Rotating black holes with primary scalar hair in beyond Horndeski gravity produce shadows whose diameter increases for negative Q and whose distortion increases for positive Q, with EHT bounds on M87* restricting but not ruling out the (a, Q) parameter space.
Regular Black Hole Metric with Three Constants of Motion
6 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
According to the no-hair theorem, astrophysical black holes are uniquely characterized by their masses and spins and are described by the Kerr metric. Several parametric spacetimes which deviate from the Kerr metric have been proposed in order to test this theorem with observations of black holes in both the electromagnetic and gravitational-wave spectra. Such metrics often contain naked singularities or closed timelike curves in the vicinity of the compact objects that can limit the applicability of the metrics to compact objects that do not spin rapidly, and generally admit only two constants of motion. The existence of a third constant, however, can facilitate the calculation of observables, because the equations of motion can be written in first-order form. In this paper, I design a Kerr-like black hole metric which is regular everywhere outside of the event horizon, possesses three independent constants of motion, and depends nonlinearly on four free functions that parameterize potential deviations from the Kerr metric. This metric is generally not a solution to the field equations of any particular gravity theory, but can be mapped to known four-dimensional black hole solutions of modified theories of gravity for suitable choices of the deviation functions. I derive expressions for the energy, angular momentum, and epicyclic frequencies of a particle on a circular equatorial orbit around the black hole and compute the location of the innermost stable circular orbit. In addition, I write the metric in a Kerr-Schild-like form, which allows for a straightforward implementation of fully relativistic magnetohydrodynamic simulations of accretion flows in this metric. The properties of this metric make it a well-suited spacetime for strong-field tests of the no-hair theorem in the electromagnetic spectrum with black holes of arbitrary spin.
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2026 6representative citing papers
A rotating black-hole metric with a dark-matter halo is derived, but the proposed halo profiles do not make the spacetime asymptotically flat as claimed.
BlackHawk v3.0 adds Hawking temperatures and greybody factors for multiple regular black hole metrics to an existing public code via numerical routines.
Combining regular black hole metrics with memory burden suppresses evaporation and opens a 10^6-10^8 g PBH mass window that can comprise all dark matter.
Preliminary analysis of orbiting spacecraft around a black hole to test the compact object's nature and General Relativity under the assumption of deceleration capability.
GWTC-4 inspirals yield tighter constraints on Johannsen parameters α13 and ε3, both consistent with zero and thus with the Kerr geometry.
citing papers explorer
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Rotating Black Holes with Primary Scalar Hair: Shadow Signatures in Beyond Horndeski Gravity
Rotating black holes with primary scalar hair in beyond Horndeski gravity produce shadows whose diameter increases for negative Q and whose distortion increases for positive Q, with EHT bounds on M87* restricting but not ruling out the (a, Q) parameter space.
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A metric solution for rotating black holes embedded in dark matter halos with central spikes
A rotating black-hole metric with a dark-matter halo is derived, but the proposed halo profiles do not make the spacetime asymptotically flat as claimed.
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$\tt BlackHawk$ $\tt v3.0$: Hawking Radiation from Regular Black Holes
BlackHawk v3.0 adds Hawking temperatures and greybody factors for multiple regular black hole metrics to an existing public code via numerical routines.
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Memory burden effect of regular primordial black holes
Combining regular black hole metrics with memory burden suppresses evaporation and opens a 10^6-10^8 g PBH mass window that can comprise all dark matter.
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Testing Black Holes with Interstellar Missions: I. Orbiting Probes
Preliminary analysis of orbiting spacecraft around a black hole to test the compact object's nature and General Relativity under the assumption of deceleration capability.
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Improved Constraints on Non-Kerr Deviations from Binary Black Hole Inspirals Using GWTC-4 Data
GWTC-4 inspirals yield tighter constraints on Johannsen parameters α13 and ε3, both consistent with zero and thus with the Kerr geometry.