Regular black holes with finite gravitational mass term

What the study found: The authors report a neutral, non-singular spacetime geometry obtained by including non-local gravitational self-energy. They say this leads to a regular black-hole-like solution of the Ayon-Beato-Garcia type without electric charge, and to extremal particle–black hole objects of order the Planck mass.
Why the authors say this matters: The authors conclude that these extremal objects are thermodynamically stable, have vanishing Hawking temperature, and could be a viable dark matter candidate. They also frame the work as a way to describe gravity using a coordinate-independent quantity derived from gravitational self-energy.
What the researchers tested: The study uses a non-local gravitational theory inspired by T-duality, in which particle mass is smeared over a region rather than treated as point-like. The authors derive non-local gravitational self-interaction from the Newtonian gravitational potential and energy density, and incorporate this into the spacetime metric.
What worked and what didn't: The approach produced a finite, regularized gravitational mass term and a regular solution of the Ayon-Beato-Garcia type without electric charge. The abstract reports the existence of extremal configurations and states that they are thermodynamically stable with zero Hawking temperature. No failed test, negative result, or comparison with other models is described in the abstract.
What to keep in mind: The summary is limited to the abstract, so details about assumptions, calculations, or external validation are not provided. The abstract does not describe limitations beyond the scope of the model itself.

Key points

• Non-local gravitational self-energy is used to obtain a neutral, non-singular spacetime geometry.
• The authors derive a finite, regularized gravitational mass term and a regular Ayon-Beato-Garcia type solution without electric charge.
• The abstract reports extremal particle–black hole objects of Planck-mass scale.
• These objects are described as thermodynamically stable with vanishing Hawking temperature.
• The authors say they could be a viable dark matter candidate.