Thus it is reasonable that the black hole entropy should be a monotonic function of area, and it turns out to be simplest such function. This increasing behavior is reminiscent of thermodynamic entropy of closed systems. One way to understand why is to recall the "area theorem" (Hawking 1971, Misner, Thorne and Wheeler 1973): the event horizon area of a black hole cannot decrease it increases in most transformations of the black hole. It turns out that these three parameters enter only in the same combination as that which represents the surface area of the black hole. This measure works equally well for mono-, poly-, and heterodisperse populations and represents an unbiased route to evaluation and optimization of nanoparticle synthesis. How to express the black hole entropy in a concrete formula? It is clear at the outset that black hole entropy should only depend on the observable properties of the black hole: mass, electric charge and angular momentum. Herein, we propose the use of information entropy as an alternative and assumption-free method for describing nanoparticle size distributions. Hence it makes sense to attribute entropy to a black hole. In ordinary physics entropy is a measure of missing information. It is the configuration corresponding to the maximum of entropy at equilibrium. Boltzmann's entropy describes the system when all the accessible microstates are equally likely. Thus a black hole can be said to hide information. Since is a natural number (1,2,3.), entropy is either zero or positive ( ln 1 0, ln 0 ). By blocking all signal travel through it, the event horizon prevents an external observer from receiving information about the black hole (save for the mentioned few parameters see Figure 2).Thus by analogy one needs to associate entropy with a black hole. Thermodynamic entropy quantifies the said multiplicity. In thermodynamics one meets a similar situation: many internal microstates of a system are all compatible with the one observed (macro)state. Thus there are many possible internal states corresponding to that black hole. For any specific choice of these parameters one can imagine many scenarios for the black hole's formation. A stationary black hole is parametrized by just a few numbers (Ruffini and Wheeler 1971): its mass, electric charge and angular momentum (and magnetic monopole charge, except its actual existence in nature has not been demonstrated yet).Associating entropy with the black hole provides a handle on the thermodynamics. Thus a thermodynamic description of the collapse from that observer's viewpoint cannot be based on the entropy of that matter or radiation because these are unobservable. However, the hole's interior and contents are veiled to an exterior observer. A black hole is usually formed from the collapse of a quantity of matter or radiation, both of which carry entropy.pressure 100 kPa, 20 degrees C or 1 atm and 0 degrees C, etc.) - not absolute entropy, down to the solidus or liquidus. There are several ways to justify the concept of black hole entropy (Bekenstein 1972, 1973). begingroup Im not familiar with this software, but I would say that likely your 'Entropy' function is actually giving you an entropy change, presumably from some 'standard' conditions (e.g. Is it meaningful or desirable to associate entropy with it ? Is this possible at all ? Only the hole's mass \(M\ ,\) angular momentum \(J\) and electric charge \(Q\) are sensed by an exterior observer.Ī black hole may be described as a blemish in spacetime, or a locale of very high curvature. Although this result was obtained for a particular case, its validity can be shown to be far more general: There is no net change in the entropy of a system undergoing any complete reversible cyclic process.Figure 2: Due to the disposition of the local light cone, the event horizon stops any signals bearing interior information from exiting the black hole. There is no net change in the entropy of the Carnot engine over a complete cycle. However, we know that for a Carnot engine,
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