Chronology |
Current Month |
Current Thread |
Current Date |

[Year List] [Month List (current year)] | [Date Index] [Thread Index] | [Thread Prev] [Thread Next] | [Date Prev] [Date Next] |

*From*: Bob Sciamanda <trebor@VELOCITY.NET>*Date*: Sun, 18 Feb 2001 22:23:52 -0500

I'll start the ball rolling by observing that your equation for the escape

velocity is correct, but your words leading up to it are not. You have set

the total energy equal to zero, not the Lagrangian (recall that the

potential energy here is negative). Also two language/grammar nitpicks :

Several times you refer to the "faith" of a star - perhaps you meat

"fate"? - You also say that the stiffness of a body "effects" the speed of

sound - that should be "affects"?

Bob

Bob Sciamanda (W3NLV)

Physics, Edinboro Univ of PA (em)

trebor@velocity.net

www.velocity.net/~trebor

----- Original Message -----

From: "Robert B Zannelli" <Spinoza321@AOL.COM>

To: <PHYS-L@lists.nau.edu>

Sent: Sunday, February 18, 2001 2:13 PM

Subject: Rossetta Stones of Physics ( Black Holes)

Disclaimer:on

It is certainly not my intention to lecture to the many eminent Physicist

this list especially at such a basic level. However for those nonspecialist

or non professional physicist who are members of this list I thought thisideas

posting, which I posted to another Physics list earlier, might be

interesting. The subject matter of this posting is hardly new as these

were developed circa 1970s. Nevertheless I welcome comments or criticismfrom

anyone. If list members feel this type of post is inappropriate for thislist

I request they inform me of that by private email or list posting.more

Dear List Members:

Perhaps nothing in science has captured the popular imagination

than what John Wheeler has named Black Holes. These are stars which due tohave

their great mass have shrunk to what are called singularities once they

exhausted their fusion fuel. While the life cycle of stars is afascinating

story, in itself, I will only touch upon that story briefly and limit thisof

post to talk about the amazing properties of black holes.

Stars that have reached the end of their fusion energy production

lives have one of three possible faiths. Stars which have a residual mass

less than about 1.3 solar masses become what are called white dwarfs whichdegeneracy,

are immensely dense remnants of the original star. For this class of dead

star further collapse is prevented by what is called the electron

the internal pressure due the Pauli exclusion principal preventingelectrons

from all being in the same Quantum State. For those stars that retaingreater

than 1.3 solar masses after burnout electron degeneracy is insufficient toneutron

generate the pressure to prevent further collapse and these stars become

neutron stars. Here the internal balancing pressure is generated by

degeneracy and the star is called a neutron star.This

However for the those stars which retain greater than about 2 solar

masses there is no force in the universe that can stop their collapse.

is due to the strictures of special relativity. There are two equivalentways

to explain this. First in special relativity we must remember that massand

energy are the same thing. This means that as the stars internal pressurethis

increases to combat the gravitational force which is collapsing the star

very same pressure which is a form of energy begins itself to increase thethemselves

gravitational force. At a sufficiently high pressure the gravitational

effects of this pressure become greater than the pressure effects

and the faith of the star is sealed. It must collapse to a singularity.effects

The second way to look at this is that the stiffness of any body

the speed of sound through that body. At about 2 solar masses thestiffness

factor would have to have to generate sound velocities greater than thespeed

of light which is prohibited by SR.the

What makes a black hole such a unique entity is the fact that when a

black hole forms it produces an event horizon which causes an unbeatable

information barrier which actually cuts off the interior of the black hole

from our universe. Let us see why. For any gravitational body the escape

velocity is (The velocity necessary for any thing within the confines of

gravitational force of the body to escape to infinity) is given by settingand

the lagrangian (The difference of kinetic and potential energy) to zero

solving for the velocity in the equation. Therefore we get:increases. In

m*(v^2)/2=GM*m/r which gives us v=(2*G*M/r)^.5

From this we can see that as r gets smaller the escape velocity

fact at some point this velocity reaches the speed of light. The surfacearea

of this star that corresponds to the radius where the escape velocity isthe

speed of light is called the event horizon. This is where the barrier isthat

divides the unobservable interior of the black hole from our Universe.relationships

This is given by the equation:

A=16*pi*(G*M)^2/(c^4)

Which is derived by some simple algebra from the above

(This is for a non spinning zero charged black hole only. While a zeroas

charged black hole is likely a nonspinning one is not. However this will

serve for the purposes of this post)

So it would appear that we could say that a black hole could be described

a cold absolute zero temperature entity. ( Since it emits zero energy intoall

the Universe) However this is not really true. This is where the story of

black holes gets even more interesting. As anyone who knows anything at

about physics knows that general relativity and Quantum mechanics are likemay

oil and water. However thanks to the work of Steven Hawking and others we

have the first small convergence of these two theories. Where these twoof

theories may converge if ever so slightly is at the surface of the event

horizons of black holes.

To understand why this is so we must look a little closer at the nature

black holes. First it is believed that black holes retain only threehair

properties after their collapse. These are mass, electrical charge and

angular momentum. This is known in Cosmology as the "black holes have no

theorem." This means that during a black hole collapse there is a greatloss

of information which in the language of physics means there is a greatthermodynamic

entropy increase. ( Entropy is the measure of disorder in any system) This

interesting fact caused physicist to look at black holes from a

perspective.of

The first hints came in 1970 from with the realization that surface area

a black hole always increases when additional matter falls into it. Sinceof

this represents a further loss of information it means a further increase

entropy. This led to Jacob D. Berkenstein an Israeli Physicist to proposeit's

that the area of the event horizon of a black hole was proportional to

entropy. S=K*A Where K is a constant of proportion, S is Entropy and A isdue

the area of the event horizon. However if this true then it follows that

black holes cannot really be so black. Let us see why. ( The following is

to the work of Stephan Hawking.)1822-1888)

In thermodynamics the following relationship holds dS=dE/T where S is

entropy and E is the energy of the system and T is the temperature of the

system. ( This relationship is due to the work of Rudolf Clausius

Now we already know that E and M are proportional due to specialRelativity

and given that according to Berkenstein S and A are also proportional wecan

derive the following relationship.measure

F=GM/(r^2) and A=4*pi(r^2) we have F=4*pi*G*M/F where F is a

of the gravitational field,A is the area of the event horizon, and M isthe

mass of the black hole. Given this relationship is easy to see thatdA=K*dM/F

Where K is a constant of proportionality. This of course means that F isevent

proportional to the temperature of the black hole at the surface of the

horizon. This is a certainly not zero. Given that we have determined thatthe

temperature of the black hole is not zero we are left with the conclusionto

that black hole must radiate energy.

Of course given the limitations of classical physics there is no way

that any thing can breach the event horizon light speed barrier. But theIn

black hole must emit energy since it's temperature is not zero. However

thanks to the work of Stephan Hawking we have a way out of this quandary.

Quantum Mechanics we have what are known as virtual processes. This is dueto

the uncertainty principal which is on the order of:the

deltaE*deltat=>hbar/2

Where delta E is the uncertainty of energy for any system and deltat is

time interval under consideration and hbar is Planck's constant divided byviolated

2*pi. What this means is that the conservation of mass energy may be

but only for a time deltat=(hbar/2)/deltaE where deltaE the energythe

uncertainty in question. The larger the mass energy violation the shorter

time it last for. Now let us look at the boundary of the event horizon.These

mass energy violations produce particle pairs a particle and it's antiThis

particle since all other conservation laws must hold. This means that a

possible virtual particle pair may be an electron and an anti electron.

would mean that the time interval where this could occur would be on thethe

order of:

t=(hbar/2)*(2*M)

Where M is the mass of the electron. Therefore this process

could occur on the order of x=t*C where C is the speed of light and x is

maximum separation of the particle and anti particle. This processes arehas a

occurring continuously everywhere in the Universe. In fact this process

measurable effect known as the Casimir effect named after it's discoverer.interval

Normally these virtual particle pairs recombine within the time

defined by the uncertainty principal. However when this process happensnear

the surface of an event horizon there is a finite chance that the particlemay

pair will end up on opposite sides of he event horizon. Since no particle

exceed the speed of light this means that this particle pair can nevermass

recombine. The particle outside the event horizon escapes acquiring the

energy of the particle pair while the particle that has penetrated theevent

horizon carries an equal negative energy to insure that mass energy isindirectly

conserved. Effectively the black hole has radiated energy.

The probability for this process to occur is proportional to the

curvature of space time in the vicinity of the event horizon which is

indirectly proportional to the area of the event horizon therefore

proportional to the mass of the black hole. Hawking has shown that we maytemperature

calculate the temperature of a black hole with the following equation;

T=h*(c^2)/(16*(pi^2)*K*G*M)

Where K is Boltzmann's constant which may be simplified to:

T(Degress Kelvin)=6E-8/M(solar masses)

From this it is obvious that as black hole radiant energy their

increases until as M approaches zero they explode with incredible energy.years.

This is a truly remarkable result.

However given the likely masses of black holes this process takes a long

time. Hawking has shown that:

t=(approx) 1E66 *(M^3) with M in solar masses and t in

2

No black hole in our Universe assuming it had a mass of at least

solar masses has enough time to have exploded. However it is possible thatthey

were processes which could have produced black holes of very small mass

values during the early history of our Universe and these black holes if

exist could be exploding even now.

Bob Zannelli

- Prev by Date:
**Re: sparks** - Next by Date:
**Bar magnets, was magnetic circuits** - Previous by thread:
**Rossetta Stones of Physics ( Black Holes)** - Next by thread:
**Re: Rossetta Stones of Physics ( Black Holes)** - Index(es):