@Steve,
There’s a very nicee app called ‘Photomath’
Point it at an equation, push the button and it will solve it for you eg graph plotting etc. solution steps worked out for you.
Don’t know how teachers are dealing with kids homework with sort of stuff floating around, but for an old fart like me it’s fantastic
(Does trig, simple interaction/differentiation as well)
There’s a very nicee app called ‘Photomath’
Point it at an equation, push the button and it will solve it for you eg graph plotting etc. solution steps worked out for you.
Don’t know how teachers are dealing with kids homework with sort of stuff floating around, but for an old fart like me it’s fantastic
(Does trig, simple interaction/differentiation as well)
What is going on inside is not accessible to an outside observer. I think there is no anwer.
The mass, not the rate.
You can calculate the size of the BH from the Swartzchild radius formula - per the earlier posts ( there’s lots of these calculators around)
Schwarzschild Radius
Schwarzschild Radius
The only thing growing is the mass.
The singularity has no size, it is a point in the mathematical sense.
It is the center of the Swartzchild sphere of radius Rs = 2 G M / c²
A black hole is a weird object, one cannot talk about it's size or growth like for a usual object.
My understanding is: Everything that enters in the Swartzchild sphere goes into the singularity; Wether it is matter m or radiation where it's energy E has an equivalent mass m = E/c². The only thing that grows is the mass of the BH, consequently the Schartzchild radius.
Inside the event horizon, space stretches out toward the infinitely dense singularity. Adding mass to the black hole increases the stretching of space and causes the interior volume of the black hole to grow ever larger and larger.
We can see none of this happening from outside the event horizon. We see the exterior volume remain much the same, expanding only slightly as mass falls into the event horizon.
The volume of a sphere depends on the cube of the radius (volume = 4/3 x pi x radius^3). Double the radius, and the volume goes up by 2 x 2 x 2 = 8 times.
This means we would have to combine eight identical, solid plasticine balls together in order to produce one solid ball of twice the radius. The density of the plasticine (mass/volume) would obviously remain the same as both the mass and the volume have increased proportionately.
Now, black holes are not solid balls. The radius of the event horizon of a black hole depends directly on the mass of the black hole. Double the mass and the radius of the event horizon doubles too.
If we could take just two identical black holes and combine them, the radius of the event horizon doubles and the mass doubles too. But volume has gone up by eight times! So the average density actually decreases, and is one quarter what we started with.
The volume, as observed from ouside the event horizon, is 4/3 x pi x radius^3 where the radius is the Schwarzchild radius. This is the volume in Euclidean space and simple enough for all of us to understand.
However, inside the event horizon, we are dealing with non-Euclidean geometry and the 3-D spatial volume depends on the geometry of curved space. That's where 'simple' no longer applies!
However, inside the event horizon, we are dealing with non-Euclidean geometry and the 3-D spatial volume depends on the geometry of curved space. That's where 'simple' no longer applies!
Oh I see, so the mass accumulating requires space(room) so space stretches to accomodate?, all the while increasing distance to the singularity? If the singularity is infinitely dense, is this not just another way of saying nothing can ever reach the point of it?
No no -)) - inside the event horizon it is still Euclidean geometry that is at hand or at least we can just assign that it is. As in any other space-time room. What happens is that temperature is falling and with that time. At the singularity, which is the centre of the BS (Black Sphere), the temperature is in fact 0K and time stand still. The size of this sub-sphere, called the I0KS (Inner 0K Sphere) is proportional to the Schwarzchild radius and grov and shrink as mass enters the BS or leaves by Hawking Radiation ;-).
This is quite new insights and you read it first here...
//
-)) - inside the event horizon it is still Euclidean geometry that is at hand or at least we can just assign that it is. As in any other space-time room. What happens is that temperature is falling and with that time. At the singularity, which is the centre of the BS (Black Sphere), the temperature is in fact 0K and time stand still. The size of this sub-sphere, called the I0KS (Inner 0K Sphere) is proportional to the Schwarzchild radius and grov and shrink as mass enters the BS or leaves by Hawking Radiation ;-). This is quite new insights and you read it first here...
//
Outside, I doubt we are dealing with Euclidean geometry; Close ( whatever this means) to the event horizon, gravity is humongous.inside the event horizon, we are dealing with non-Euclidean geometry and the 3-D spatial volume depends on the geometry of curved space. That's where 'simple' no longer applies!
I think gravity is continuously increasing while crossing the event horizon, without a discontinuity at the crossover.
Inside a black hole, there is a strange mix of space and time.
Seen from the outside, the black hole has only a finite size in space. Inside, the singularity extends infinitely and is not really a point in space as we like to think of it.
Time is finite inside a black hole (it starts at the event horizon and ends at the singularity). Matter can reach the singularity in a finite time. The singularity, because it is infinite in extent, can contain an infinite amount of matter.
From a distance, a black hole is just like any other mass in the Universe. It's only when you get extremely close, within a few Schwarzschild radii, that you start noticing the departures from Newtonian gravity.
What is 'this'?
You need to include a noun in your sentence!
Anyway, I'm off to read my Hi-Fi magazine and have a glass of Sauvignon Blanc.
OK, I started this about inside volume and outside volume of a BH. This warps my brain because I do not know how volumes are defined close, within few Rs.
I even wonder wether volumes are defined or relevant.
"Hi-Fi World" of course.
Did I ever tell you the story of how I failed to get a job on "Hi-Fi World" aged 27?
I told Noel Keywood his Editor was a pompous and ignorant idiot. Didn't go down well with his Editor, who recommended that he and I weren't going to get along well! Ah well, Noel went with the Status Quo. Doubtless wanted a quiet life.
I am the opposite. I want excitement in my life. Look at this fairground attraction: The Wall of Death!
Wall of death - Wikipedia
I was up for it. What's the worst that can happen? Paid my 2 bob out of my weekly pocket-money and got suspended in mid-air defying Gravity. Quite surprising that it worked.
To get to the point, what rips you apart in a Black Hole is not Gravity. It is the Tidal Force. IIRC, that is the differential of Gravity. Pulls your wee toes away from your haed.
Did I ever tell you the story of how I failed to get a job on "Hi-Fi World" aged 27?
I told Noel Keywood his Editor was a pompous and ignorant idiot. Didn't go down well with his Editor, who recommended that he and I weren't going to get along well! Ah well, Noel went with the Status Quo. Doubtless wanted a quiet life.
I am the opposite. I want excitement in my life. Look at this fairground attraction: The Wall of Death!
Wall of death - Wikipedia
I was up for it. What's the worst that can happen? Paid my 2 bob out of my weekly pocket-money and got suspended in mid-air defying Gravity. Quite surprising that it worked.
To get to the point, what rips you apart in a Black Hole is not Gravity. It is the Tidal Force. IIRC, that is the differential of Gravity. Pulls your wee toes away from your haed.
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