Black holes, as the most mysterious celestial bodies in the universe, have received limited research from humans. This article reviews the history of observing black holes and present the dynamical method for measuring their mass. Drawing on reported dynamical estimates, I built a dataset of stellar-mass black holes and obtained an average mass of 8.016 M⊙, which is consistent with the theoretical lower limit of 5M⊙. Although I verified that most black holes apply to the theoretical lower limit of 5M⊙ proposed in previous studies, it is possible for Swift J1727.8-1613, XTE J1650-500, GRS 1716-249, GRS 1009-45, GRO J0422+32, H 1705-250, 3A 1524-617, 1H 1659-487 with a minimum mass below 5M⊙.

This paper uses X-ray reflection light spectrum method as the key. It studies how to measure the spin number (a*) of star-mass black holes. The spin number (a*) is linked to the radius of the Innermost Stable Circular Orbit (ISCO). The big change of the Fe Kα line in the reflection light spectrum (caused by Doppler effect and gravity red-shift) is the key to find out a*. We use three telescopes together to get data: NICER, NuSTAR, Insight-HXMT. We use the relxill model series to fit the data. We get results for 3 typical black holes: Cygnus X-1: Its spin is extremely fast (a*>0.9985). 4U 1543-47: Its spin is medium. GX 339-4: Its spin is very fast, and its iron amount is 5 times more than the Sun’s. We compare this method with the continuous spectrum fitting method. The reflection light spectrum method is more accurate for checking spin, tilt angle and iron amount. But it depends on the model (for example, the result of GX 339-4 is conflicting). We need to check it many times to reduce mistakes. The conclusion says: Long-time material absorption makes the black hole’s spin reach the maximum. Jet feedback stops the spin from getting faster. In the future, with new telescopes (eXTP, Athena) and studies on medium-mass black holes, we can understand the spin’s change rules better.