According to the second paper linked in the summary, there are theoretical models of black holes that do not feature singularities. The solutions to Einstein's general relativity equations that feature singularities--like Schwarzchild (spherical, non-rotating) and Kerr (rotating) black holes--require space to be flat far away from them. This is incompatible with the universe we live in, which is expanding at an accelerating rate. From the second paper:
Existing models for astrophysical BHs are necessarily provisional. They feature singularities, horizons, and unrealistic boundary conditions (e.g., Visser 2009). Though singularities and horizons are of theoretical interest (e.g., Harlow 2016), the Kerr solution reduces to flat spacetime at spatial infinity. This is incompatible with our universe, which is in concordance with a perturbed Robertson Walker (RW) cosmology to sub-percent precision (e.g., Aghanim et al. 2020; Dodelson & Schmidt 2020). Thus, regardless of singularities and horizons, Kerr is only appropriate for intervals of time short compared to the reciprocal expansion rate of the universe, and can only be consistently interpreted as an approximation to some more general solution.
As for black hole models without singularities
Efforts to construct a BH model in general relativity (GR) with realistic RW boundary conditions have been ongoing for nearly a century, but have met with limited success. Early work by McVittie (1933) generalized the Schwarzschild solution to arbitrary RW spacetimes. Nolan (1993) constructed a non-singular interior for this solution, and progress has been made in understanding its horizon/causal structure (e.g., Kaloper et al. 2010; Lake & Abdelqader 2011; Faraoni et al. 2012; da Silva et al. 2013). Faraoni & Jacques (2007) constructed solutions featuring dynamical phenomena such as horizons that comove with the universe's expansion, evolution of interior energy densities and pressures, and time-varying mass. These solutions are significant, because they show how heuristic application of Birkhoff's theorem in cosmological settings can fail in the presence of strong gravity (see Lemaître 1931; Einstein & Straus 1945; Callan et al. 1965; Peebles 1993). Time-varying mass in particular has been studied by Guariento et al. (2012) and Maciel et al. (2015), but its interpretation remains largely unexplored. All of these solutions, however, are incompatible with Kerr on short timescales because they do not spin. A BH solution that satisfies observational constraints at small and large scales simultaneously has yet to be found.
The measurements described in the paper claim to show that black holes grow and gain mass due to the expansion of the universe without absorbing the mass of stars and gases around them. If this interpretation of their data is true, this may be enough to show that actual black holes do not have singularities.
Cosmologically coupled mass change allows for experimental distinction between singular and non-singular BHs, complementing constraints from short-timescale data (e.g., Sakai et al. 2014; Cardoso et al. 2016; Uchikata et al. 2016; Yunes et al. 2016; Cardoso & Pani 2017; Chirenti 2018; Konoplya et al. 2019; Maggio et al. 2020).
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Our result provides a single-channel explanation for the disparity in SMBH masses between local ellipticals and their 7–10 Gyr antecedents (Farrah et al. 2023). Furthermore, the recovered value of k = 3 is consistent with SMBHs having vacuum energy interiors. Our study thus makes the existence argument for a cosmologically realistic BH solution in GR with a non-singular vacuum energy interior.
