We investigate geodesic motion, shadow observables and thin-disk accretion for the regular black hole generated by a non-local gravitational self-energy contribution. The geometry is controlled by a zero-point length and can be followed smoothly from the Schwarzschild limit to a cold extremal remnant. We compute the photon ring, critical impact parameter, apparent shadow radius, null Lyapunov exponent, innermost stable circular orbit, orbital frequencies and Novikov-Thorne flux profile. As the self-energy scale grows, both the photon ring and the ISCO move outward, while the photon-ring frequency and instability exponent decrease. The horizon-normalized shadow area increases by about a factor of 2.7 for the near-extremal benchmark, although the same shadow radius decreases when normalized by the ADM mass. The ISCO binding efficiency grows modestly, whereas the zero-torque thin-disk flux peak moves outward and falls to about 61% of the Schwarzschild peak as the solution approaches the remnant regime. These trends identify a coherent set of optical, orbital and accretion signatures of the gravitational-self-energy regularization.
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Orbital, Shadow and Thin-Disk Signatures of a Regular Black Hole with Gravitational Self-Energy
Author Information
Received: 23 May 2026 | Revised: 25 Jun 2026 | Accepted: 26 Jun 2026 | Published: 29 Jun 2026
Abstract
Keywords
regular black holes | black hole shadows | geodesic motion | ISCO | thin-disk accretion | gravitational self-energy
References
- 1.
Bardeen, J.M. Non-singular general-relativistic gravitational collapse. In Proceedings of the International Conference GR5, Tbilisi, USSR, 9–16 September 1968; p. 174.
- 2.
Hayward, S.A. Formation and evaporation of nonsingular black holes. Phys. Rev. Lett. 2006, 96, 031103.
- 3.
Konoplya, R.A.; Zhidenko, A. Dark matter halo as a source of regular black-hole geometries. Phys. Rev. D 2026, 113, 043011.
- 4.
Nicolini, P.; Smailagic, A.; Spallucci, E. Noncommutative geometry inspired Schwarzschild black hole. Phys. Lett. B 2006, 632, 547–551.
- 5.
Spina, A. Black Holes in Asymptotic Safety: A Review of Solutions and Phenomenology. Int. J. Grav. Theor. Phys. 2025, 1, 8.
- 6.
Ayon-Beato, E.; Garcia, A. Regular black hole in general relativity coupled to nonlinear electrodynamics. Phys. Rev. Lett. 1998, 80, 5056–5059.
- 7.
Jusufi, K.; Singleton, D. Regular black holes with gravitational self-energy as dark matter. Eur. Phys. J. C. 2026, 86, 530.
- 8.
Synge, J.L. The escape of photons from gravitationally intense stars. Mon. Not. R. Astron. Soc. 1966, 131, 463–466.
- 9.
Bardeen, J.M. Timelike and null geodesics in the Kerr metric. In Black Holes; DeWitt, C.; DeWitt, B.S., Eds.; Gordon and Breach: New York, NY, USA, 1973; pp. 215–239.
- 10.
Luminet, J.P. Image of a spherical black hole with thin accretion disk. Astron. Astrophys. 1979, 75, 228–235.
- 11.
Falcke, H.; Melia, F.; Agol, E. Viewing the shadow of the black hole at the Galactic center. Astrophys. J. Lett. 2000, 528, L13–L16.
- 12.
Event Horizon Telescope Collaboration. First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole. Astrophys. J. Lett. 2019, 875, L1.
- 13.
Chandrasekhar, S. The Mathematical Theory of Black Holes; Oxford University Press: Oxford, UK, 1983.
- 14.
Cardoso, V.; Miranda, A.S.; Berti, E.; et al. Geodesic stability, Lyapunov exponents, and quasinormal modes. Phys. Rev. D 2009, 79, 064016.
- 15.
Bardeen, J.M.; Press, W.H.; Teukolsky, S.A. Rotating black holes: Locally nonrotating frames, energy extraction, and scalar synchrotron radiation. Astrophys. J. Lett. 1972, 178, 347–370.
- 16.
Novikov, I.D.; Thorne, K.S. Astrophysics of black holes. In Black Holes; DeWitt, C.; DeWitt, B.S., Eds.; Gordon and Breach: New York, NY, USA, 1973; pp. 343–450.
- 17.
Page, D.N.; Thorne, K.S. Disk-accretion onto a black hole. Time-averaged structure of accretion disk. Astrophys. J. Lett. 1974, 191, 499–506.
- 18.
Konoplya, R.A. Further clarification on quasinormal modes/circular null geodesics correspondence. Phys. Lett. B 2023, 838, 137674.
- 19.
Konoplya, R.A.; Stuchl´ık, Z. Are eikonal quasinormal modes linked to the unstable circular null geodesics? Phys. Lett. B 2017, 771, 597–602.
- 20.
Bolokhov, S.V. Black holes in Starobinsky-Bel-Robinson Gravity and the breakdown of quasinormal modes/null geodesics correspondence. Phys. Lett. B 2024, 856, 138879.
- 21.
Shakura, N.I.; Sunyaev, R.A. Black holes in binary systems. Observational appearance. Astron. Astrophys. 1973, 24, 337–355.
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