Black hole size
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Black Hole Size: Event Horizon, Photon Sphere, and Shadow
The size of a black hole is typically described using three main parameters: the event horizon radius (R+), the photon sphere radius (Rph), and the black hole shadow radius (Rsh). For static black holes in Einstein gravity, these radii are related by a sequence of inequalities: the event horizon is the smallest, followed by the photon sphere, and then the shadow, with all three bounded above by a value proportional to the black hole's mass (M) Lu2019Lü2020. Specifically, for a given mass, the Schwarzschild (non-rotating, uncharged) black hole reaches the maximum possible size for each of these parameters, saturating the upper bounds Lu2019Lü2020.
Schwarzschild Black Holes: The Largest for a Given Mass
Among all static black holes, the Schwarzschild black hole is the largest for a given mass. The relationships between the radii are given by inequalities such as 3/2 R+ ≤ Rph ≤ (1/√3) Rsh ≤ 3M, where M is the black hole mass . This means that, for the same mass, no other static black hole can have a larger event horizon, photon sphere, or shadow than a Schwarzschild black hole Lu2019Lü2020. These bounds also have implications for the maximum entropy a black hole can have for a given energy Lu2019Lü2020.
Rotating Black Holes: Smaller Apparent and Actual Sizes
When black holes rotate, as in the case of Kerr black holes, both their actual and apparent sizes become smaller compared to non-rotating (Schwarzschild) black holes of the same mass. The sequence of inequalities relating the horizon, photon sphere, and shadow still holds, but rotation reduces these radii . The shadow of a rotating black hole also appears skewed depending on the observer's viewpoint, especially when viewed from the equatorial plane .
Observational Evidence: Event Horizon Telescope Results
Recent observations of the supermassive black hole at the center of our galaxy (Sagittarius A*) by the Event Horizon Telescope show that the observed shadow size is within about 10% of the predictions for a Kerr black hole, supporting the theoretical models of black hole size and confirming that the external spacetime of astrophysical black holes matches the Kerr metric .
Volume Inside a Black Hole
The three-dimensional volume inside a spherical black hole, as defined by certain geometric methods, is surprisingly large and grows with time after the collapse of the original object. This large internal volume may have implications for discussions about the black hole information paradox .
Cosmological and Theoretical Upper Bounds
There are theoretical upper bounds on the size of black holes, especially in the context of our accelerating universe with a positive cosmological constant. These bounds take into account factors like angular momentum, gravitational waves, and matter, and are particularly relevant for black holes in the early universe . Additionally, thermodynamic arguments suggest that black holes have a finite lower temperature and, therefore, an upper bound on their horizon radius, which is comparable to the Hubble horizon (the size of the observable universe) .
Conclusion
In summary, the size of a black hole is characterized by its event horizon, photon sphere, and shadow, with the Schwarzschild black hole being the largest for a given mass. Rotation reduces the size, and observational data confirm these theoretical predictions. There are also cosmological and thermodynamic limits to how large a black hole can be, ensuring that even the biggest black holes have an upper bound to their size Lu2019Lü2020Shiromizu2022+3 MORE.
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