Ultimate fate of matter and black holes as gravitational coupling vanishes

Determine the ultimate fate of matter and black holes in the limit in which the bimetric cosmological model’s function α(t) tends to infinity, causing the effective gravitational constant G(t) and gravitational-interaction propagation speed c_grav(t) to approach zero, beyond what can be established within classical gravity alone.

Background

The paper studies a bimetric cosmological model in which the gravitational and matter metrics are related by a time-dependent function α(t). For the class of solutions considered, α(t) diverges at a finite cosmic time, while the effective gravitational coupling G(t)=G_0/α(t)^3 and gravitational propagation speed c_grav(t)=c_0/α(t) both vanish. The authors argue that this weakening of gravity could dissolve gravitationally bound structures and cause black-hole horizons to shrink, potentially converting matter into radiation and producing a radiation-dominated state compatible with Conformal Cyclic Cosmology.

However, the paper does not rigorously establish the behavior of matter, black-hole horizons, or Hawking evaporation when both G and c_grav become dynamical and tend to zero. The unresolved problem is therefore to determine the actual final state in this limit, which the authors state cannot be settled by classical gravity alone and may require a quantum theory of gravity.