Hi Dipayankar;
I believe Jeff was refering to Hawkings Black Hole Formula;
Black hole entropy
Black hole entropy is the entropy carried by a black hole.
If black holes carried no entropy, it would be possible to violate the second law of thermodynamics by throwing mass into the black hole. The only way to satisfy the second law is to admit that the black holes have entropy whose increase more than compensates for the decrease of the entropy carried by the object that was swallowed.
Starting from theorems proved by Stephen Hawking, Jacob Bekenstein conjectured that the black hole entropy was proportional to the area of its event horizon divided by the Planck area. Later, Stephen Hawking showed that black holes emit thermal Hawking radiation corresponding to a certain temperature (Hawking temperature). Using the thermodynamic relationship between energy, temperature and entropy, Hawking was able to confirm Bekenstein's conjecture and fix the constant of proportionality at 1/4:
where k is Boltzmann's constant, and is the Planck length. The black hole entropy is proportional to its area A. The fact that the black hole entropy is also the maximal entropy that can be squeezed within a fixed volume was the main observation that led to the holographic principle. The subscript BH either stands for "black hole" or "Bekenstein-Hawking".
Although Hawking's calculations gave further thermodynamic evidence for black hole entropy, until 1995 no one was able to make a controlled calculation of black hole entropy based on statistical mechanics, which associates entropy with a large number of microstates. In fact, so called "no hair" theorems appeared to suggest that black holes could have only a single microstate. The situation changed in 1995 when Andrew Strominger and Cumrun Vafa calculated the right Bekenstein-Hawking entropy of a supersymmetric black hole in string theory, using methods based on D-branes. Their calculation was followed by many similar computations of entropy of large classes of other extremal and near-extremal black holes, and the result always agreed with the Bekenstein-Hawking formula.
Best to all,
Pat
Compactifications
F-theory is formally a 12-dimensional theory, but the only way to obtain an acceptable background is to compactify this theory on a two-torus. By doing so, we obtain type IIB superstring theory in 10 dimensions. The SL(2,Z) S-duality symmetry of the resulting type IIB string theory is manifest because it arises as the group of large diffeomorphisms of the two-dimensional torus.
More generally, one can compactify F-theory on an elliptically fibered manifold (elliptic fibration), i.e. a fiber bundle whose fiber is a two-dimensional torus (also called an elliptic curve). For example, a subclass of the K3 manifolds is elliptically fibered, and F-theory on a K3 manifold is dual to heterotic string theory on a two-torus. (Eight dimensions are large.
Sorry, but this stuff has absolutely no relevance, certainty, simplicity, or truth.
=
MJA
PS: Nonsense
The truth of everything is less than one inch,it is only equal and the lion is one.One is free when the door is opened,education has the key.=
I think I just had a brain anurism.![]()
Hi everyone;
This is completely off the subject, but I just received pictures of my grandson at 10 months old, and I had to share them with you. He is my only grandchild, and to me represents life and joy. He is the same one that I posted at the end of my AN IDEA.( 1st post )
Very best to all,
Pat
What a lovely pic, Pat; he's adorable. His eyes, to me, convey a sense of wisdom.
~neutralino
If you haven't found something strange during the day, it hasn't been much of a day - John A. Wheeler.
Woooooooooooooow!
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