Ten theses on black hole entropy (original) (raw)
Related papers
An elementary introduction is given to the problem of black hole entropy as formulated by Bekenstein and Hawking, based on the so-called Laws of Black Hole Mechanics. Wheeler's 'It from Bit' picture is presented as an explanation of plausibility of the Bekenstein-Hawking Area Law. A variant of this picture that takes better account of the symmetries of general relativity is shown to yield corrections to the Area Law that are logarithmic in the horizon area, with a finite, fixed coefficient. The Holographic hypothesis, tacitly assumed in the above considerations, is briefly described and the beginnings of a general proof of the hypothesis is sketched, within an approach to quantum gravitation which is non-perturbative in nature, namely Non-perturbative Quantum General Relativity (also known as Quantum Geometry). The holographic entropy bound is shown to be somewhat tightened due to the corrections obtained earlier. A brief summary of Quantum Geometry approach is included, with a sketch of a demonstration that precisely the log area corrections obtained from the variant of the It from Bit picture adopted earlier emerges for the entropy of generic black holes within this formalism.
Entropy Defined, Entropy Increase and Decoherence Understood, and Some Black-Hole Puzzles Solved
1998
Statistical mechanics explains thermodynamics in terms of (quantum) mechanics by equating the entropy of a microstate of a closed system with the logarithm of the number of microstates in the macrostate to which it belongs, but the question `what is a macrostate?' has never been answered except in a vague, subjective, way. However Hawking's discovery of black hole evaporation led to a formula for black hole entropy with no subjective element. In this letter, we argue from this result, together with the assumption that `black hole thermodynamics is just ordinary thermodynamics applied to black holes', that a macrostate for a general (quantum gravitational) closed system is an equivalence class of matter-gravity microstates with the same expectation values for the matter degrees of freedom alone. Not only does this finally answer the question `what is entropy?', but it also predicts the equality of the thermodynamic entropy of a black hole with the matter and the g...
Black Hole Entropy: Certain Quantum Features
On Recent Developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories (In 3 Volumes), 2002
The issue of black hole entropy is reexamined within a finite lattice framework along the lines of Wheeler, 't Hooft and Susskind, with an additional criterion to identify physical horizon states contributing to the entropy. As a consequence, the degeneracy of physical states is lower than that attributed normally to black holes. This results in corrections to the Bekenstein-Hawking area law that are logarithmic in the horizon area. Implications for the holographic entropy bound on bounded spaces are discussed. Theoretical underpinnings of the criterion imposed on the states, based on the 'quantum geometry' formulation of quantum gravity, are briefly explained.
Black Hole Entropy and Quantum Gravity
Indian J Phys, 1998
An elementary introduction is given to the problem of black hole entropy as formulated by Bekenstein and Hawking. The information theoretic basis of Bekenstein's formulation is briefly reviewed and compared with Hawking's approach. The issue of calculating the entropy by actual counting of microstates is taken up next within two currently popular approaches to quantum gravity, viz., string theory and canonical quantum gravity. The treatment of the former assay is confined to a few remarks, mainly of a critical nature, while some of the computational techniques of the latter approach are elaborated. We conclude by trying to find commonalities between these two rather disparate directions of work.
Black Hole Entropy is Quantum Intrinsic Entropy
International Journal of Physics, 2022
The author proposes a new black hole model. The particles only satisfying the special merging condition can merge together to form a black hole. The particles have intrinsic entropy in quantum mechanics. The particles arrange together by a special distribution to form a special thermodynamic system. The special thermodynamic system is just the black hole. The black hole entropy is just the sum of the intrinsic entropy of these particles merging to form the black hole. The black hole entropy is a kind of intrinsic entropy in quantum mechanics, and the black hole temperature is a kind of intrinsic temperature in quantum mechanics. The special distribution is named by black hole distribution. The black hole can be seen as a special quantum condensation system which be named by black hole condensation. The merging condition has several different physical meanings. It is an equal temperature condition, and it is a correspondence condition also. The particles have a new property named by correspondence radius. We can derive out the Verlinde entropy gravity proposal formula from this black hole model. And we can prove that the Verlinde entropy gravity proposal formula only hold true in the process of black hole merging. The Verlinde entropy gravity theory is not correct universally.
QUANTIZATION OF BLACK HOLES ENTROPY AND ITS COSMOLOGICAL CONSEQUENCES
Modern Physics Letters A, 2013
Starting from a quantization relation for primordial extremal black holes with electric and magnetic charges, it is shown that their entropy is quantized. Furthermore the energy levels spacing for such black holes is derived as a function of the level number n, appearing in the quantization relation. Some interesting cosmological consequences are presented for small values of n. By producing a mismatch between the mass and the charge the black hole temperature is derived and its behavior investigated. Finally extending the quantum relation to Schwarzschild black holes their temperature is found to be in agreement with the Hawking temperature and a simple interpretation of the microscopic degrees of freedom of the black holes is given.
Entropy
We give a review, in the style of an essay, of the author's 1998 matter-gravity entanglement hypothesis which, unlike the standard approach to entropy based on coarsegraining, offers a definition for the entropy of a closed system as a real and objective quantity. We explain how this approach offers an explanation for the Second Law of Thermodynamics in general and a non-paradoxical understanding of information loss during black hole formation and evaporation in particular. It also involves a radically different from usual description of black hole equilibrium states in which the total state of a black hole in a box together with its atmosphere is a pure state-entangled in just such a way that the reduced state of the black hole and of its atmosphere are each separately approximately thermal. We also briefly recall some recent work of the author which involves a reworking of the string-theory understanding of black hole entropy consistent with this alternative description of black hole equilibrium states and point out that this is free from some unsatisfactory features of the usual string theory understanding. We also recall the author's recent arguments based on this alternative description which suggest that the AdS/CFT correspondence is a bijection between the boundary CFT and just the matter degrees of freedom of the bulk theory.
Problems in black-hole entropy interpretation
Il Nuovo Cimento B, 1997
Some proposals for black-hole entropy interpretation are exposed and investigated. In particular, the author considers the so-called "entanglement entropy" interpretation, in the framework of the brick wall model, and the divergence problem arising in the one-loop calculations of various thermodynamical quantities, like entropy, internal energy and heat capacity. It is shown that the assumption of equality of entanglement entropy and Bekenstein-Hawking entropy appears to give inconsistent results. These will be a starting point for a different interpretation of black-hole entropy based on peculiar topological structures of manifolds with "intrinsic" thermodynamical features. It is possible to show an exact relation between black-hole gravitational entropy and topology of these Euclidean space-times. The expression for the Euler characteristic, through the Gauss-Bonnet integral, and the one for entropy for gravitational instantons are proposed in a form which make...
Black Hole Thermodynamics: More Than an Analogy?
2016
Black hole thermodynamics (BHT) is regarded as one of the deepest clues we have to a quantum theory of gravity. It motivates scores of proposals in the field, from the thought that the world is a hologram to calculations in string theory. The rationale for BHT playing this important role, and for much of BHT itself, originates in the analogy between black hole behavior and ordinary thermodynamic systems. Claiming the relationship is “more than a formal analogy,” black holes are said to be governed by deep thermodynamic principles: what causes your tea to come to room temperature is said additionally to cause the area of black holes to increase. Playing the role of philosophical gadfly, we pour a little cold water on the claim that BHT is more than a formal analogy. First, we show that BHT is often based on a kind of caricature of thermodynamics. Second, we point out an important ambiguity in what systems the analogy is supposed to govern, local or global ones. Finally, and perhaps w...
Remarks on the Entropy of Non-Stationary Black Holes
The definition of entropy obtained for stationary black holes is extended in this paper to the case of non-stationary black holes. Entropy is defined as a macroscopical thermodynamical quantity which satisfies the first principle of thermodynamics. In the non-stationary case a volume term appears since the solution does not admit a Killing vector. *