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"Foundations of Black Hole Accretion Disk Theory"
Marek A. Abramowicz and P. Chris Fragile 
Abstract
1 Introduction
2 Three Destinations in Kerr’s Strong Gravity
2.1 The event horizon
2.2 The ergosphere
2.3 ISCO: the orbit of marginal stability
2.4 The Paczyński–Wiita potential
2.5 Summary: characteristic radii and frequencies
3 Matter Description: General Principles
3.1 The fluid part
3.2 The stress part
3.3 The Maxwell part
3.4 The radiation part
4 Thick Disks, Polish Doughnuts, & Magnetized Tori
4.1 Polish doughnuts
4.2 Magnetized Tori
5 Thin Disks
5.1 Equations in the Kerr geometry
5.2 The eigenvalue problem
5.3 Solutions: Shakura–Sunyaev & Novikov–Thorne
6 Slim Disks
7 Advection-Dominated Accretion Flows (ADAFs)
8 Stability
8.1 Hydrodynamic stability
8.2 Magneto-rotational instability (MRI)
8.3 Thermal and viscous instability
9 Oscillations
9.1 Dynamical oscillations of thick disks
9.2 Diskoseismology: oscillations of thin disks
10 Relativistic Jets
11 Numerical Simulations
11.1 Numerical techniques
11.2 Matter description in simulations
11.3 Polish doughnuts (thick) disks in simulations
11.4 Novikov–Thorne (thin) disks in simulations
11.5 ADAFs in simulations
11.6 Oscillations in simulations
11.7 Jets in simulations
11.8 Highly magnetized accretion in simulations
12 Selected Astrophysical Applications
12.1 Measurements of black-hole mass and spin
12.2 Black hole vs. neutron star accretion disks
12.3 Black-hole accretion disk spectral states
12.4 Quasi-Periodic Oscillations (QPOs)
12.5 The case of Sgr A*
13 Concluding Remarks
Acknowledgements
References
Footnotes
Figures
Tables
Figure 3
Figure 3: Evidence for the existence of the ISCO from data recorded by the Rossi X-ray Timing Explorer satellite from neutron star binary source 4U 1636–536 [33]. The source shows quasi-periodic oscillations (QPOs) with frequencies in the range 650 Hz < ν < 900 Hz. The sharp drop in the quality factor (bottom panel) seen at ∼ 870 Hz may be attributable to the ISCO [34].

Marek A. Abramowicz and P. Chris Fragile, "Foundations of Black Hole Accretion Disk Theory",
Living Rev. Relativity, 16 (2013), 1, doi:10.12942/lrr-2013-1, URL (accessed <date>): http://www.livingreviews.org/lrr-2013-1.
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