# Does Gravitational Time Dilation stack on top of Time Dilation caused by Velocity?

Using 1 CM from the Event Horizon of Super Massive Black Hole, SGR A, as the reference point. The particles within the accretion disk are traveling at extreme high speeds. Assume this speed increases as the particles orbit closer and closer to the EH.

Are the particles within the accretion disk of Super Massive BH SGR A subject to time dilation both from 1) the gravitational field of SGR A at 1 cm from Event Horizon ...and 2) from the the acceleration of the particles traveling around the BH as they approach the EH?

Does the acceleration of particles act as an interference to the affects of the gravitational time dilation? And if not, or if these two types of time dilation affect the time intervals for this group of particles, When would an observer 1 light year from the EH see the particles enter the EH? A) Before Impacting the EH, B) After impacting the EH, or C) Never?

• There's some info about time dilation near rotating black holes in this Physics.SE answer. A recent estimate of the spin parameter of the Sagittarius A* black hole is $a=0.65\pm0.05$; there are no stable orbits 1 cm from its event horizon. – PM 2Ring Oct 20 '19 at 11:36
• Thank You for your answer, – Richard Oct 20 '19 at 13:28
• Please assume there are hot clumps of gas that orbit the BH SGR A at 30% of C - All should agree when answering this question there are no stable orbits when we think in terms of planets orbiting our sun, or moons orbiting our planet; as the conditions at this relative point would break up matter this close to the EH. I am speaking solely about the particles traveling within the accretion disk at speeds up to 30% of the speed of light. Does the time dilation at 1 CM from SGA's BH stack on top of the time dilation from the velocity of the particles in the accretion disk? – Richard Oct 20 '19 at 13:37
• Matter in an accretion disk is in orbit, so the inner radius of the accretion is at the ISCO - the innermost stable circular orbit. Of course, some of the matter in the accretion disk is being pulled into the BH, so it doesn't have a stable orbit. OTOH, Sgr A* (fortunately) doesn't really have much of an accretion disk, just the gas clouds you mentioned. There are several stars that are orbiting it, although at a fair distance from the event horizon. – PM 2Ring Oct 20 '19 at 13:49
• You may like to browse the existing questions about rotating black holes. We have many more pages here on black holes, but they generally assume that the BH is a simple Schwarzschild BH, not a rotating Kerr BH. The Physics stack also has many pages on black holes & general relativity. The quick answer to your question is, yes, for bodies orbiting a BH there's time dilation due to velocity and time dilation due to gravity. Hopefully, one of our professionals will give you a more complete answer. – PM 2Ring Oct 20 '19 at 13:56