# Does an object orbiting close to a black hole appear to orbit slower due to time dilation?

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#### Ray Gunn

What is time dilation?
When close to a black hole, EMR VECTORS are altered giving us a relative time reading.
Time itself does not change.
Note from my original question that I'm referring to a measurement of the object's orbital velocity or period as it would appear to an observer "far away" from the black hole.

From other comments, the velocity or period would appear slower. And thus to correctly calculate the black hole's mass based on the closely orbiting object requires a calculation based on GR.

My next question ... Let's say you discover Object1 in an apparent "slow" orbit around Object2. Wouldn't you be mislead, by that apparent slow orbital period, into thinking that Obect1 is orbiting a "low mass" Object2?

#### Unclear Engineer

Going back a step, wouldn't the time near a black hole actually slow down, not just appear to slow down. We do already have measurements that indicate that clocks do run more slowly on Earth's surface than in orbit around Earth, where the gravitational force is lower than on the surface. Doesn't the GR equation result in the passage of time stopping at the event horizon, not just appearing to stop? That is one of the things that makes me think we are missing some theoretical component in the conditions that exist around black holes. How would matter ever get inside the event horizon to make the super-massive things we seem to see in the centers of galaxies?

As for the "next question", I think Ray Gunn is correct that the mass of a black hole would not be calculated to be as high as it really is if it is based on close-in orbital velocities and not calculated with the proper GR equations for orbital mechanics.

#### Helio

Going back a step, wouldn't the time near a black hole actually slow down, not just appear to slow down. We do already have measurements that indicate that clocks do run more slowly on Earth's surface than in orbit around Earth, where the gravitational force is lower than on the surface. Doesn't the GR equation result in the passage of time stopping at the event horizon, not just appearing to stop?
That's a good question. The few books I've read all seem to state that any change in the rate of time experience will not exist for the unfortunate inbound ships. They would not sense time was coming close to stopping, nor would time appear to slow down. The observers from afar, however, would measure something different.

AFAIK, time simply behaves differently for different reference frames, though I can't imagine being able to "see" something stop at the EH since what flashlight would work in this case?

That is one of the things that makes me think we are missing some theoretical component in the conditions that exist around black holes. How would matter ever get inside the event horizon to make the super-massive things we seem to see in the centers of galaxies?
Indeed.

#### Catastrophe

##### "There never was a good war, or a bad peace."
Time dilation defined
Time dilation is the slowing of time as perceived by one observer compared with another, depending on their relative motion or positions in a gravitational field.17 Nov 2021

What is time dilation? | Live Science

Cat

#### Dragrath

Why would this happen at the event horizon? Something in free fall is not seeing any forces other than tidal forces, which tend to pull it apart, rather than compact it.

I tend to think of what is inside a black hole by extending what I think about neutron stars. At least in theory, a neutron star could accrete additional matter until it's surface escape velocity reaches the speed of light, and it would become a small black hole. I don't know of any reason why the material in the neutron star would suddenly change at that point in the accretion process, so I think of a small black hole as being a neutron star inside of an event horizon. I do agree that the material in the neutron star compacts as it accretes more material, and might change phase at a subatomic level to become the mass of quarks or whatever at some point in its mass increase. But, that would make the surface of the star become a smaller and smaller fraction of the space inside its event horizon.

So, I would expect some radial distance between the event horizon and and star surface inside. Working again from what is thought about neutron stars, it is when the accreting matter hits the star's surface that fusion reactions occur and make the events our astronomers see.

Once the event horizon exceeds the star's surface radius, I would still expect that accreting material fuses or whatever when it reaches the star's surface, but we would no longer be able to see that happen from outside, because no light or matter would escape past the event horizon.

If there are other factors involved that change that expectation, please educate me.

And, yes, I do know that neutron stars usually have complicating features like extreme spin rates and extreme magnetic fields, but I don't see how those change the thinking about the event horizon itself not being the location of nuclear fusion or disassembly into quarks. Those features might even tear things apart outside the event horizon and prevent some of the accretions, as we think we see happening around black holes.
In terms of physics I'm not aware of anything which would cause what they described frankly what goes on within or at the event horizon is not known as we have no theories which can be applied directly within this regime In all likelihood our models will break down before one reaches the event horizon in order to resolve the information paradox meaning any assumptions about this region are at best informed guessing and at worst baseless wild speculation.

One important consideration from the context of General relativity and gravitational time dilation is that the curvature of space can be thought of as a rotation of the 4 velocity vector with a magnitude of c (the speed of light in a vacuum better described in terms of the speed of information) this like with acceleration in non inertial frames of reference induces gravitational redshift time dilation and length contraction in this case even within inertial frames of reference. As a consequence from such a frame of reference radiation would appear both more luminous as more photons will cross their light cone but also blue shifted as the larger universe appears speed up relative to their frame of reference. To external frames of reference away from the black hole they will both slow down and be strongly redshifted. For reference the light captured by the Event horizon Telescope around M87* (Sag A* is slightly more complicated in its analysis by our galaxy and its smaller size) is light bent around a region known as the photon sphere as the orbital speed approaches and becomes the speed of light at roughly 1.5 times the Schwarzschild radius for a nonrotating black hole. This light was originally emitted as high energy X-rays by the much further out accretion disk of which the closest extent to the black hole the Innermost Stable Circular Orbit(ISCO) will be 3 times the Schwarzschild radius for the same nonrotating black hole and thus is completely unobservable to the Event Horizon Telescope.

This general relativistic effect becomes more and more extreme the more warped spacetime becomes and thus if X ray light gets stretched into radio light anything closer will becomes warped much more extremely . I.e. from a inertial frame of reference at the Photon sphere those same Xrays that we see as radio waves would be blueshifted from their frame of reference while you would intersect with even more of those light rays as they cross your path due to curvature. As the general relativistic effects intensify closer to the black hole these extreme effects would asymptotically blow up to infinity as outgoing light gets asymptotically stretched out to longer and longer wavelengths (Eventually converging towards the range of the Hawking radiation as the warping of spacetime approaches the event horizon with the luminosity dropping off greatly over time and the reverse will also be true i.e. to the infalling observer in an inertial frame of reference all that radiation is going to become more and more luminous and higher energy at least as long as this trend continues closer to the black hole than the photon sphere which is the closest distance we can probe.

As a consequence should this trend continue and assuming Hawking radiation exists the region immediately around the black hole will become extremely hot and luminous from the perspective of an infalling observer as they effectively crash into everything else that has been falling into the black hole. This is what has led to the idea of the black hole "firewall" a insanely hot radiative boundary region which rapidly fully ionizes and pushes back against infalling material such that nothing actually can ever cross the event horizon once it forms. The natural implication of this is that a black hole can in essence be re-contextualized as an explosion dilated to the extent it appears frozen in time. This is why hawking himself titled his famous paper "black hole explosions".

In truth assuming Hawking radiation is real, when you get down into the nitty gritty details the information paradox really is only relevant for the information of what actually created the black hole as the radiation which prevents things from falling in from the perspective of a near horizon inertial reference frame should imply that said information will be radiated out when the black hole approaches its evaporation timescale. The problem that isn't addressed in this limit is the case of the information which made the black hole itself and unfortunately testing this principal requires such a vast timescale its well beyond human observational limits even in the distant far flung future.

Of course in an accelerating frame of reference this gets even more complicated by the more familiar special relativistic time dilation length contraction and blueshift/redshift but that is beyond this discussion as even the example of just considering the varying extent of curvature for various purely inertial frames of reference is hard enough. Still it seems extremely improbable that one could accelerate long enough in such a way that this time dilation component can greatly effect the overall results.

There is recent work with a concept called the gravitational path integral which suggests this information does get out via quantum entanglement like effects even without needing anything beyond quantum mechanics and general relativity so its possible this paradox is a non issue. However experimentalists point out that as it can't be observed it doesn't really matter what the theory says which is frankly somewhat simplistic as we may be able to someday construct observable implications form the underlying principals.

That's a good question. The few books I've read all seem to state that any change in the rate of time experience will not exist for the unfortunate inbound ships. They would not sense time was coming close to stopping, nor would time appear to slow down. The observers from afar, however, would measure something different.

AFAIK, time simply behaves differently for different reference frames, though I can't imagine being able to "see" something stop at the EH since what flashlight would work in this case?

Indeed.
Yes and no check the above wall of text for context. Yes the rate of time for any observer always feels normal within their frame of reference, however the perspective of other frames of reference will be affected. I.e. time far away from the black hole will appear to be sped up, length extended and blueshifted just as said infalling inertial frame of reference will appear to be slowed down length contracted and redshifted.
Also remember that hawking radiation was only derived in the context of a very distant observer and thus what Hawking radiation looks like to a infalling inertial frame of reference close to the black hole is unaddressed. However if you account for the relative effects of curvature it implies that said radiation is both highly time dilated and redshifted so the actual fluctuations produced by breaking the quantum vacuum assuming general relativity holds up as one approaches the black hole must be blueshifted length extended and sped up such that it might be better to think of infalling observers falling towards a micro black hole at its moment of evaporation.
If Hawking radiation is real and GR applies close to the event horizon then you can never fall into a black hole as you are falling through time towards its moment of evaporation something like ~10^40+ years in the future for monster black holes at the hearts of galaxies. So perhaps its better to think of it as falling to the heat death of the Universe?

The point is that people i.e. science communicators and occasionally even practicing scientists often seem forget that its called General Relativity for a reason.

All inertial frames of reference are relative to every other frame of reference and there is always an effect on length time and wavelengths of light based on the relative local curvature of those regions of spacetime. For some reason people tend to forget to apply the reverse transformations consistently when discussing the infalling inertial frames of reference for a gravitational well. In most cased the effects of this curvature induced changes to time dilation length contraction and wavelengths of light are so tiny they can be neglected however around compact stellar remnants this is no longer the case.

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Absolute zero

#### Unclear Engineer

Dragrath, thanks for typing all of that explanation.

One question: You posted "As a consequence should this trend continue and assuming Hawking radiation exists the region immediately around the black hole will become extremely hot and luminous from the perspective of an infalling observer as they effectively crash into everything else that has been falling into the black hole. This is what has led to the idea of the black hole "firewall" a insanely hot radiative boundary region which rapidly fully ionizes and pushes back against infalling material such that nothing actually can ever cross the event horizon once it forms. "

In the frame of reference of the infalling material, why would they perceive that they "crash into everything else that has been falling into the black hole"? It seems to me that the infalling observer would always continue to see the stuff that went in before get pulled father away and the stuff that is falling in after getting left farther behind - i.e., "spaghettification".

And, from the perspective of a distant observer, the infalling material would appear to just slow down and go to undetectably low wave length of light emissions, correct? So we just can't see what happens.

One of the things that has always bothered me about cosmology adopting quantum mechanics principles is the principle that "information" can never be lost or destroyed. I have never fully believed that, and, since it is a logical negative, I realize that it cannot ever be fully proven. So, when somebody tells me that something in cosmology can't happen because it would cause the loss/destruction of information, I find that argument very unconvincing.

In particular, why wouldn't information be able to become "unobtainable" between different parts of the universe? We already seem to accept that the light currently being emitted from objects now more than 13.8 billion light years away from us will never reach us. Why can't we assume that information that falls into a black hole and will never reach us is not "lost"? That information is somewhere, just in a place where we can't get to it (or it to us).

So, I see that as less of a challenge to the underlying "principle" than doubting the idea that smashing a huge mount of matter into quarks (or something even smaller) doesn't "lose" any information, and, somehow, that process is reversible to the point that the whole universe somehow "knows" how to return itself to any previous state, but that actually doing so is just extremely highly improbable.

#### Harry Costas

The core of a non classical Black hole creates expanding and contracting vector fields.
In so doing time will be effected differently from both directions.
The EH is created by the vector fields pulled in by the core. EMR cannot escape and in so doing communication is impossible.
If you had a method of tracking time, that is not affected by the vector fields, than both observers will records the same time.
Time itself does not change, the mechanism in recording time changes the time from observer A internal to observer B external to the EH.
Matter that enters the EH photo-disintegrates to the same properties of the core.