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In physics, black hole thermodynamics is the area of study that seeks to reconcile the laws of thermodynamics with the existence of black hole event horizons. Much as the study of the statistical mechanics of black body radiation led to the advent of the theory of quantum mechanics, the effort to understand the statistical mechanics of black holes has had a deep impact upon the understanding of quantum gravity, leading to the formulation of the holographic principle. A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ...
As the temperature decreases, the peak of the black body radiation curve moves to lower intensities and longer wavelengths. ...
For a less technical and generally accessible introduction to the topic, see Introduction to quantum mechanics. ...
This article does not cite any references or sources. ...
The holographic principle is a speculative conjecture about quantum gravity theories, proposed by Gerard t Hooft and improved and promoted by Leonard Susskind, claiming that all of the information contained in a volume of space can be represented by a theory which lives in the boundary of that region. ...
Image File history File links Black_Hole_Merger. ...
Image File history File links Black_Hole_Merger. ...
For other uses, see Black hole (disambiguation). ...
The laws of thermodynamics, in principle, describe the specifics for the transport of heat and work in thermodynamic processes. ...
Black hole entropy
Black hole entropy is the entropy carried by a black hole. For a less technical and generally accessible introduction to the topic, see Introduction to entropy. ...
For other uses, see Black hole (disambiguation). ...
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. The second law of thermodynamics is an expression of the universal law of increasing entropy. ...
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: Stephen William Hawking, CH, CBE, FRS, FRSA, (born 8 January 1942) is a British theoretical physicist. ...
Jacob David Bekenstein (born May 1, 1947) is a physicist who has contributed to the foundation of black hole thermodynamics and to other aspects of the connections between information and gravitation. ...
For the science fiction film, see Event Horizon (film). ...
In physics, Hawking radiation (also known as Bekenstein-Hawking radiation) is a thermal radiation thought to be emitted by black holes due to quantum effects. ...
Thermodynamics (Greek: thermos = heat and dynamic = change) is the physics of energy, heat, work, entropy and the spontaneity of processes. ...
 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". The Boltzmann constant (k or kB) is the physical constant relating temperature to energy. ...
The Planck length, denoted by , is the unit of length approximately 1. ...
The holographic principle is a speculative conjecture about quantum gravity theories, proposed by Gerard t Hooft and improved and promoted by Leonard Susskind, claiming that all of the information contained in a volume of space can be represented by a theory which lives in the boundary of that region. ...
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. Statistical mechanics is the application of probability theory, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. ...
In astrophysics, the no-hair theorem states that black holes are completely characterized only by three externally observable parameters: mass, electrical charge, and angular momentum. ...
American theoretical physicist who works on string theory. ...
Cumrun Vafa is a leading string theorist from Harvard University where he started as a Harvard Junior Fellow. ...
This article or section is in need of attention from an expert on the subject. ...
Interaction in the subatomic world: world lines of pointlike particles in the Standard Model or a world sheet swept up by closed strings in string theory String theory is a model of fundamental physics whose building blocks are one-dimensional extended objects called strings, rather than the zero-dimensional point...
In theoretical physics, D-branes are a special class of p-branes, named for the physicist Johann Dirichlet. ...
In theoretical physics, an extremal black hole is a black hole with the minimal possible mass that can be compatible with the given charges and angular momentum. ...
In theoretical physics, a near-extremal black hole is a black hole which is not far from the minimal possible mass that can be compatible with the given charges and angular momentum. ...
Loop quantum gravity, viewed as the main competitor of string theory, also offered a slightly more heuristic calculation of the black hole entropy. This calculation confirms that the entropy is proportional to the surface area, with the proportionality constant dependent on the only free parameter in LQG, Immirzi parameter. Loop quantum gravity (LQG), also known as loop gravity and quantum geometry, is a proposed quantum theory of spacetime which attempts to reconcile the seemingly incompatible theories of quantum mechanics and general relativity. ...
The Immirzi parameter (also known as the Barbero-Immirzi parameter) is a numerical coefficient appearing in loop quantum gravity, a nonperturbative theory of quantum gravity. ...
The laws of black hole mechanics The four laws of black hole mechanics are physical properties that black holes are believed to satisfy. The laws, analogous to the laws of thermodynamics, were discovered by Brandon Carter, Stephen Hawking and James Bardeen. For other uses, see Black hole (disambiguation). ...
Thermodynamics (from the Greek θεÏμη, therme, meaning heat and δυναμις, dynamis, meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. ...
Brandon Carter is a theoretical physicist, most famous for his work on the properties of black holes and for introducing the anthropic principle. ...
Stephen William Hawking, CH, CBE, FRS, FRSA, (born 8 January 1942) is a British theoretical physicist. ...
James M. Bardeen is an American physicist, well known for his work in general relativity, particularly his role in formulating the laws of black hole mechanics. ...
Statement of the laws The laws of black hole mechanics are expressed in geometrized units. In physics, especially in the general theory of relativity, geometrized units or sometimes geometric units, is a physical unit system in which all physical quantities are expressed in the unit of length: meter. ...
The Zeroth Law The horizon has constant surface gravity for a stationary black hole. The surface gravity of a Killing horizon is the acceleration, as exerted at infinity, needed to keep an object at the horizon. ...
The First Law We have  , where M is the mass, A is the horizon area, Ω is the angular velocity, J is the angular momentum, Φ is the electrostatic potential, κ is the surface gravity and Q is the electric charge. This article or section is in need of attention from an expert on the subject. ...
Angular velocity describes the speed of rotation and the orientation of the instantaneous axis about which the rotation occurs. ...
This gyroscope remains upright while spinning due to its angular momentum. ...
Electric potential is the potential energy per unit charge associated with a static (time-invariant) electric field, also called the electrostatic potential, typically measured in volts. ...
The surface gravity of a Killing horizon is the acceleration, as exerted at infinity, needed to keep an object at the horizon. ...
Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. ...
The Second Law The horizon area is, assuming the weak energy condition, a non-decreasing function of time, The energy conditions refer to various constraints which can be imposed on a spacetime that any physically reasonable matter distributions in physics are expected to satisfy. ...
The Third Law It is not possible to form a black hole with vanishing surface gravity. κ=0 is not possible to achieve.
Discussion of the laws
The Zeroth Law The zeroth law is analogous to the zeroth law of thermodynamics which states that the temperature is constant throughout a body in thermal equilibrium. It suggests that the surface gravity is analogous to temperature. T constant for thermal equilbrium for a normal system is analogous to κ constant over the horizon of a stationary black hole. The zeroth law of thermodynamics may be succintly stated as: If two thermodynamic systems A and B are in thermal equilibrium, and B and C are also in thermal equilibrium, then A and C are in thermal equilibrium. ...
In thermodynamics, a thermodynamic system is in thermodynamic equilibrium if its energy distribution equals a Maxwell-Boltzmann-distribution. ...
For other uses, see Temperature (disambiguation). ...
The First Law The left hand side, dM, is the change in mass/energy. Although the first term does not have an immediately obvious physical interpretation, the second and third terms on the right hand side represent changes in energy due to rotation and electromagnetism. Analogously, the first law of thermodynamics is a statement of energy conservation, which contains on its right hand side the term T dS. Electromagnetism is the physics of the electromagnetic field: a field which exerts a force on particles that possess the property of electric charge, and is in turn affected by the presence and motion of those particles. ...
The first law of thermodynamics, a generalized expression of the law of the conservation of energy, states: // Description Essentially, the First Law of Thermodynamics declares that energy is conserved for a closed system, with heat and work being the forms of energy transfer. ...
For the physical concepts, see conservation of energy and energy efficiency. ...
The Second Law The second law is the statement of Hawking's area theorem. Analogously, the second law of thermodynamics states that the entropy of a closed system is a non-decreasing function of time, suggesting a link between entropy and the area of a black hole horizon. However, this version violates the second law of thermodynamics by matter losing (its) entropy as it falls in, giving a decrease in entropy. Generalised second law introduced as total entropy = black hole entropy + outside entropy The second law of thermodynamics is an expression of the universal law of increasing entropy. ...
For a less technical and generally accessible introduction to the topic, see Introduction to entropy. ...
The Third Law Extremal black holes have vanishing surface gravity. Stating that κ cannot go to zero is analogous to the third law of thermodynamics which, in its weak formulation, states that it is impossible to reach absolute zero temperature in a physical process. The strong version of the third law of thermodynamics, which states that as the temperature approaches zero, the entropy also approaches zero, does not have an analogue for black holes. However, the strong version is violated by many known systems in condensed matter physics, and has therefore been rejected as a law. The third law of thermodynamics (hereinafter Third Law) states that as a system approaches the zero absolute temperature (hereinafter ZAT), all processes cease and the entropy of the system approaches a minimum value. ...
Absolute zero is the lowest possible temperature where nothing could be colder, and no heat energy remains in a substance. ...
Interpretation of the laws The four laws of black hole mechanics suggest that one should identify the surface gravity of a black hole with temperature and the area of the event horizon with entropy, at least up to some multiplicative constants. If one only considers black holes classically, then they have zero temperature and, by the no hair theorem, zero entropy, and the laws of black hole mechanics remain an analogy. However, when quantum mechanical effects are taken into account, one finds that black holes emit thermal radiation (Hawking radiation) at temperature In astrophysics, the no-hair theorem states that black holes are completely characterized only by three externally observable parameters: mass, electrical charge, and angular momentum. ...
For a less technical and generally accessible introduction to the topic, see Introduction to quantum mechanics. ...
“Radiant heat†redirects here. ...
In physics, Hawking radiation (also known as Bekenstein-Hawking radiation) is a thermal radiation thought to be emitted by black holes due to quantum effects. ...
 . From the first law of black hole mechanics, this determines the multiplicative constant of the Bekenstein-Hawking entropy which is  .
Beyond Black Holes Hawking and Page showed that black hole thermodynamics is more general than black holes, that cosmological event horizons also have an entropy and temperature.
More fundamentally, t'Hooft and Susskind used the laws of black hole thermodynamics to argue for a general Holographic Principle of nature, which asserts that consistent theories of gravity and quantum mechanics must be lower dimensional. Though not yet fully understood in general, the holographic principle has led to the only complete theories of quantum gravity, such as the AdS/CFT correspondence. The holographic principle is a speculative conjecture about quantum gravity theories, proposed by Gerard t Hooft and improved and promoted by Leonard Susskind, claiming that all of the information contained in a volume of space can be represented by a theory which lives in the boundary of that region. ...
In physics, the AdS/CFT correspondence (anti-de-Sitter space/conformal field theory correspondence), sometimes called the Maldacena duality, is the conjectured equivalence between a string theory defined on one space, and a quantum field theory without gravity defined on the conformal boundary of this space, whose dimension is lower...
See also Stephen William Hawking, CH, CBE, FRS, FRSA, (born 8 January 1942) is a British theoretical physicist. ...
Jacob David Bekenstein (born May 1, 1947) is a physicist who has contributed to the foundation of black hole thermodynamics and to other aspects of the connections between information and gravitation. ...
References - J. M. Bardeen, B. Carter and S. W. Hawking, "The four laws of black hole mechanics", Commun. Math. Phys. 31, 161 (1973).
- J. D. Bekenstein, "Black holes and entropy", Phys. Rev. D 7, 2333 (1973).
- S. W. Hawking, "Black hole explosions?", Nature 248, 30 (1974).
- S. W. Hawking, "Particle creation by black holes", Commun. Math. Phys. 43, 199 (1975).
- S. W. Hawking and G. F. R. Ellis, "The large-scale structure of space-time", Cambridge University Press (1973).
- S. W. Hawking, "The Nature of Space and Time", (1994) [1]
External links - Black Hole Thermodynamics
- Black hole entropy on arxiv.org
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