Cardy formula

In physics, the Cardy formula is important because it gives the entropy of black holes. In recent years, this formula has appeared in not only the calculation of the entropy of BTZ black holes but also in checking the AdS/CFT correspondence and the holographic principle.

In 1986 J. L. Cardy discovered the following formula Cardy (1986), which gives the entropy of a (1+1)-dimensional conformal field theory (CFT):

Here $c$ is the central charge, $L_0 = ER$ is the product of the total energy and radius of the system, and the shift of $c/24$ is caused by the Casimir effect. $c$ and $L_0$ lie in the Virasoro algebra of this CFT. In 2000 E. Verlinde extended this formula to the arbitrary (n+1)-dimensions Verlinde (2000), so it is also called Cardy-Verlinde formula. Consider a AdS space with the metric

where R is the radius of a n-dimensional sphere. The dual CFT lives on the boundary of this AdS space. The entropy of the dual CFT can be given by this formula as

where E_c is the Casimir effect, E total energy. The above reduced formula gives the maximal entropy

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Formula

In science, a formula is a concise way of expressing information symbolically as in a mathematical or chemical formula. The informal use of the term formula in science refers to the general construct of a relationship between given quantities. The plural of formula can be spelled either as formulas or formulae (from the original Latin).

In mathematics, a formula is an entity constructed using the symbols and formation rules of a given logical language. For example, determining the volume of a sphere requires a significant amount of integral calculus or its geometrical analogue, the method of exhaustion; but, having done this once in terms of some parameter (the radius for example), mathematicians have produced a formula to describe the volume: This particular formula is:

Having obtained this result, and knowing the radius of any sphere in question, we can quickly and easily determine its volume. Note that the volume V and the radius r are expressed as single letters instead of words or phrases. This convention, while less important in a relatively simple formula, means that mathematicians can more quickly manipulate larger and more complex formulas. Mathematical formulas are often algebraic, closed form, and/or analytical.

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The Formula (1980 film)

The Formula is a mystery film directed by John G. Avildsen released by Metro-Goldwyn-Mayer in 1980. It features a preeminent cast including Marlon Brando, George C. Scott, John Gielgud, and Marthe Keller. Craig T. Nelson also makes a brief appearance as a geologist.

Plot

The film opens in the final days of World War II as the Russians are on the outskirts of Berlin. A German army Panzer Korps general (Richard Lynch) is dispatched to the Swiss border with top secret materials, with orders to hide them from the Allies.

In contemporary Los Angeles, Lt. Barney Caine (George C. Scott) is assigned to solve the murder of his former boss and friend Tom Neeley, which presumably occurred during a drug deal gone wrong. However, Neeley has written 'Gene' on a newspaper in his own blood, and Caine finds a map of Germany with the name 'Obermann' on it. Caine is surprised to learn that Neeley provided drugs at parties hosted by the tycoon Adam Steiffel (Marlon Brando). When he interviews Neeley's ex-wife (Beatrice Straight), he quickly catches her in several lies, and when he returns to interview her a second time, he finds her shot dead in her hot tub.

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