Astronomers do find massive compact objects in the X-ray Binaries, in the Quasars, in the center of many galaxies.

In most of the cases, the radius of such objects could be few Schwarzschild Radii  (Rs = 2 GM/c2 ) or even close to Rs. On the other hand we know that Neutron Stars, White Dwarfs, or other COLD objects cannot have masses more than ~3 solar masses. And thus, astronomers usually call such massive compact objects as ``Black Holes'' (BHs). Indeed, in General Relativity (GR),  there are beautiful exact solutions which suggest likely existence of  BHs.

However, the gravitational mass of  say, a Schwarzschild BH, appears as an INTEGRATION CONSTANT. But it has been found that this integration constant has the unique value =0, which means that Schwarzschild BHs too have the unique gravitational mass M=0, even if they would have arbitrary large baryonic masses (Mitra, Journal of Math. Phys., Volume 50, p. 042502, 2009). This E=Mc2 =0 state need not at all mean that the point singularity in the BH is devoid of matter. On the other hand, it only means that, the grip of gravitation for a singularity is so intense that the negative self-gravitational energy offsets all other positive sources of mass energy such as baryonic rest mass, heat and other internal energies. And a BH can become the ultimate ground state of continued collapse  only if it would correspond to E=0. Further, as a horizon encloses this singularity, it can become a state of absolute peace! The 40 year old puzzle of origin of BH entropy and Information loss too vanish with the realization that true BHs have M=0; and a surface area A=0, so that S=k ln 1=0. Thus trivially S=A=0.

Accordingly, the so-called "Black Holes'' (or anything else with finite masses) cannot be true "Black Holes''! On the other hand they must be something else whose surface gravitational redshift z>>1 (True BHs have z=Infty).
And the maiden BH alternative suggested by this blogger  way back in 1998 was 

"Eternally Collapsing Object'' (ECO).

By ignoring the historical developments, the true nature of the ECOs, as it transpired later is:

An Eternally Collapsing Object (ECO) is a Ball of Self-Gravitating&Ever Contracting Extremely Hot Plasma/Fire. For such HOT stars, the concept of Chandrasekhar or Oppenheimer -Volkoff Mass Upper limits get invalidated. Incidentally, in 1960s, Sir Fred Hoyle and Nobel Laureate William Fowler had proposed that Quasars contain Hot Radiation Pressure Supported Stars rather than BHs. In addition, the idea of ECO arose as it was found that continued spherical gravitational collapse avoids formation of ``trapped surfaces'', those trap doors of "no return''.

Thus all singularity theorems of Hawking and Penrose get invalidated. In the absence of "trapped surfaces'', in principle a collapse process can rebound, as found by many numerical studies of radiative/physical gravitational collapse. And if there could be reversal of the collapse process, there can certainly be quasi-static states too.

An ECO is such a quasi-static state. The idealized ECO picture is obtained by considering the contraction process to remain so (i.e., no expansion).

This is a real possibility because the proper co-moving radial length of the collapsing object may continuously get stretched as the space-time membrane gets relentless stretched by the tidal forces. Note, if the collapse process would indeed approach  a singular state, the radial metric coefficient  grr --> Infty.

Then the radial  proper length l too can be tend to be Infinite. In fact, a specific example was shown where for an ultra-relativistic final Equation of State of the collapsing matter, indeed, proper radius l-->Infty.
Irrespective of this, it was shown that the luminosity of the radiation, trapped by the relentless self-gravity of the collapsing star itself, can attain its  "Eddington Value''. This means that a radiation supported quasi-static state is bound to occur sooner or later during continued gravitational collapse; and an ECO is such a Radiation Pressure Supported Relativistic Star. However, in contrast to the similar quasi-Newtonian stars envisaged by Hoyle and Fowler, ECOs are extremely general relativistic with z>>1.

For an illustrative version of the physics behind ECOs, please see: