Topic
Extremal black hole
About: Extremal black hole is a research topic. Over the lifetime, 9654 publications have been published within this topic receiving 384266 citations.
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TL;DR: In this article, it is shown that quantum mechanical effects cause black holes to create and emit particles as if they were hot bodies with temperature, which leads to a slow decrease in the mass of the black hole and to its eventual disappearance.
Abstract: In the classical theory black holes can only absorb and not emit particles. However it is shown that quantum mechanical effects cause black holes to create and emit particles as if they were hot bodies with temperature\(\frac{{h\kappa }}{{2\pi k}} \approx 10^{ - 6} \left( {\frac{{M_ \odot }}{M}} \right){}^ \circ K\) where κ is the surface gravity of the black hole. This thermal emission leads to a slow decrease in the mass of the black hole and to its eventual disappearance: any primordial black hole of mass less than about 1015 g would have evaporated by now. Although these quantum effects violate the classical law that the area of the event horizon of a black hole cannot decrease, there remains a Generalized Second Law:S+1/4A never decreases whereS is the entropy of matter outside black holes andA is the sum of the surface areas of the event horizons. This shows that gravitational collapse converts the baryons and leptons in the collapsing body into entropy. It is tempting to speculate that this might be the reason why the Universe contains so much entropy per baryon.
10,923 citations
TL;DR: The standard Einstein-Maxwell equations in 2+1 spacetime dimensions, with a negative cosmological constant, admit a black hole solution that appears as a negative energy state separated by a mass gap from the continuous black hole spectrum.
Abstract: The standard Einstein-Maxwell equations in 2+1 spacetime dimensions, with a negative cosmological constant, admit a black hole solution. The 2+1 black hole---characterized by mass, angular momentum, and charge, defined by flux integrals at infinity---is quite similar to its 3+1 counterpart. Anti--de Sitter space appears as a negative energy state separated by a mass gap from the continuous black hole spectrum. Evaluation of the partition function yields that the entropy is equal to twice the perimeter length of the horizon.
3,640 citations
TL;DR: The Bekenstein-Hawking area entropy relation S BH = A 4 was derived for a class of five-dimensional extremal black holes in string theory by counting the degeneracy of BPS solition bound states.
3,497 citations
TL;DR: This article derived expressions for the mass of a stationary axisymmetric solution of the Einstein equations containing a black hole surrounded by matter and for the difference in mass between two neighboring such solutions.
Abstract: Expressions are derived for the mass of a stationary axisymmetric solution of the Einstein equations containing a black hole surrounded by matter and for the difference in mass between two neighboring such solutions. Two of the quantities which appear in these expressions, namely the area A of the event horizon and the “surface gravity” κ of the black hole, have a close analogy with entropy and temperature respectively. This analogy suggests the formulation of four laws of black hole mechanics which correspond to and in some ways transcend the four laws of thermodynamics.
3,494 citations
TL;DR: It is provided evidence that this value of shear viscosity to volume density of entropy may serve as a lower bound for a wide class of systems, thus suggesting that black hole horizons are dual to the most ideal fluids.
Abstract: The ratio of shear viscosity to volume density of entropy can be used to characterize how close a given fluid is to being perfect. Using string theory methods, we show that this ratio is equal to a universal value of [h-bar]/4pikB for a large class of strongly interacting quantum field theories whose dual description involves black holes in anti–de Sitter space. We provide evidence that this value may serve as a lower bound for a wide class of systems, thus suggesting that black hole horizons are dual to the most ideal fluids.
2,721 citations