The final stage of the most massive stars, where gravity is so strong that not even light can escape.
Among the most dramatic outcomes of stellar evolution, none is more extreme than stellar black holes The emergence of objects with such a density that the escape velocity at their surface exceeds the speed of light. Formed from the collapsed cores of massive stars (usually above ~20–25 M⊙), these black holes represent the final chapter of a violent cosmic cycle, ending core collapse supernova or by direct collapse without a pronounced blast wave. In this article, we will review the theoretical foundations of stellar black hole formation, the observational evidence for their existence and properties, and how they shape high-energy phenomena such as X-ray binaries and gravitational wave mergers.
1. The beginnings of stellar-mass black holes
1.1 The final fates of massive stars
High-mass stars (≳ 8 M⊙) leave the main sequence much faster than lower-mass stars, eventually synthesizing elements up to iron Beyond iron, fusion no longer provides a net energy benefit, so as the iron nucleus grows and reaches a mass that the electron or neutron degeneracy pressure can no longer support against further compression, the nucleus collapses during a supernova.
Not all supernova cores stabilize as neutron stars. In the case of particularly massive protostars (or if certain core conditions are met), the gravitational potential can exceed the degeneracy pressure limit, causing the collapsed core to transform into a neutron star. black holeIn some cases, extremely massive or low-metal stars can avoid a bright supernova and collapse directly, creating a stellar black hole without a bright explosion. [1], [2].
1.2 Collapse into a singularity (or a region of extreme spacetime curvature)
General relativity predicts that if mass is compressed into a volume smaller than Schwarzschild radius (Rs = 2GM/c2), the object becomes black hole – a region from which light can no longer escape. The classical solution shows an event horizon forming around a central singularity. Quantum gravity corrections remain speculative, but from a macroscopic point of view, black holes appear as regions of extremely curved spacetime that strongly influence their surroundings (accretion disks, jets, gravitational waves, etc.). The mass of a stellar-mass black hole typically ranges from a few to a few tens of M⊙ (and in rare cases over 100 M⊙, for example, in certain compounds or in low metal conditions) [3], [4].
2. The path of a core-collapse supernova
2.1 Iron core collapse and possible consequences
Inside a massive star, after completion silicon combustion stage, is formed iron group nucleus, which becomes inert. The burning layers remain around it, but when the mass of the iron core approaches Chandrasekhar limits (~1.4M⊙), further fusion can no longer generate energy. The core collapses rapidly, and densities suddenly increase to the nuclear level. Depending on the initial mass of the star and its mass loss history:
- If the mass of the nucleus after the bounce is ≲2–3 M⊙, may occur neutron star after a successful supernova.
- If the mass or "fallen" material is greater, the nucleus collapses into stellar black hole, perhaps weakening or extinguishing the brightness of the explosion.
2.2 “Failed supernovae” or faint explosions
Recent models suggest that some massive stars may not produce a bright supernova if the shock wave does not receive enough energy from neutrinos or if a large amount of mass falls back into the core. From an observational perspective, this could be seen as the star "extincting" without a bright eruption - "a failed supernova" – directly forming a black hole. While such direct collapses are theoretically possible, they are still an active area of observation and research. [5], [6].
3. Alternative formation pathways
3.1 Paired instability supernova or direct collapse
Extremely massive, metal-poor stars (≳ 140 M⊙) may experience pair instability supernova, completely destroying the star without a trace. Or within a certain mass range (about 90–140 M⊙) may undergo a partial binary instability phase with pulsating outbursts before the star eventually collapses. Some of these trajectories may yield fairly massive black holes – related to the LIGO/Virgo gravitational wave events, where high-mass black holes are detected.
3.2 Binary interactions
In close binary systems mass transfer or stellar mergers can form heavier helium nuclei or Wolf-Rayet stars, eventually leading to black holes that can exceed the mass expected for a single star. Gravitational wave data from black hole mergers, often 30–60 M⊙, shows that binary systems and complex evolutionary pathways can produce unexpectedly massive stellar black holes [7].
4. Evidence from the observation of stellar black holes
4.1 X-ray binaries
One of the main ways to confirm the existence of a stellar black hole is X-ray binary systems: a black hole accretes material from the wind of a companion star or through the Roche limit. The processes in the accretion disk release gravitational energy, creating intense X-ray emission. By analyzing the orbital dynamics and mass functions, astronomers determine the mass of the compact object. If it exceeds the neutron star limit (~2–3 M⊙), the object is classified as a black hole [8].
Key examples of X-ray binaries
- Cygnus X-1: One of the first credible black hole candidates, discovered in 1964; ~15 M⊙ black hole.
- V404 Cygni: Distinguished by bright outbursts revealing ~9 M⊙ black hole.
- GX 339–4, GRO J1655–40 and others: Periodically changes states, shows relativistic jets.
4.2 Gravitational waves
Since 2015, the LIGO-Virgo-KAGRA collaborations have detected numerous merging stellar black holes through gravitational waves signals. These events reveal black holes 5–80 M⊙ interval (sometimes more). The waveforms of the spiral and ringdown phases are consistent with Einstein's general theory of relativity predictions for black hole mergers, confirming that stellar black holes often exist in binaries and can merge, releasing enormous doses of energy in the form of gravitational waves. [9].
4.3 Microlensing and other methods
Theoretically microlensing events can reveal black holes as they pass in front of distant stars and distort their light.Some of the microlensing signatures may belong to free-roaming black holes, but precise identification is difficult. Wide-field time-domain surveys may reveal more free-roaming black holes in the disk or halo of our Galaxy.
5. Structure of a stellar black hole
5.1 Event horizon and singularity
From a classical point of view event horizon there is a limit beyond which escape velocity exceeds the speed of light. Any incident matter or photons irreversibly cross this horizon. At the center, the general theory of relativity predicts singularity – a point (or ring in the case of rotation) with infinite density, although the actual effects of quantum gravity remain an unsolved problem.
5.2 Rotation (Kerr black holes)
Stellar black holes often rotate, taking over the angular momentum of the parent star. Rotating (Kerr) a black hole is characterized by:
- Ergosphere: The area beyond the horizon where the rotation of space-time (frame-dragging) is extremely strong.
- Rotation parameter: Usually defined by a dimensionless quantity a* = cJ/(GM2), which ranges from 0 (no rotation) to close to 1 (maximum rotation).
- Accretion efficiency: Rotation strongly affects how matter can rotate towards the horizon, changing X-ray scattering patterns.
Observations (e.g. Fe Kα line profiles or continuous spectral features of the accretion disk) in some X-ray binaries allow us to estimate the spin of the black hole. [10].
5.3 Relativistic jets
When a black hole accretes matter in X-ray binaries, it can release relativistic jets along the rotation axis, using the Blandford–Znajek mechanism or disk MHD processes. Such jets can manifest as "microquasars" and demonstrate a connection between stellar black holes and AGN jet phenomena from supermassive black holes.
6. Role in astrophysics
6.1 Environmental feedback
The accretion of matter into a stellar black hole in star-forming regions can create X-ray feedback, heating the nearby gas environment and potentially affecting star formation or the chemical state of molecular clouds. Although this effect is not as global as in the case of supermassive black holes, these smaller black holes can still affect the environment in star clusters or star-forming complexes.
6.2 r-process nucleosynthesis?
The merger of two neutron stars can create a more massive black hole or a stable neutron star. This process, associated with kilonova eruptions, is one of the main r-process sources of heavy element production (e.g. gold, platinum). Although the final outcome is a black hole, the environment around the merger determines important astrophysical nucleosynthesis.
6.3 Sources of gravitational waves
Stellar black holes Mergers generate some of the strongest gravitational wave signals. The detected spiral and ringdown stages reveal 10–80 M⊙ mass black holes, and also provides cosmic distance checks, relativity checks, and information on the evolution of massive stars and the frequency of binary origin in various galactic environments.
7. Theoretical challenges and future observations
7.1 Mechanisms of black hole formation
Open questions remain about what mass a star needs to directly form a black hole, or how "fallen" mass after a supernova can significantly change the final mass of the core.Observation data on "failed supernova"or rapid faint collapses could confirm these scenarios. Large-scale transient studies (Rubin Observatory, next-generation wide-field X-ray missions) could identify cases where massive stars disappear without a bright explosion."
7.2 Condition at extremely high densities
While neutron stars provide direct constraints on the supernuclear density, black holes obscure their internal structure below the event horizon. The boundary between the maximum possible mass of a neutron star and the formation of a black hole is related to the inaccuracies of nuclear physics. Observations of massive neutron stars (~2–2.3 M⊙) forces us to reconsider theoretical boundaries.
7.3 Merger dynamics
As gravitational wave detectors detect more and more black hole binaries, statistical analysis of spin axes, mass distributions, and displacements (redshifts) is revealing clues about the star-forming metal content, cluster dynamics, and binary evolutionary paths that produce these merging black holes.
8. Conclusions
Stellar black holes marks the spectacular end of the most massive stars – objects in which matter is compressed so much that not even light can escape. Born during core collapse supernova (with fallen mass) or in some cases of direct collapse, they have a few to a few dozen solar masses (and occasionally more). They are revealed in X-ray binaries, in strong gravitational waves in the signals merging and sometimes in a fainter supernova trace if the explosion is extinguished.
This cosmic cycle—the birth of a massive star, a short bright life, a cataclysmic death, and the emergence of a black hole—changes the galactic environment, returning heavier elements to the interstellar medium and giving rise to “high-energy” phenomena. Current and future surveys (from all-sky X-rays to gravitational wave catalogs) will increasingly reveal how these black holes form, evolve in binary systems, rotate, and possibly merge, offering a deeper understanding of stellar evolution, fundamental physics, and the interplay of matter and spacetime at their most extreme.
References and further reading
- Oppenheimer, JR, & Snyder, H. (1939). "On Continued Gravitational Contraction." Physical Review, 56, 455–459.
- Woosley, SE, Heger, A., & Weaver, TA (2002). "The evolution and explosion of massive stars." Reviews of Modern Physics, 74, 1015–1071.
- Fryer, C. L. (1999). "Massive Star Collapses into Black Holes." The Astrophysical Journal, 522, 413–418.
- Belczynski, K., et al. (2010). "On the Maximum Mass of Stellar Black Holes." The Astrophysical Journal, 714, 1217–1226.
- Smartt, S. J. (2015). "Progenitors of Core-Collapse Supernovae." Publications of the Astronomical Society of Australia, 32, e016.
- Adams, S. M., et al. (2017). "The search for failed supernovae with the Large Binocular Telescope: confirmation of a disappearing star." Monthly Notices of the Royal Astronomical Society, 468, 4968–4981.
- Abbott, BP, et al. (LIGO Scientific Collaboration and Virgo Collaboration). (2016). "Observation of Gravitational Waves from a Binary Black Hole Merger." Physical Review Letters, 116, 061102.
- Remillard, RA, & McClintock, JE (2006). "X-Ray Properties of Black-Hole Binaries." Annual Review of Astronomy and Astrophysics, 44, 49–92.
- Abbott, R., et al. (LIGO-Virgo-KAGRA Collaborations) (2021). "GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo During the Second Part of the Third Observing Run." arXiv:2111.03606.
- McClintock, JE, Narayan, R., & Steiner, JF (2014). "Black Hole Spin via Continuum Fitting and the Role of Spin in Powering Transient Jets." Space Science Reviews, 183, 295–322.