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Topic: Laws of black hole mechanics

Related Topics

Black hole entropy

Black hole thermodynamics

Hawking radiation

Second law of thermodynamics

Thermodynamics

Stephen Hawking

Quantum gravity

Spontaneous emission

	Black hole - Wikipedia, the free encyclopedia
		Intermediate-mass fl holes have been proposed as a possible power source for ultra-luminous X ray sources, and in 2004 detection was claimed of an intermediate-mass fl hole orbiting the Sagittarius A* supermassive fl hole candidate at the core of the Milky Way galaxy.
		Black holes require the general relativistic concept of a curved spacetime: their most striking properties rely on a distortion of the geometry of the space surrounding them.
		Using the first law of fl hole mechanics, it follows that the entropy of a fl hole is one quarter of the area of the horizon.
	en.wikipedia.org /wiki/Black_hole (5021 words)

	Laws of black hole mechanics - Wikipedia, the free encyclopedia
		The zeroth law is analogous to the zeroth law of thermodynamics which states that the temperature is constant throughout a body in thermal equilibrium.
		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 fl hole horizon.
		The four laws of fl hole mechanics suggest that one should identify the surface gravity of a fl hole with temperature and the area of the event horizon with entropy, at least up to some multiplicative constants.
	en.wikipedia.org /wiki/Laws_of_black_hole_mechanics (610 words)

	Laws - Hutchinson encyclopedia article about Laws (Site not responding. Last check: 2007-09-11)
		Church influence led to the adoption of Roman law throughout western continental Europe, and it was spread to Eastern Europe and parts of Asia by the French Code Napoléon in the 19th century.
		Unique to English law is the doctrine, or principle, of stare decisis (Latin ‘to stand by things decided’), which requires that courts abide by former precedents (or decisions) when the same points arise again in litigation (law suits).
		In the 19th century there was major reform of the law (for example, the abolition of many capital offences, in which juries would not in any case convict) and of the complex system of law courts.
	encyclopedia.farlex.com /Laws (520 words)

	Formation of a Black Hole
		A nonspinning, uncharged fl hole is known as a Swarzschild fl hole.
		However as he gets closer to the fl hole, he feels a variation of gravitational pull between his head and his feet if either his head or his feet are closer to the fl hole.
		A white hole is the opposite of a fl hole.
	www.csvrgs.k12.va.us /Courses/IntroTech/pages/blackholes.html (2011 words)

	[No title]
		Thus, for N strings attached to the fl hole the efficiency of string channels is increased by factor N. We discuss restrictions on N which exist because of the finite thickness of strings, the gravitational backreaction and thermal fluctuations.
		For the Reissner-Nordström fl hole, A=4p G(2n+p+1) and Q=me, for integers n,p,m.
		Topology of Black Holes and Geometry of Solitons
	www.phys.ualberta.ca /~gravity/bh3conference/abstractstitles1.html (3981 words)

	1 Introduction
		The cornerstone of this relationship is fl hole thermodynamics, where it appears that certain laws of fl hole mechanics are, in fact, simply the ordinary laws of thermodynamics applied to a system containing a fl hole.
		At the purely classical level, fl holes in general relativity (as well as in other diffeomorphism covariant theories of gravity) obey certain laws which bear a remarkable mathematical resemblance to the ordinary laws of thermodynamics.
		Primary among these are the ``fl hole information paradox'' and issues related to the degrees of freedom responsible for the entropy of a fl hole.
	www.univie.ac.at /EMIS/journals/LRG/Articles/lrr-2001-6/node1.html (487 words)

	13.3 Quasi-local laws of black hole dynamics
		Black holes are usually introduced in asymptotically flat spacetimes [172, 173, 175, 387], and hence it was natural to derive the formal laws of fl hole mechanics/thermodynamics in the asymptotically flat context (see for example [34, 50, 51], and for a recent review see [392
		Apparently, the detailed microscopic (quantum) theory of gravity is not needed to derive the fl hole entropy, and it can be derived even from the general principles of a conformal field theory on the horizon of the fl holes [100, 101, 102, 296, 103].
		There is an extensive literature of the quasi-local formulation of the fl hole dynamics and relativistic thermodynamics in the spherically symmetric context (see for example [185, 187, 186, 190] and for non-spherically symmetric cases [275, 189, 74]).
	www.univie.ac.at /EMIS/journals/LRG/Articles/lrr-2004-4/articlesu35.html (985 words)

	[No title] (Site not responding. Last check: 2007-09-11)
		At the quantum mechanical level, this means that the potential energy of interaction between the particles in two disjoint regions is a 'surface effect': for precise mathematical specifications of this, see [3, Ch.4].
		Black Hole Thermodynamics} \vskip 0.3cm According to Classical General Relativity, the collapse of a star, due to gravitational implosion, results in the formation of a Black Hole [15, Pt.7], i.e.
		This proposal was supported [7,17] by Hawking's subsequent argument that Black Holes act as sources of thermal radiation, of quantum mechanical origin, with temperature corresponding to the assumed form, ${\lambda}A,$ of the BH entropy.
	www.ma.utexas.edu /mp_arc/papers/94-207 (2476 words)

	Nat' Academies Press, Gravitation, Cosmology, and Cosmic-Ray Physics (1986)
		Supermassive fl holes of a million to a billion solar masses might be able to form in the nuclei of galaxies by stellar coalescence and accretion.
		A fl hole may be born in a more or less excited state, depending on the degree of disorder in the gravitational collapse of its progenitor star, but it quickly relaxes to a stationary state by the emission of gravitational waves.
		The energy can be tapped by immersing the fl hole in a suitable configuration of conductors and magnetic fields, in which case it acts as a kind of electrical generator, or it can be tapped mechanically by suitable arrangements of particles traversing a certain region near the fl hole, called the ergosphere.
	www.nap.edu /openbook.php?record_id=630&page=61 (4312 words)

	How Does Your Black Hole Grow?
		Laws for calculating a growing fl hole's surface area, mass, and angular momentum, could improve predictions for observations to be made by LIGO, a facility recently built with the goal of detecting gravitational waves from space.
		Black holes are easiest to study theoretically when they are unchanging and isolated from everything else.
		In fl hole computer simulations, he says, the new laws could be used to ensure that a result is physically reasonable and not mere computer fantasy.
	focus.aps.org /story/v10/st27 (544 words)

	Een eenvoudig verhaal (Site not responding. Last check: 2007-09-11)
		Black holes therefore serves as probes for the yet unknown theory of quantum gravity.
		The theory of fl holes is a well-developed subject in general relativity, and one of the cornerstones of this theory is formed by the laws of fl hole mechanics.
		This lead Bekenstein to the conjecture that fl holes are, in fact, thermodynamic ensembles and that their area is a measure for the entropy.
	www.phys.uu.nl /~kaeppeli/eeneenvoudigverhaal.html (626 words)

	Vodkapundit - The Escape of Dr. Hans Reinhardt?
		* Therefore, the laws of fl hole mechanics are the laws of thermodynamics is disguise.
		Any fl hole with a Hawking temperature less than that of the cosmic microwave background (~2.7K) accretes mass due to infalling photons (a fl hole with this temperature would be about the mass of the Moon).
		The fl body temperature of a fl hole is inversely proportional to its mass.
	www.vodkapundit.com /archives/006165.php (682 words)

	Black Holes and Quasars
		A Black Hole radiates with a temperature proportional to its surface gravity.
		For a fl hole of one solar mass, with a circumference of 18.5 kilometers the maximum spin rate is calculated as 0.000062 of a second per revolution.
		Holes with a larger mass will have an even longer lifespan as the larger the hole the lower its temperature and surface gravity and therefore the more weakly it emits particles.
	dnausers.d-n-a.net /dnetGOjg/Black/Holes.htm (2682 words)

	2 Classical Black Hole Thermodynamics
		These laws of fl hole mechanics apply to stationary fl holes (although a formulation of these laws in terms of isolated horizons will be briefly described at the end of this section).
		However, there is good reason to believe that the ``Planck-Nernst theorem'' should not be viewed as a fundamental law of thermodynamics [1] but rather as a property of the density of states near the ground state in the thermodynamic limit, which happens to be valid for commonly studied materials.
		Such an approach toward the formulation of the laws of fl hole mechanics has recently been taken via the notion of an isolated horizon, defined as a null hypersurface with vanishing shear and expansion satisfying the additional properties stated in [4].
	relativity.livingreviews.org /Articles/lrr-2001-6/node2.html (2148 words)

	jhproject
		American theoretical physicist; showed that many or most fl holes in our Universe should be rapidly spinning and, with Petterson, predicted the influence of the holes' spins on surrounding accretion disks; with Carter and Hawking, discovered the four laws of fl-hole mechanics.
		German born, Swiss/American theoretical physicist; Nobel laureate; formulated the laws of special relativity and general relativity; showed that light is simultaneously a particle and a wave; opposed the concept of a fl hole.
		Student of Wheeler's; with Bekenstein, showed that one cannot discern, by any external study of a fl hole, what kinds of particles were among the material that formed it; with Hawking, discovered that govern the evolution of a fl holes horizon; with Hawking is developing insights into the laws of quantum gravity.
	www.physics.sfsu.edu /~lwilliam/sota/worms/Scientists.htm (443 words)

	seminar (Site not responding. Last check: 2007-09-11)
		Black holes remain one of the most fascinating predictions of general relativity.
		I will assume no prior knowledge of relativity, and so will start by definining what a fl hole is and then go on to outline how they form, the evidence for their existence, and their basic properties.
		From there, I'll turn to the laws of fl hole mechanics, explain their intimate (and surprising!) connection to thermodynamics, and then discuss the far-reaching implications of that connection.
	www.physics.mun.ca /seminars/2002/seminar080502.html (133 words)

	[No title] (Site not responding. Last check: 2007-09-11)
		The arena normally used in fl holes thermodynamics was recently generalized to incorporate a broad class of physically interesting situations.
		After a general introduction to fl hole thermodynamics as a whole, these recent developments are briefly summarized.
		This confirms the idea that the entropy of fl holes can be accounted for by counting string states, and suggests that the level spacing of the quantum states of Schwarzschild fl holes is exponentially small, and very much blurred by radiative effects.
	www.wiley-vch.de /contents/jc_2257/20003-5.html (1870 words)

	Blacks Law (Site not responding. Last check: 2007-09-11)
		Black's Law Dictionary is regarded by many as the definitive legal dictionary for the law of the United States.
		The four laws of fl hole mechanics are analogous to the laws of thermodynamics.
		In constructing a derivation of this law, he considered the possible ways of distributing electromagnetic energy over the different modes of charged oscillators in matter.
	www.wwwtln.com /finance/19/blacks-law.html (1017 words)

	Imagine the Universe! Dictionary A-D (Site not responding. Last check: 2007-09-11)
		An X-ray binary is a special case where one of the stars is a collapsed object such as a white dwarf, neutron star, or fl hole, and the separation between the stars is small enough so that matter is transferred from the normal star to the compact star star, producing X-rays in the process.
		This is analogous to the second law of thermodynamics, with the surface areas of the fl holes being a measure of the entropy of the system.
		In quantum mechanics, all particles also have wave characteristics, where the wavelength of a particle is inversely proportional to its momentum and the constant of proportionality is the Planck constant.
	imagine.gsfc.nasa.gov /docs/dict_ad.html (2472 words)

	Kerr Fest: Golden Age of Black Hole Physics
		The 10 year period from Roy Kerr's discovery of the rotating fl hole solution in 1963 until Stephen Hawking's discovery of fl hole evaporation in December 1973 represents a Golden Age of Black Hole Physics.
		Although fl holes were a theoretical possibility ever since Karl Schwarzschild discovered the non-rotating solution in 1916, and considered by many to be a strong physical possibility following Robert Oppenheimer and Hartland Snyder's work in 1939, until 1963 there remained a strong school of opposition to the idea.
		The terminology that "fl holes have no hair" in respect of various uniqueness and "no hair" results, was also due to John Wheeler and was introduced in an article co-authored with Remo Ruffini in 1971 [2].
	www2.phys.canterbury.ac.nz /kerrfest/timeline.html (942 words)

	List of participants
		A dynamical first law is derived by introducing a new perturbative formulation for dynamic horizons in which "slowly evolving" trapping horizons may be viewed as perturbatively non-isolated.
		Binary fl hole spacetimes with a helical Killing vector are studied in a projection formalism.
		The two Killing horizons of spherical topology which characterize the fl holes, the cylinder of light where the Killing vector changes from timelike to the spacelike, and infinity are singular points of the equations.
	www.tat.physik.uni-tuebingen.de /~heraeus/heraeus_participants.html (5353 words)

	Vurdalak \| Archived Seminar #10: Can’t Win, Can’t Break Even, Can’t Get Out of the Game
		Up till now, all the fl holes we’ve looked at — from the tiny ones born in the Big Bang to the monsters gobbling up whole galaxies — have been what physicists call classical.
		Sure, it was weird, but fl holes are weird in general, so this newfound ability to swallow entropy whole was just the latest in a long line of weird things they did.
		This was serious stuff: the Second Law is such a bedrock principle of physics that saying fl holes didn’t obey it might mean there really was no such thing as a fl hole.
	www.vurdalak.com /soapbox/archives/archivedseminar10.htm (3025 words)

	David Chow \| Black Holes \| References
		Black holes and solitons in string theory", Phys.
		These are reviews on the subject of fl holes in string theory; furthermore, the Maldacena reference is his PhD thesis.
		Michell was the first person to predict the existence of fl holes in Newtonian gravity.
	www.damtp.cam.ac.uk /user/ddkc2/bhreferences.html (1097 words)

	seminar (Site not responding. Last check: 2007-09-11)
		The laws of fl hole mechanics, and their similarily to the laws of thermodynamics, are some of the more remarkable results to emerge from classical general relativity.
		For example, the standard definition of a fl hole involves an ``event horizon'' which can only be located after the entire history of the universe is known.
		In this talk we describe recent efforts to reformulate the laws in a more local manner so that they are applicable to physically interesting situations.
	www.physics.mun.ca /seminars/2003/seminar120503.html (92 words)

	Physics 776, Fall 2003
		He finds that dA is independent of the fl hole parameters, and is equal to 2 in units of the Planck length squared, l_p^2 = hbar G (with c=1).
		In the scenario with the thermal photon beam impinging on the fl hole, he also notes that the quantum fluctuations are dominating the process.
		This is the 1st law of fl hole mechanics, as derived by Wald.
	www.physics.umd.edu /grt/taj/776b/notes.html (7230 words)

	Wiley-VCH Print Out (Site not responding. Last check: 2007-09-11)
		Particular emphasis is put on the crucial role of higher curvature terms and of modifications of the area law in obtaining agreement between the macroscopic entropy, which is a geometric property of fl hole solutions and the microscopic entropy, which is computed by state counting in Calabi-Yau compactifications of string or M-theory.
		The ensuing warped-geometry is determined completely and used to show that the variation of the Calabi-Yau volume along the orbifold direction varies quadratically with distance instead linearly as suggested by an earlier first order approximation.
		In the second part of this thesis we propose a mechanism for obtaining a small cosmological constant.
	www.wiley-vch.de /contents/pr.php?opfi=./jc_2244/20011-3.html (491 words)

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