What is the minimum mass for a Black Hole?

Question

I'm doing some self-research into black holes from a thermodynamic standpoint and I'm wondering, what's the minimum mass or combination of mass, pressure, density, etc. required to create a black hole?

Answer 1

Einstein's equations do not put any lower limit on the mass of a black hole. In order for something to be a black hole, it must have a mass-to-radius ratio that satisfies this:

M/r > c²/(2G) = 6.7 * 10^26 kg/m

where:
M = object's mass
r = object's radius
c = speed of light
G = universal gravitational constant

Notice that you can choose an arbitrarily small "M", as long as you also shrink "r" sufficiently.

Notice also that--contrary to popular opinion--black holes can have an arbitrarily small density (ρ):

ρ = M/(4πr^3/3)
= (1/(4πr²/3))(M/r)
> (1/(4πr²/3))(c²/(2G))

So there's a relationship between density and radius: according to the above equation, you can reduce a black hole's density to that of cotton candy, provided you make its radius large enough.

As far as NATURAL processes go:
-- It's known that sufficiently massive stars will (when they run out of fuel) will automatically collapse under their own weight until they reach that M/r ratio and become black holes. They have to be at least 1.5 solar masses for that to happen.
-- It's now thought that supermassive black holes (tens of millions of solar masses) exist at the centers of most galaxies. We're not sure how they formed.
-- Stephen Hawking hypothesized that microsopically small black holes may have formed during the high pressures right after the big bang.

Note that Hawking also said that black holes are not truly "black", but that they "evaporate" at a rate which increases as their radius decreases. According to him, a sufficiently small (sub-microscopic) black hole would evaporate so fast that it would literally explode. In that sense, there is a lower limit to a black hole's mass (I don't know exactly what it is, but it would be somewhat less than, say, an average mountain's mass.)

Answer 2

Strictly, there is no minimum mass for a black hole provided that the density can be increased sufficiently. So for instance an electron has a Schwarzchild radius of around 10^-57 m and would technically be capable of forming a black hole if it could be confined within this space.

However, what is normall meant by minimum mass is the minimum mass required to form a black hole by gravitational collapse alone. There is no truly definitive answer to this (because many assumption must be made) but generally it is taken that a start of at least 3 solar masses is required to undergo gravitational collapse to a black hole. The star may lose mass during its collapse (it would inevitably nova), but would have to end up with a mass greater than 1.44 solar masses as this is the mass which degeneracy pressure can support against further gravitational collapse (the Chandresakar limit).

Answer 3

When a black hole steps into focus between earth and star (x) the light from the source (x) will stretch and banish after some time. That is one of many ways to actually see where the black hole is. In optical view the black hole is the radius of lack of light, in the centre it is completely black because no light can escape it, on its boundaries the light is stretched because of gravity - so you can get the picture. From the standard perspective, time on the sun surface for an object that is not moving would flow pretty the same as on earth maybe 0.001s slower, cant calculate right now. Standard time rate would be the time rate of an object that is not moving and that is isolated from any gravitational forces, like an object in outer space. It would be pretty the same as our time rate. Time in standstill ∆t=0 was before the big bang. Cern is working on to create a small black holes 10^-15 m in radius at LHC.

Answer 4

I I found a chart that shows the full spectrum.

Radius for Black Hole of a Given Mass
Object Mass Black Hole Radius
Earth 5.98 x 1027 g 0.9 cm
Sun 1.989 x 1033 g 2.9 km
5 Solar Mass Star
9.945 x 1033 g 15 km
Galactic Core
109 Solar Masses 3 x 10^9 km

Answer 5

well a black hole is not formed until the star has a minimum mass............

this is the chandrashekhar limit and is about 1.4 times the mass of the sun (1.98892 × 10^30 kilograms)......... (yes ours).....

so you cant exactly say the mass of a black hole but you can give the mass of the star that formed the black hole........

Answer 6

we don't know all of the black holes in the universe .. there may be dozens kinds of 'em ! SO there is no answers..