Black hole questions

Hello i have some questions about black holes to the ats members that are way smarter than me on the subject. Thank you for answering. If a question does not make sense because of a misunderstanding of bh mechanic on my part pls indicate it to me.



Been wondering what is the distance between the singularity and the event horizon of a 1solarmass bh? Or an equation to find the radius of any blackhole.


When a massive enough to become bh star goes supernova, how long does it take for the entire mass to fall back to singularity and become a bh? If not instantanous, how do we call the object in transition from the shattered star to a black hole.


Howcome black holes have the same mass as the star they were before the supernova if so much of the star's matter has been blasted into space?


Also, if an object orbiting that star survived the blast of its supernova, would its orbit remain unchanged since the bh has the same mass as the original star?

How is infinite mass in zero volume even a mathemathical possibility? How is this explained mathematically.

originally posted by: Golantrevize
Or an equation to find the radius of any blackhole.

You can find the diameter of a black hole. The radius may be undefined.

a reply to: Bedlam


You mean "under defined" which in relation to Wikipedia there would be a referent, to a request for more substance?

In relation to the OP...

How come black holes have the same mass as the star they were before the supernova if so much of the star's matter has been blasted into space?

Exactly what is your premise based on?

Properties

By the no-hair theorem, a black hole can only have three fundamental properties: mass, electric charge and angular momentum (spin). It is believed that black holes formed in nature all have spin, but no definite observation of the spin has been recorded. The spin of a stellar black hole is due to the conservation of angular momentum of the star that produced it.

The gravitational collapse of a star is a natural process that can produce a black hole. It is inevitable at the end of the life of a star, when all stellar energy sources are exhausted. If the mass of the collapsing part of the star is below the Tolman–Oppenheimer–Volkoff (TOV) limit for neutron-degenerate matter, the end product is a compact star — either a white dwarf (for masses below the Chandrasekhar limit) or a neutron star or a (hypothetical) quark star. If the collapsing star has a mass exceeding the TOV limit, the crush will continue until zero volume is achieved and a black hole is formed around that point in space.

The maximum mass of a neutron star is not well known. In 1939, it was estimated at 0.7 solar masses, called the TOV limit. In 1996, a different estimate put this upper mass in a range from 1.5 to 3 solar masses.[3]

In the theory of general relativity, a black hole could exist of any mass. The lower the mass, the higher the density of matter has to be in order to form a black hole. (See, for example, the discussion in Schwarzschild radius, the radius of a black hole.) There are no known processes that can produce black holes with mass less than a few times the mass of the Sun. If black holes that small exist, they are most likely primordial black holes. Until 2016, the largest known stellar black hole was 15.65±1.45 solar masses.[4] In September 2015, a black hole of 62±4 solar masses was discovered in gravitational waves as it formed in a merger event of two smaller black holes.[5] As of April 2008, XTE J1650-500 was reported by NASA[6] and others[7][8] to be the smallest-mass black hole currently known to science, with a mass 3.8 solar masses and a diameter of only 15 miles (24 kilometers). However, this claim was subsequently retracted. The more likely mass is 5–10 solar masses.

There is observational evidence for two other types of black holes, which are much more massive than stellar black holes. They are intermediate-mass black holes (in the centre of globular clusters) and supermassive black holes in the centre of the Milky Way and other galaxies.

en.wikipedia.org...

a reply to: Kashai

Geometry near an event horizon is non-Euclidean. The distance from the event horizon to the center of the singularity may be undefined.

a reply to: Bedlam


Where have you observed a definition where the response was not infinity in response to a singularity?

a reply to: Golantrevize

Firstly, one solar mass is a little small for a black hole. I'm not sure of how anything in nature could form such a low mass singularity. It is possible that a singularity could evaporate over time to produce a one solar mass singularity but my guess is that it would be unstable and without the restraining gravitational force, may (possibly) explode like a supernova (how an unstable rapid evaporation might appear to us). Theoretically, you can have smaller singularities but the density would have to be very high and I'm not really convinced that 'density' even makes sense in terms of a black hole.

Anyway, the (theoretical) Schwatzchild radius for one solar mass is 2.95 km (or 1.835 miles).

The equation that describes Schwarzschild radius is well addressed with this Wikipedia article. As you see, it is really dependent upon mass. There are supermassive black holes and their radius is large.

The star would actually take significant time for all the mass to reach the point of singularity (if it ever does occur). This is because of significant time dilation occurring as the matter accelerates towards the speed of light and the gravitational field bends spacetime similar to effects at light speed. From our external frame of reference, the infalling matter must 'stop' at that radius because its light can no longer reach us, being trapped by the gravitational field creating an escape velocity faster than 'c'. From this external reference frame, the matter would slow and stop as it approached the Schwarzschild radius, but from the reference frame of the infalling matter (ignoring tidal forces) the passage of time of the external universe would seem to speed up. Some have argued that it may be possible for the infalling matter to 'see' nearly the entire history of the universe before the matter hit the singularity, which it would be accelerating towards at an apparently normal rate (from its reference frame).

Also, As the accreted matter falls inside the boundary of the Schwarzschild radius, it adds to the mass of the black hole and, therefore, enlarges the Schwarzschild radius.

When a signifcantly massive star (approx 3 solar masses or more) consumes all its fuel, it begins to collapse. This collapse preceeds the supernova explosion and, because of tidal differences, draws mass inward faster if it is closer to the point of singularity. This opens a gap between the Schwartzchild radius and the outer infalling matter (this differential tidality is sometimes referred to as 'spaghettification', where a glob of matter gets stretched out into a spaghetti-like string of particles). The acceleration of the outer infalling matter would produce massive heating, which causes the explosion of those outer layers. One should note that by this time, the black hole already exists so the escaping mass/energy is not large as a percentage of the captured mass. There has also been some speculative work that suggests that the heating of infalling matter creates more mass, most of which will eventually fall into the black hole. This leads to the black hole mass being very similar to the mass of the original material, even if some mass/energy is lost.

Because the total mass of the system remains largely unchanged, any orbiting object will remain in orbit according to standard orbital mechanics, but the actual outcome depends upon many factors such as the nova ejection and tidal forces within orbiting masses and so is more likely going to be 'turbulent' (which means bloody hard to calculate). In fact, the mathematics may seem fairly simple but are not because of the dynamics of everything. All movements are accelerating, mass and energy are interchanging, time (and space) is dilating, every bit is affecting every other bit and at the core of it all, is a paradox, which leads to:

Your final question mentions infinite mass, which is not the case. Black holes have finite masses and this is evidenced mathematically by their Schwatzchild radii. Although, we don't have anything in Physics that can explain how you can fit any mass into a space smaller than the Planck length. All reality overlaps.

a reply to: chr0naut

Thanks!

That was one item I was going to point out. Unless the LHC is making mini black holes (see the Wikipedia link. I.e, they are not doing that), there is the other issue of mass.

OP, there are solar mass BHs and super massive BHs. They differ by... astronomical amounts! One is light hour(s) across and the other is light days!

I am just getting reading up on this myself (astronomy is not my realm of great knowledge... just enough to get by)! So good questions. And check out the Event Horizon telescope thread!!!

a reply to: chr0naut

Wow...this is a great answer!

I was going to distill things down a little bit, for the sake of simplicity, but your answer is fantastic.

To the OP:

I was going to say...

1. The radius of the event horizon is a function of mass.

2. Time is relative depending on the observers point of view. In other words, the time of "collapse" depends on one's vantage point.

3. The gravitational field before the supernova keeps most of the ejecta within the sphere of influence of the ultimate event. Over time this mass increases.

4. Yes, for a while, but over time the mass of the black hole would increase and steadily draw nearby mass into it.

5. Infinite mass in zero volume is not a possibility. However, remember time factors into this. It's not about volume, but rather mass. Volume has little bearing when contemplating black holes.

Again, more simplistic answers, but Chr0naut's answers are far more thorough.

originally posted by: Flyingclaydisk
a reply to: chr0naut

Wow...this is a great answer!

I was going to distill things down a little bit, for the sake of simplicity, but your answer is fantastic.

To the OP:

I was going to say...

1. The radius of the event horizon is a function of mass.

2. Time is relative depending on the observers point of view. In other words, the time of "collapse" depends on one's vantage point.

3. The gravitational field before the supernova keeps most of the ejecta within the sphere of influence of the ultimate event. Over time this mass increases.

4. Yes, for a while, but over time the mass of the black hole would increase and steadily draw nearby mass into it.

5. Infinite mass in zero volume is not a possibility. However, remember time factors into this. It's not about volume, but rather mass. Volume has little bearing when contemplating black holes.

Again, more simplistic answers, but Chr0naut's answers are far more thorough.

Thanks. Your answers were pretty good too.

a reply to: Golantrevize

The first thing to be stated here is this is all theoretical. Black holes have in no way shape or form been studied. Quite a bit of sci-fi literature seems to be taken as 'fact'.
#1 There is no distance between the singularity and the event horizon according to modern physics. Infinite curvature results in (selectively) non-renormalizable gobbledegook meaning they can touch.
#2 The speed of light is generally thought to constrain this.
#3 We have very little knowledge of bh masses. We have zero data on solar mass black holes.
#4 Orbital calculations are notoriously erratic and frustrating. It takes very little to perturb an orbit.
#5 It is not explained mathematically. The infinities which are so "normal" in most quantum theories are deemed "non-renormalizable" when it comes to large masses and general st curvature.

originally posted by: Kashai
a reply to: Bedlam


Where have you observed a definition where the response was not infinity in response to a singularity?

That's where your problem comes trying to measure a radius.

Here is a good deal of data from NASA on black hole observations.


NASA-Led Study Explains Decades of Black Hole Observations


www.nasa.gov...

Thanks for everyone who answered here, i understand a bit more.

One thing to note is I was talking about the distance between the event horizon and the singularity and not the sc radius. I understood from an answer that space would be so curved that distances would not be measurable from eh to singularity. Ty everone

a reply to: Bedlam


Admit it. You like teaching.

a reply to: Golantrevize


A point would be that when is comes to a measurement of the radius of a black hole, there is a problem as we get infinity.

In consideration it is possible that what we define as infinity is not infinity but otherwise as a permutation, specifically outside our comprehension.

If you stop motion you stop activity presenting that whatever motion applies otherwise then becomes the activity.


Hypothetically speaking what would happen to earths orbit if the moon were to suddenly disappear?