in the external gravitational field of Kerr black hole by its redshift