Schwarzschild radius and black hole entropy

[hkhandrika]

I know that the schwartzchild radius is 2GM/C^2 = Rs, but what does this actually mean? Is this the radius of the event horizon, or the distance from the singularity to the event horizon, or something else?

Also, how does one measure the entropy of a black hole, and what can this entropy show us?

Thanks for your time.

Harish

 

[pervect]

Probably the best description is "something else". At any distance R from the black hole in Schwarzschild coordinates, the circumference of a circle of constant R will be 2*pi*R.

 

[hkhandrika]

Ok, but what is the distance from? The event horizon? The singularity, or some calculated center of the BH? Also, what about the entropy of a black hole. What exactly can it tell us, and how does one go about calculating it. Sorry for being so persistent/annoying. I hadn't checked the question since I was caught up with work, and I've always wanted to know. Thanks a lot for your help.

 

[hkhandrika]

Nm... I got the answer from my Physics GSI. Thanks for the help anyway.

 

[extremevidlak]

The Schwartzchild radius is the size of an object compared to its mass. It is the radius for a given mass where, if you collapse that mass to fit that radius, nothing can stop it from collapsing into a gravitational singularity or 'black hole'. Commonly found when discussing the theory of gravitation and general relativity.

(source: http://wiki.answers.com)​

 

[Suede]

Looking at his original paper addressing the Mercury orbit problem:

http://www.sjcrothers.plasmaresources.com/schwarzschild.pdf"
K. Schwarzschild, Sitzungsberichte der Deutschen Akademie der Wissenschaften zu Berlin, Klasse fur Mathematik, Physik, und Technik (1916) pp 189.


This is the original paper Einstein saw and agreed with, translated into English.

 

[Chronos]

Swarzschild is a tragic reminder of the gratuitous evils of war.

 

[jovian]

Schwartzchild Radius. A Conseptual Approach

Basics behind Schwartzchild Radius, conceptual physics: There exist's a gravitational attraction between matter and its self. I encourage you to recall the Cavendish experiment. Where physicist Henry Cavendish was able to first measure and quantify this attraction. Applying matter is attracted to matter principles, we realize things like, it is our gravitational attraction to the mass of the Earth that keeps us on it. In the case of large planets the gravitational force is directly proportional to the mass of that planet. Especially stars, such as our sun, the mass of that body causes such great gravitational forces in attraction to itself that the mass decreases in diameter. As the mass decreases in diameter the gravitational forces become more and more concentrated (force per unit of area in measurement). As we all know, light is a particle and has mass. When the force of gravity of that star becomes so dense that not even light can escape, you have the niasense of a schwartzchild Radius, and the event horizon for the star to become a black hole... Singularities result, due to fourth dimensional influences in time-space, but that's a different topic.
The calculation is a simple plug and calculate formula containing the gravitational constant (thanks first formally measured by the above mentioned Cavendish Experiment), the speed of light, and the mass of the gravitating object.

 

[Matterwave]

Addressing the other question...the entropy of a black hole is as of yet uncertain, AFAIK. Classically, a black hole should have 0 entropy because it has only 1 state (singularity), but this violates the second law of thermodynamics whenever matter falls into the black hole (the entropy of the matter goes to 0). Hawking took a different approach to derive the entropy of a black hole. I forget the exact formulation, but his predictions lead to a finite entropy (actually quite large) for a black hole. Since entropy is no longer 0, this also leads to a finite temperature, i.e. the black hole radiates as a black body at some temperature. This is called Hawking radiation.

Don't quote me on this...I'm not 100%. XD

 

[George Jones]

Hawking took a different approach to derive the entropy of a black hole. I forget the exact formulation, but his predictions lead to a finite entropy (actually quite large) for a black hole. Since entropy is no longer 0, this also leads to a finite temperature, i.e. the black hole radiates as a black body at some temperature. This is called Hawking radiation.

Don't quote me on this...I'm not 100%. XD

Using a combination of hand waving, I wrote a something about Hawking radiation and blavk hole entropy,

https://www.physicsforums.com/showthread.php?t=205711.

 

[jovian]

Corelation between Hawking Radiation and Black Holes

Basic Conceptual Physics: Hawking Radiation. Applying the understanding the basic concept of subatomic particles and antiparticles, positive and negative matter. Simply put after this event horizon of the schwartzschild radius (I have previously commented on above), in the formation of a black hole, the subatomic particle having negative mass does not have enough energy to escape the black hole and thus contributes to the decrease in mass of this body; but the subatomic counterpart with positive mass has just enough energy to leave the force of the black hole (if memory serves me, at half the speed of light) and is emitted as radiation by the outside observer. A a radiation that behaves very similar to heat, what we now refer to as hawking radiation.