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By black hole model (or model black hole), I refer to mathematical structures or computer calculations demonstrating aspects of black holes. Black holes vary only in mass, electric charge, and rotation (no-hair theorem), though interactions with other astronomical objects (black hole mergers, accretion disks) can lead to modeling challenges. Some principal mathematical models:
All four of these are exact according to general relativity (GR) and the characteristics they are designed to handle, but they grow more mathematically challenging as they grow more general, and it is often useful to approximate with a simpler model from this list if charge or rotation are minor influences. In modeling observations or realistic scenarios, the Kerr model is common. Charge is typically ignored as unlikely to remain significant: the electric force assists accretion of the opposite charge. Significant rotation is considered common and the Schwarzschild model is often no more than a gross approximation of an actual black hole.
Additional models have been developed, some being approximations of the above, and others including additional factors or adjusting GR rules to accommodate theoretical issues (such as the black-hole information paradox) and/or observed phenomena. The term nonsingular black hole model refers to one class of these alternative models. Others are associated with various metrics (including theoretical modified GR metrics).
An extremal black hole is a black hole at a lower limit: at the minimal mass possible given its charge and rotation, a concept relevant to the latter three models. Theory has suggested that one would be stable, i.e., it would not emit Hawking radiation.