As I understand black holes, they're considered "black" because the escape velocity is, or exceeds, the speed of light. Alternatively, the escaping light is redshifted infinitely.

The Schwarzschild radius of an object is the radius of a sphere with equivalent mass for which the escape velocity is c.

Logically, this effect would occur on a continuum and wouldn't simply be state-dependent. That is, if you add a differential amount of mass to an object repeatedly it will (eventually) gradually redshift out of visibility and become a black hole. It won't simply vanish when the appropriate mass has been collected.

This suggests to me that, somewhere, there exist objects with enough mass to be highly redshifted but not enough to be "black."

Would it be possible to identify such an object from associated effects, such as gravitational lensing, or, without closer inspection, could it simply be mistaken for an extremely hot brown dwarf? (Or option C, is there a reason this couldn't happen?)

  • $\begingroup$ "When the photon is emitted at a distance equal to the Schwarzschild radius, the redshift will be infinitely large, and it will not escape any finite distance from the Schwarzschild sphere." - Gravitational Redshift extracted direct from Wiki $\endgroup$ – user6760 Dec 26 '18 at 3:48
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    $\begingroup$ @user6760 Yes, but if a photon is emitted just outside the Schwarzschild radius then the redshift would be finite and the photon would be hypothetically detectable. Yes? I'm asking about a massive object whose redshift is finite but extremely large. $\endgroup$ – CoilKid Dec 26 '18 at 3:56
  • $\begingroup$ Give me some moment to imagine how a universe long photon being emitted would be like... $\endgroup$ – user6760 Dec 26 '18 at 4:12
  • $\begingroup$ As a supplement to the great answer by @JohnRennie , you might be interested in Buchdal's theorem. For some recent related research, see arxiv.org/abs/gr-qc/0605097 and arxiv.org/abs/1606.03046. $\endgroup$ – Chiral Anomaly Dec 26 '18 at 5:43

The answer is generally believed to be option C, but there are loopholes.

The problem is that if you start with a neutron star and add mass the neutron star does not change smoothly and continuously to a black hole. A neutron star is supported by the degeneracy pressure of the neutrons within it, and once the pressure due to gravity is great enough to overcome the degeneracy pressure the star collapses abruptly into a black hole. This means there is a maximum size of neutron star that is currently believed to be 2.16 solar masses. The heaviest neutron star found so far has a mass of 2.01 solar masses.

If you take a neutron star near the maximum mass and add extra mass it won't simply grow and redshift gradually. Instead it will collapse abruptly (and probably very violently) into a black hole when the maximum mass is exceeded. The objects with intermediate red shifts that you describe cannot exist because they would be unstable with respect to collapse into a black hole.

The loopholes are because we don't understand the equation of state of highly compressed matter well enough to state with absolute confidence that this is what happens. For example is has been suggested that when the neutron star collapses it could transition to an even denser, but stable, form of matter called quark matter and form a quark star. This would appear as an object similar to the objects you talk about, though it's hard to comment on what its surface red shift would be since the idea is so speculative.


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