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Understanding the Size and Growth of Black Holes
Black Hole Volume and Growth Over Time
The volume inside a black hole, particularly a spherical one, can be surprisingly large. This volume grows over time since the collapse of the object, reaching a simple asymptotic form that has a compelling geometrical interpretation. This growth is significant and may have implications for discussions on the information paradox1.
Physical Limits on Black Hole Mass
There is a physical limit to the mass a black hole can achieve through luminous accretion of gas. This limit is approximately (5 \times 10^{10} M_{\odot}) for typical parameters, but can reach up to (2.7 \times 10^{11} M_{\odot}) in extreme cases, such as with maximal prograde spin. The largest black hole masses observed so far are close to but below this limit. Black holes can grow beyond this mass through non-luminous means, such as mergers with other black holes, but they cannot become luminous accretors again2.
Constraints on Primordial Black Holes
Primordial black holes (PBHs) are subject to various constraints based on their mass. Those smaller than approximately (10^{15}) grams would have evaporated by now due to Hawking radiation, while larger ones are constrained by gravitational lensing, dynamical effects, and their influence on large-scale structure. These constraints are associated with observational or theoretical uncertainties, but PBHs could still play a significant cosmological role and provide a unique probe of the early Universe3 9.
Formation of Supermassive Black Holes
Supermassive black holes (SMBHs) with masses up to (10^9 M_{\odot}) are found in the centers of present-day galaxies and were present as early as redshift (z \geq 6). Their formation in the early Universe is still a mystery, but direct collapse of gas clouds in primordial halos is a plausible scenario. This process can lead to the formation of seed black holes with masses between (10^5) and (10^6 M_{\odot}), which can grow further through accretion and mergers4 10.
Maximum Size in an Accelerating Universe
In the context of an accelerating Universe with a positive cosmological constant, there is a cosmological upper bound for the area of stable marginally outer trapped surfaces. This bound is tighter when considering angular momentum, gravitational waves, and matter, providing a concrete limit to the size of black holes, especially relevant in the early Universe5.
Observational Evidence of Massive Black Holes
Observations indicate that all massive galaxies host SMBHs at their centers. For instance, the giant elliptical galaxy Messier 87 has a black hole with a mass of 6.3 billion solar masses. Other galaxies, such as NGC 3842 and NGC 4889, host black holes with masses around 9.7 billion solar masses, significantly more massive than predicted by standard correlations between black-hole mass and galaxy properties8.
Schwarzschild Black Hole: The Largest for a Given Mass
In Einstein gravity, the Schwarzschild black hole is the largest for a given mass. It saturates the inequalities related to the radii of the horizon, photon sphere, and black hole shadow, making it the biggest of all for a given mass. These inequalities also include an upper bound of entropy for any quantum system with a given energy7.
Conclusion
Black holes can vary significantly in size and mass, from primordial black holes constrained by various physical effects to supermassive black holes in the centers of galaxies. The growth of black holes is limited by physical processes, but they can still achieve enormous sizes through non-luminous means. Observations and theoretical models continue to refine our understanding of these fascinating cosmic objects.
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How big is a black hole
A black hole's three-dimensional volume is large, potentially impacting the information paradox discussion.
Highly CitedHow big can a black hole grow
Black holes can grow beyond the physical limit Mmax 5 1010 M through non-luminous means like mergers with other holes, but cannot become luminous accretors again.
Constraints on primordial black holes
Primordial black holes may play an important cosmological role and provide a unique probe of the early Universe, even if they contribute only a small amount of dark matter.
Highly CitedBlack hole formation in the early Universe
Direct collapse provides a viable pathway for forming high-mass black holes at early cosmic times, with turbulence playing a central role in regulating accretion and transporting angular momentum.
Highly CitedMaximum size of black holes in our accelerating Universe
The new upper bound on black hole size in the early universe is tighter than previous results, considering angular momentum, gravitational waves, and matter.
On the Size of a Black Hole: The Schwarzschild is the Biggest
The Schwarzschild black hole is the largest black hole for a given mass, surpassing previous upper bounds and including an upper bound of entropy for quantum systems with a given energy.
Two ten-billion-solar-mass black holes at the centres of giant elliptical galaxies
Two massive black holes with masses of 9.7 billion solar masses were discovered in giant elliptical galaxies NGC 3842 and NGC 4889, suggesting different evolutionary processes influence the growth of the largest galaxies and their black holes.
Highly CitedNew cosmological constraints on primordial black holes
Primordial black holes' evaporation effects on big bang nucleosynthesis and extragalactic photon background weaken other constraints, with nonevaporating black holes having gravitational and astrophysical effects over a broader mass range.
Highly CitedThe characteristic black hole mass resulting from direct collapse in the early Universe
The direct collapse model provides the expected mass of seed black holes, with accretion rates increasing over time to a maximum value of 10 $rm M_odot/yr after $rm 104$ years.
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