Kerr-Newman Modified Gravity BH

• Kerr-Newman-Modified Gravity Black Hole is a charged, rotating solution in STVG where the deformation parameter α modifies gravitational coupling and the effective charge structure.
• The metric and horizon conditions are altered by α, leading to distinctive ergospheres, shadow morphologies, and energy-extraction behaviors not seen in standard Kerr-Newman black holes.
• Analyses using test-particle dynamics, thermodynamics, and imaging methods reveal unique insights into weak cosmic censorship, photon trajectories, and accretion physics in KN-MOG-BH systems.

Searching arXiv for the cited Kerr–Newman–Modified Gravity black hole literature to ground the article in the requested sources. The Kerr-Newman-Modified Gravity black hole (KN-MOG-BH) is a charged, rotating black-hole solution studied in Scalar-Tensor-Vector Gravity (STVG), also known as Modified Gravity (MOG), in which the usual Kerr-Newman geometry is deformed by a dimensionless MOG parameter $\alpha$. In this framework the gravitational coupling is written as $G = G_N(1+\alpha)$, and the vector sector carries a gravitational source charge $Q_g = \sqrt{\alpha G_N}\,M$. For isolated black holes with asymptotically flat boundary condition, the scalar field is constant everywhere, so these objects have no scalar monopole moment radiation; the rotating solutions are therefore discussed primarily in terms of mass, spin, electric charge when present, and the MOG deformation parameter $\alpha$ (Moffat, 2020).

1. STVG framework and the meaning of the MOG deformation

STVG extends general relativity by adding two new degrees of freedom: a scalar field gravitational coupling strength and a gravitational spin-1 vector field. In the black-hole sector, the scalar field is constant everywhere for an isolated black hole with asymptotically flat boundary condition, while the vector field introduces a gravitational charge proportional to mass, $Q_g=\sqrt{\alpha G_N}M$ (Moffat, 2020). In this sense, MOG rotating black holes are repeatedly described as Kerr-Newman-like: the additional $Q^2$-type structure is not necessarily electromagnetic, but can arise from the MOG vector field itself (Moffat, 2014).

Within this literature, “Kerr-MOG,” “Kerr-Newman-type,” and “Kerr-Newman-MOG” are closely related labels. One branch treats the rotating MOG solution with gravitational charge but no electric charge, while another keeps an explicit electric charge $Q$ and studies the charged rotating black hole in MOG directly, particularly for weak cosmic censorship and imaging problems (Moffat, 2020, Zheng et al., 2024). A common misconception is to identify the MOG charge with ordinary electric charge. The sources distinguish them explicitly: the MOG charge is gravitational in origin, while the KN-MOG spacetime may also carry an electromagnetic charge $Q$ (Moffat, 2014).

The parameter $\alpha$ is the central deformation variable. At $\alpha=0$, the general relativity limit is recovered. For $G = G_N(1+\alpha)$0, the balance among mass, charge, and angular momentum in the horizon condition is modified, and the geometry, ergosphere, observables, and energy-extraction processes are all altered in the strong-field regime (Sheoran et al., 2017).

2. Metric structure, horizons, and extremality

A commonly used charged rotating MOG parametrization defines the ADM mass as $G = G_N(1+\alpha)$1 and writes the horizon function as

$G = G_N(1+\alpha)$2

In this form, the event horizon exists when

$G = G_N(1+\alpha)$3

with equality corresponding to an extremal black hole and violation corresponding to absence of a horizon, i.e. a naked singularity (Ahmad et al., 22 Sep 2025). A closely related convention writes

$G = G_N(1+\alpha)$4

with horizon radii

$G = G_N(1+\alpha)$5

which encodes the same charged rotating MOG deformation in a different mass convention (Ahmad et al., 25 Aug 2025).

For the uncharged rotating sector, the standard Kerr-MOG metric is written with

$G = G_N(1+\alpha)$6

and reduces to Kerr when $G = G_N(1+\alpha)$7 (Moffat, 2020). The stationary limit surface and ergosphere are likewise shifted by $G = G_N(1+\alpha)$8, and several papers emphasize that the deformation parameter affects the geometry significantly in addition to the ADM mass and spin parameters (Sheoran et al., 2017).

Because the literature alternates between $G = G_N(1+\alpha)$9 and $Q_g = \sqrt{\alpha G_N}\,M$0, published extremality bounds are not always written in the same form. This suggests that comparisons across papers must track conventions carefully before attributing a monotonic physical trend to $Q_g = \sqrt{\alpha G_N}\,M$1.

3. Weak cosmic censorship and destruction experiments

The most developed KN-MOG-BH dynamical question in the recent literature concerns the weak cosmic censorship conjecture (WCCC) under test-particle or test-field absorption. In the charged rotating test-particle setup, a particle with charge $Q_g = \sqrt{\alpha G_N}\,M$2, angular momentum $Q_g = \sqrt{\alpha G_N}\,M$3, and energy $Q_g = \sqrt{\alpha G_N}\,M$4 changes the black-hole parameters according to $Q_g = \sqrt{\alpha G_N}\,M$5, $Q_g = \sqrt{\alpha G_N}\,M$6, and $Q_g = \sqrt{\alpha G_N}\,M$7. The minimum energy for absorption is

$Q_g = \sqrt{\alpha G_N}\,M$8

while WCCC violation requires the post-absorption parameters to satisfy

$Q_g = \sqrt{\alpha G_N}\,M$9

equivalently an allowed window $\alpha$0 with suitable $\alpha$1 and $\alpha$2 (Ahmad et al., 25 Aug 2025).

The charged test-particle analysis reports that the result is sensitive to multiple factors, including the sign of the particle's charge relative to that of the black hole, the direction of rotation of the particle and the black hole, and the combined effect of the MOG parameter, the black hole's charge and angular momentum. Within the test-particle approximation, the event horizon can disappear in both extremal and non-extremal KN-MOG black holes, provided the particle parameters are small and precisely adjusted. The same work states that incorporating $\alpha$3 significantly enlarges the range of permissible parameters for the test particle compared with prior Kerr-Newman analyses that did not include the modified-gravity parameter (Ahmad et al., 25 Aug 2025).

A related scalar-field analysis reaches a more qualified conclusion. Neglecting backreaction, scalar test fields with frequencies just above the superradiance threshold can overspin both extremal and nearly extremal KN-MOG black holes, producing naked singularities. When backreaction is incorporated by allowing the event horizon’s angular velocity to rise before absorption, overspinning is prevented for the extremal KN-MOG black hole but not for the nearly extremal case (Ahmad et al., 22 Sep 2025). The controversy is therefore not whether the test-body or test-field approximation can produce violations, but how much of the allowed overspinning window survives once backreaction is included.

4. Photon dynamics, shadow morphology, and disk imaging

The KN-MOG-BH shadow and thin-disk image have been studied with backward ray tracing in the charged rotating spacetime. In that analysis, increasing $\alpha$4 rounds the flat edge of the shadow, enlarges the shadow size, and decreases the deviation rate $\alpha$5, while increasing the electric charge $\alpha$6 reduces the shadow radius. The same study reports that the photon trajectory exhibits two “tails” near the Einstein ring, which elongate as the spin $\alpha$7 increases; for the accretion disk, the inner shadow expands with $\alpha$8 and decreases with $\alpha$9, and the increase of $Q_g=\sqrt{\alpha G_N}M$0 has a more obvious effect on inner shadow and image than the increase of $Q_g=\sqrt{\alpha G_N}M$1 (Zheng et al., 2024).

These results assign a dominant role to $Q_g=\sqrt{\alpha G_N}M$2 in the charged rotating MOG spacetime. A second misconception therefore concerns parameter degeneracy: although both $Q_g=\sqrt{\alpha G_N}M$3 and $Q_g=\sqrt{\alpha G_N}M$4 affect the image, the cited KN-MOG imaging study states that the influence of $Q_g=\sqrt{\alpha G_N}M$5 is much greater at the same parameter level (Zheng et al., 2024). In that sense, a nearly circular yet enlarged shadow at high spin is treated not merely as a charge effect but as a characteristic MOG signature.

Within the broader rotating MOG family, shadow and photon-orbit studies reinforce this picture. The shadow sizes of Schwarzschild-MOG and Kerr-MOG black holes increase significantly as $Q_g=\sqrt{\alpha G_N}M$6 is increased from zero (Moffat, 2015). Spherical photon-orbit analyses of Kerr-MOG derive a sixth-order polynomial for constant-radius null orbits and find that all such orbits are radially unstable; the deformation parameter $Q_g=\sqrt{\alpha G_N}M$7 constrains the rotation and changes the observable photon impact parameter (Li et al., 2024). Thick-disk radiative-transfer calculations in Kerr-MOG further report that the photon ring and central dark region expand with increasing $Q_g=\sqrt{\alpha G_N}M$8, while high-resolution polarimetric observables such as the net polarization angle $Q_g=\sqrt{\alpha G_N}M$9 and the second Fourier mode $Q^2$0 are sensitive to both $Q^2$1 and spin (Wang et al., 12 Nov 2025).

5. Accretion physics, charged particles, and energy extraction

Energetic processes around rotating MOG black holes are not uniform across mechanisms. For the charged rotating KN-MOG black hole, magnetic reconnection calculations based on the Comisso-Asenjo mechanism show that the combined effect of the MOG parameter and black-hole charge can play an increasingly important role, leading to high energy efficiency and power for energy extraction. In that framework, the rate of energy extraction increases as a consequence of the combined effect of black-hole charge and MOG parameter, and the cited study concludes that magnetic reconnection is significantly more efficient than the Blandford-Znajek mechanism (Shaymatov et al., 2023).

This conclusion coexists with a different result for the Penrose process in the uncharged Kerr-MOG sector. There, the gain in energy

$Q^2$2

decreases as $Q^2$3 increases, so the MOG parameter diminishes the value of $Q^2$4 in contrast with the extremal Kerr black hole (Pradhan, 2018). The contrast is mechanism-specific rather than contradictory: magnetic reconnection, Penrose splitting, and superradiant scattering weight the ergoregion, frame dragging, and charge sectors differently.

Charged-particle dynamics in magnetized Kerr-MOG backgrounds also show non-Kerr behavior. The magnetic field can extend the region of stable circular orbits, whereas the STVG parameter reduces the instability of the circular orbit; in some regimes, the Schwarzschild black hole captures the test particle, the Kerr black hole allows escape or capture, while in Kerr-MOG the test particle can be trapped in a region around the black hole and start orbiting it (Khan et al., 2023). Superradiance studies likewise report that MOG rotating black holes have a marked reduction of the critical frequency of mode amplification and are fainter with respect to the standard ones, with the superradiance peak frequency red shifted (Wondrak et al., 2018).

6. Thermodynamics, dual descriptions, and global structure

Thermodynamic analyses are most complete for the Kerr-MOG sector, which some papers explicitly describe as “sometimes called Kerr-Newman-MOG due to its metric structure.” In this sector, the horizon area product

$Q^2$5

is not mass-independent, unlike the universal area products familiar from Einstein gravity. The first law is verified at both the outer and inner horizons,

$Q^2$6

and the Kerr-MOG/CFT correspondence yields equal left- and right-moving central charges,

$Q^2$7

together with the extremal left-moving temperature

$Q^2$8

The associated Cardy entropy agrees with the macroscopic Bekenstein-Hawking entropy in the extremal limit (Pradhan, 2017).

Global and topological questions also enter the rotating MOG discussion. A recent analysis argues that the zero-mass limit of the Kerr-MOG black hole is equivalent to a wormhole and derives a Kerr-Schild form for the metric, whereas the zero-mass limit of the Kerr-Newman black hole does not yield a wormhole unless both the mass and charge parameters are set to zero (Pradhan et al., 2024). This result belongs to the Kerr-MOG branch rather than the explicitly electrically charged KN-MOG case, but it is part of the same rotating MOG family and sharpens the distinction between MOG-induced and electromagnetic structure.

Taken together, these thermodynamic and global results place the KN-MOG-BH in a wider MOG program in which horizon mechanics, holographic duality, shadow morphology, cosmic censorship, and energy extraction are all deformed by the same parameter $Q^2$9, while the electric charge $Q$0 adds a second charged sector with observable and dynamical consequences (Pradhan, 2017, Zheng et al., 2024).