Magnetically Charged Black Hole

• Magnetically Charged Black Holes (MCBH) are defined as black holes carrying intrinsic magnetic monopole charge, appearing in both Einstein–Maxwell and nonlinear electrodynamics frameworks.
• Analytical methods, including dyonic Kerr–Newman–de Sitter metrics and elliptic function techniques, reveal how magnetic charge alters orbital dynamics and superradiance phenomena.
• Studies of MCBHs examine thermodynamic behavior, accretion processes, and optical signatures, providing key insights for observational tests with EHT and dark matter constraints.

Searching arXiv for recent and canonical papers on magnetically charged black holes and closely related “magnetically active” black-hole scenarios. A magnetically charged black hole (MCBH) is, in the strict Einstein–Maxwell sense, a black hole carrying magnetic monopole charge, either purely magnetic or dyonic. In the modern literature, the term also covers nonlinear-electrodynamics black holes whose geometry is sourced by a magnetic charge parameter and may be regular at the core, while some astrophysical papers discuss black holes that are merely magnetically active because they acquire electric charge in an external magnetic field. These notions are not equivalent: intrinsic magnetic charge is a monopole degree of freedom, whereas a “black hole pulsar” or a boosted black hole in a magnetic field is electrically charged and magnetized, but not magnetically charged in the monopole sense (Stetsko, 2013, Levin et al., 2018, Adari et al., 2021).

Class	Defining content	Representative papers
Intrinsic monopole or dyonic MCBH	Magnetic monopole charge $Q_m$ enters the exact solution	(Stetsko, 2013, Li et al., 24 Nov 2025)
NLED magnetic black hole	Magnetic charge sources a nonlinear electromagnetic stress tensor; regularity may occur	(Kruglov, 2018, Kumaran et al., 2023, Zare et al., 2024)
Magnetically active but non-monopole black hole	Electric charge induced or sustained by an external magnetic field	(Levin et al., 2018, Adari et al., 2021, Shaymatov et al., 2021)

1. Canonical monopole and string-theoretic constructions

In Einstein–Maxwell theory, a magnetically charged black hole is the magnetic analogue of an electrically charged one: the geometry is the same class of solution, but the electromagnetic field carries a magnetic monopole component rather than, or in addition to, an electric one. A particularly explicit example is the dyonic Kerr–Newman–de Sitter spacetime, where the radial function is

$$\Delta_r=(r^2+a^2)\left(1-\frac{r^2}{\ell^2}\right)+Q_e^2+Q_m^2-2Mr,$$

so the geometry depends on $Q_e^2+Q_m^2$, while the gauge potential distinguishes electric and magnetic contributions through

$$A_t=-\frac{Q_e r+Q_m a\cos\theta}{\rho^2},\qquad A_\phi=\frac{1}{\rho^2}\left(\frac{1}{2}Q_e r a\sin^2\theta+\frac{1}{2}Q_m(r^2+a^2)\cos\theta\right).$$

In the purely magnetic limit $Q_e=0$, the Hawking temperature retains the Kerr–Newman–de Sitter functional form,

$T_H(r_H)=\frac{\Delta_r'(r_H)}{4\pi(r_H^2+a^2)},$

with magnetic charge entering implicitly through the horizon location $r_H$ (Stetsko, 2013).

A distinct monopole framework arises in low-energy string theory. The magnetically charged Garfinkle–Horowitz–Strominger solution is described by

$$ds^{2}=\frac{1-\frac{m}{r}}{1-\frac{Q^{2}}{mr}}\,dt^{2} -\left(\frac{1-\frac{m}{r}}{1-\frac{Q^{2}}{mr}}\right)^{-1}dr^{2} -r^{2}d\Omega^{2},$$

with horizon radii

$r_{+}=m,\qquad r_{-}=\frac{Q^{2}}{m}.$

The paper on phantom energy accretion emphasizes a qualitative departure from Reissner–Nordström: even for $m^{2}<Q^{2}$, “both horizons exist and one cannot obtain a naked singularity at $$\Delta_r=(r^2+a^2)\left(1-\frac{r^2}{\ell^2}\right)+Q_e^2+Q_m^2-2Mr,$$0,” and the accretion analysis is argued to preserve cosmic censorship (Sharif et al., 2012).

These constructions establish the minimal meaning of MCBH: a spacetime with intrinsic magnetic monopole charge. They also show that “magnetic charge” need not be confined to asymptotically flat, static Reissner–Nordström analogues; it can appear in rotating, de Sitter, and string-dilaton settings without changing the basic role of $$\Delta_r=(r^2+a^2)\left(1-\frac{r^2}{\ell^2}\right)+Q_e^2+Q_m^2-2Mr,$$1 as a genuine monopole parameter.

2. Nonlinear electrodynamics and the regularization program

Much of the modern MCBH literature is built in nonlinear electrodynamics (NLED), where magnetic charge sources a non-Maxwell stress tensor and the central geometry can be softened or regularized. One explicit model uses

$$\Delta_r=(r^2+a^2)\left(1-\frac{r^2}{\ell^2}\right)+Q_e^2+Q_m^2-2Mr,$$2

with a purely magnetic sector $$\Delta_r=(r^2+a^2)\left(1-\frac{r^2}{\ell^2}\right)+Q_e^2+Q_m^2-2Mr,$$3, $$\Delta_r=(r^2+a^2)\left(1-\frac{r^2}{\ell^2}\right)+Q_e^2+Q_m^2-2Mr,$$4, and $$\Delta_r=(r^2+a^2)\left(1-\frac{r^2}{\ell^2}\right)+Q_e^2+Q_m^2-2Mr,$$5. The corresponding mass function is

$$\Delta_r=(r^2+a^2)\left(1-\frac{r^2}{\ell^2}\right)+Q_e^2+Q_m^2-2Mr,$$6

and the metric is asymptotically Reissner–Nordström-like,

$$\Delta_r=(r^2+a^2)\left(1-\frac{r^2}{\ell^2}\right)+Q_e^2+Q_m^2-2Mr,$$7

In this model the center is regular, $$\Delta_r=(r^2+a^2)\left(1-\frac{r^2}{\ell^2}\right)+Q_e^2+Q_m^2-2Mr,$$8, the black hole has two horizons for $$\Delta_r=(r^2+a^2)\left(1-\frac{r^2}{\ell^2}\right)+Q_e^2+Q_m^2-2Mr,$$9, an extremal horizon near $Q_e^2+Q_m^2$0, and no horizon for $Q_e^2+Q_m^2$1, where the solution becomes a regular soliton-like object. Its thermodynamics exhibits a second-order phase transition at $Q_e^2+Q_m^2$2, with a stable canonical branch for $Q_e^2+Q_m^2$3 (Kruglov, 2018).

A different NLED construction yields an asymptotic, magnetically charged, non-singular black hole with lapse

$Q_e^2+Q_m^2$4

which approaches

$Q_e^2+Q_m^2$5

at large radius. The associated energy density,

$Q_e^2+Q_m^2$6

suppresses the core strongly enough to support a de Sitter-like regular interior, and the paper studies the resulting deflection angle, shadow, and greybody bounds (Kumaran et al., 2023).

Another widely used regular magnetic solution has

$Q_e^2+Q_m^2$7

For this metric the event and Cauchy horizons exist for $Q_e^2+Q_m^2$8, become extremal near $Q_e^2+Q_m^2$9, and disappear for larger $$A_t=-\frac{Q_e r+Q_m a\cos\theta}{\rho^2},\qquad A_\phi=\frac{1}{\rho^2}\left(\frac{1}{2}Q_e r a\sin^2\theta+\frac{1}{2}Q_m(r^2+a^2)\cos\theta\right).$$0. The curvature analysis in that work shows a more delicate point: regularity holds numerically for $$A_t=-\frac{Q_e r+Q_m a\cos\theta}{\rho^2},\qquad A_\phi=\frac{1}{\rho^2}\left(\frac{1}{2}Q_e r a\sin^2\theta+\frac{1}{2}Q_m(r^2+a^2)\cos\theta\right).$$1, whereas very small $$A_t=-\frac{Q_e r+Q_m a\cos\theta}{\rho^2},\qquad A_\phi=\frac{1}{\rho^2}\left(\frac{1}{2}Q_e r a\sin^2\theta+\frac{1}{2}Q_m(r^2+a^2)\cos\theta\right).$$2 can spoil it (Zare et al., 2024).

NLED does not, however, guarantee regularity. In a NED-inspired magnetically charged black hole immersed in a Hernquist dark-matter halo,

$$A_t=-\frac{Q_e r+Q_m a\cos\theta}{\rho^2},\qquad A_\phi=\frac{1}{\rho^2}\left(\frac{1}{2}Q_e r a\sin^2\theta+\frac{1}{2}Q_m(r^2+a^2)\cos\theta\right).$$3

the metric function is finite at $$A_t=-\frac{Q_e r+Q_m a\cos\theta}{\rho^2},\qquad A_\phi=\frac{1}{\rho^2}\left(\frac{1}{2}Q_e r a\sin^2\theta+\frac{1}{2}Q_m(r^2+a^2)\cos\theta\right).$$4, but the paper explicitly finds divergent curvature invariants there. This makes the model an important counterexample to the common identification of “NLED magnetic black hole” with “regular black hole” (Jha, 31 Dec 2025).

3. Orbital dynamics, scattering, and superradiant phenomena

Magnetic charge alters particle dynamics in ways that are absent in electrically charged or neutral backgrounds. For the static magnetic analogue of Reissner–Nordström,

$$A_t=-\frac{Q_e r+Q_m a\cos\theta}{\rho^2},\qquad A_\phi=\frac{1}{\rho^2}\left(\frac{1}{2}Q_e r a\sin^2\theta+\frac{1}{2}Q_m(r^2+a^2)\cos\theta\right).$$5

the photon-sphere radius is

$$A_t=-\frac{Q_e r+Q_m a\cos\theta}{\rho^2},\qquad A_\phi=\frac{1}{\rho^2}\left(\frac{1}{2}Q_e r a\sin^2\theta+\frac{1}{2}Q_m(r^2+a^2)\cos\theta\right).$$6

and the ISCO is determined by

$$A_t=-\frac{Q_e r+Q_m a\cos\theta}{\rho^2},\qquad A_\phi=\frac{1}{\rho^2}\left(\frac{1}{2}Q_e r a\sin^2\theta+\frac{1}{2}Q_m(r^2+a^2)\cos\theta\right).$$7

For an electrically charged test particle, the paper derives an exact latitude formula for stable off-equatorial circular orbits,

$$A_t=-\frac{Q_e r+Q_m a\cos\theta}{\rho^2},\qquad A_\phi=\frac{1}{\rho^2}\left(\frac{1}{2}Q_e r a\sin^2\theta+\frac{1}{2}Q_m(r^2+a^2)\cos\theta\right).$$8

and shows that these orbits are a unique consequence of magnetic charge: in the analogous electrically charged Kerr–Newman spacetime they are forbidden. The maximum latitude deviation occurs at the ISCO, and the analysis finds stability against synchrotron radiation even for extremely small $$A_t=-\frac{Q_e r+Q_m a\cos\theta}{\rho^2},\qquad A_\phi=\frac{1}{\rho^2}\left(\frac{1}{2}Q_e r a\sin^2\theta+\frac{1}{2}Q_m(r^2+a^2)\cos\theta\right).$$9 (Li et al., 24 Nov 2025).

In the magnetically charged GHS stringy black hole, the separation of the Hamilton–Jacobi equation gives an especially clear division of dynamical roles. The angular equations depend on the electric charge of the test particle through the combination $Q_e=0$0, while the radial and temporal equations depend on the magnetic charge of the test particle through $Q_e=0$1. The radial motion is solved exactly in terms of Weierstrass elliptic functions, and the work identifies critical values of the black-hole magnetic charge, the particle magnetic charge, and the Carter constant that delimit bound, plunging, and “Magnetic Rutherford scattering” regimes (González et al., 2017).

Rotating magnetic NLED black holes also support superradiant scattering. In the Ghosh–Kumar rotating solution,

$Q_e=0$2

a neutral massive scalar satisfies the usual horizon-frequency condition with

$Q_e=0$3

and superradiance occurs for

$Q_e=0$4

The associated bound-state instability window is

$Q_e=0$5

The paper finds that magnetic charge enlarges the allowed superradiant frequency range and yields amplification behavior closely paralleling Kerr–Newman in some parameter ranges, suggesting a partial correspondence between magnetic NLED charge and electric Kerr–Newman charge in scalar-wave dynamics (Karmakar, 2024).

Taken together, these results indicate that magnetic charge is not merely a parameter in the metric function. It changes the topology of allowed charged-particle orbits, the structure of scattering thresholds, and the size of superradiant instability windows.

4. Thermodynamics, accretion, and relic magnetic black holes

The thermodynamics of MCBHs depends strongly on the underlying model. In the NLED example with

$Q_e=0$6

the Hawking temperature

$Q_e=0$7

vanishes at $Q_e=0$8, and the heat capacity diverges at $Q_e=0$9, marking a second-order phase transition and separating stable and unstable branches (Kruglov, 2018). In the dyonic Kerr–Newman–de Sitter case, semiclassical fermion tunnelling reproduces the standard thermal factor, with the magnetic charge affecting the temperature implicitly through the horizon radius rather than via a separate magnetic chemical potential for electrically charged fermions (Stetsko, 2013).

Accretion can probe whether magnetic charge destabilizes the horizon structure. For the stringy magnetically charged black hole, steady spherical phantom-energy accretion gives

$T_H(r_H)=\frac{\Delta_r'(r_H)}{4\pi(r_H^2+a^2)},$0

so phantom energy decreases the mass. The critical-point analysis yields bounds on the mass-to-charge ratio, and the paper concludes that, unlike the Reissner–Nordström case, phantom accretion cannot drive the solution to an extremal or naked state; cosmic censorship remains valid (Sharif et al., 2012).

Extremal magnetic black holes are of special interest because they need not Hawking radiate. In one convention for relic extremal magnetic black holes,

$T_H(r_H)=\frac{\Delta_r'(r_H)}{4\pi(r_H^2+a^2)},$1

with Dirac quantization implying $T_H(r_H)=\frac{\Delta_r'(r_H)}{4\pi(r_H^2+a^2)},$2. Because extremal objects have zero Hawking temperature, much lighter primordial black holes could survive to the present if they are extremal (Diamond et al., 2021).

A substantially richer relic scenario appears when Standard Model physics is included. Magnetically charged black holes can support an electroweak-symmetric corona outside the horizon whenever the near-horizon magnetic field exceeds the electroweak restoration scale, with an upper charge bound

$T_H(r_H)=\frac{\Delta_r'(r_H)}{4\pi(r_H^2+a^2)},$3

In this regime the total mass is approximated by

$T_H(r_H)=\frac{\Delta_r'(r_H)}{4\pi(r_H^2+a^2)},$4

and the viable mass interval quoted in that analysis is

$T_H(r_H)=\frac{\Delta_r'(r_H)}{4\pi(r_H^2+a^2)},$5

Non-extremal states evaporate rapidly through a large number of effectively two-dimensional charged-fermion modes in the corona and become nearly extremal on short timescales, while observational limits include an Andromeda Parker-bound extension,

$T_H(r_H)=\frac{\Delta_r'(r_H)}{4\pi(r_H^2+a^2)},$6

of the dark-matter abundance, and solar neutrino bounds reaching

$T_H(r_H)=\frac{\Delta_r'(r_H)}{4\pi(r_H^2+a^2)},$7

in some mass ranges (Bai et al., 2020).

5. Optical appearance, strong lensing, and EHT-scale observables

Magnetic charge also modifies the optical diagnostics of strong gravity. A rotating magnetically charged black hole surrounded by quintessence is described by

$T_H(r_H)=\frac{\Delta_r'(r_H)}{4\pi(r_H^2+a^2)},$8

and the spherical-photon-orbit impact parameters are

$T_H(r_H)=\frac{\Delta_r'(r_H)}{4\pi(r_H^2+a^2)},$9

The paper shows that increasing magnetic charge $r_H$0 generally reduces the shadow size, while increasing the quintessence strength $r_H$1 enlarges it and slightly enhances distortion; smaller $r_H$2 increases the shadow area (Sun et al., 2022).

For static NLED models, the shadow is controlled by the critical impact parameter

$r_H$3

In the asymptotic, magnetically charged, non-singular model, magnetic charge tends to reduce the weak-field deflection angle relative to Schwarzschild, while a plasma medium increases it. The same work derives shadow and greybody properties and quotes an EHT-based upper bound

$r_H$4

at $r_H$5 confidence for its regularization parameter (Kumaran et al., 2023).

For the regular MCRBH with

$r_H$6

the photon sphere and shadow radius both decrease with $r_H$7, and EHT shadow-size constraints give

$r_H$8

from M87* at $r_H$9, and

$$ds^{2}=\frac{1-\frac{m}{r}}{1-\frac{Q^{2}}{mr}}\,dt^{2} -\left(\frac{1-\frac{m}{r}}{1-\frac{Q^{2}}{mr}}\right)^{-1}dr^{2} -r^{2}d\Omega^{2},$$0

from Sgr A* at $$ds^{2}=\frac{1-\frac{m}{r}}{1-\frac{Q^{2}}{mr}}\,dt^{2} -\left(\frac{1-\frac{m}{r}}{1-\frac{Q^{2}}{mr}}\right)^{-1}dr^{2} -r^{2}d\Omega^{2},$$1 (Zare et al., 2024).

Environmental degeneracies can be severe. In a NED-inspired magnetically charged black hole immersed in a Hernquist dark-matter halo, increasing magnetic charge decreases both the horizon radius and the critical impact parameter, whereas increasing the halo parameters $$ds^{2}=\frac{1-\frac{m}{r}}{1-\frac{Q^{2}}{mr}}\,dt^{2} -\left(\frac{1-\frac{m}{r}}{1-\frac{Q^{2}}{mr}}\right)^{-1}dr^{2} -r^{2}d\Omega^{2},$$2 and $$ds^{2}=\frac{1-\frac{m}{r}}{1-\frac{Q^{2}}{mr}}\,dt^{2} -\left(\frac{1-\frac{m}{r}}{1-\frac{Q^{2}}{mr}}\right)^{-1}dr^{2} -r^{2}d\Omega^{2},$$3 increases them. The paper identifies explicit parameter triples for which $$ds^{2}=\frac{1-\frac{m}{r}}{1-\frac{Q^{2}}{mr}}\,dt^{2} -\left(\frac{1-\frac{m}{r}}{1-\frac{Q^{2}}{mr}}\right)^{-1}dr^{2} -r^{2}d\Omega^{2},$$4, $$ds^{2}=\frac{1-\frac{m}{r}}{1-\frac{Q^{2}}{mr}}\,dt^{2} -\left(\frac{1-\frac{m}{r}}{1-\frac{Q^{2}}{mr}}\right)^{-1}dr^{2} -r^{2}d\Omega^{2},$$5, the strong-deflection angle, and lensing observables all coincide with the Schwarzschild values, showing that “nullification of competing effects” can make a magnetically charged dark-matter-halo black hole observationally indistinguishable from Schwarzschild in strong lensing alone (Jha, 31 Dec 2025).

6. Conceptual boundaries and related non-monopole scenarios

A persistent source of confusion is the use of magnetic language for black holes that are not magnetically charged in the monopole sense. In the “black hole pulsar” scenario, a Kerr black hole in the dipolar magnetic field of a neutron-star companion acquires an electric Wald charge,

$$ds^{2}=\frac{1-\frac{m}{r}}{1-\frac{Q^{2}}{mr}}\,dt^{2} -\left(\frac{1-\frac{m}{r}}{1-\frac{Q^{2}}{mr}}\right)^{-1}dr^{2} -r^{2}d\Omega^{2},$$6

Its own magnetic field is then the dipole of a spinning electric charge, not a magnetic monopole. The analysis explicitly states that the geometry remains effectively Kerr, not Kerr–Newman or dyonic, because $$ds^{2}=\frac{1-\frac{m}{r}}{1-\frac{Q^{2}}{mr}}\,dt^{2} -\left(\frac{1-\frac{m}{r}}{1-\frac{Q^{2}}{mr}}\right)^{-1}dr^{2} -r^{2}d\Omega^{2},$$7 is small, and that the system is “not a magnetically charged black hole in the monopole sense” (Levin et al., 2018).

The same distinction appears in boosted-black-hole charging. A Schwarzschild black hole moving through an asymptotically uniform magnetic field sees an induced electric field at infinity,

$$ds^{2}=\frac{1-\frac{m}{r}}{1-\frac{Q^{2}}{mr}}\,dt^{2} -\left(\frac{1-\frac{m}{r}}{1-\frac{Q^{2}}{mr}}\right)^{-1}dr^{2} -r^{2}d\Omega^{2},$$8

and can accumulate electric charge dynamically. The four-potential includes

$$ds^{2}=\frac{1-\frac{m}{r}}{1-\frac{Q^{2}}{mr}}\,dt^{2} -\left(\frac{1-\frac{m}{r}}{1-\frac{Q^{2}}{mr}}\right)^{-1}dr^{2} -r^{2}d\Omega^{2},$$9

The resulting object is electromagnetically active, but it is not intrinsically magnetically charged; the paper gives no closed-form boosted analogue of the Wald charge and emphasizes that charge buildup is determined by chaotic gravito-electrodynamics rather than monopole hair (Adari et al., 2021).

A related but still distinct case is the magnetized Reissner–Nordström black hole, which is electrically charged and immersed in a strong external magnetic field. There the combined effect of electric charge and magnetic field can shrink the ISCO and mimic Kerr spin up to

$r_{+}=m,\qquad r_{-}=\frac{Q^{2}}{m}.$0

but the black hole still carries electric charge rather than intrinsic magnetic monopole charge (Shaymatov et al., 2021).

The modern MCBH literature therefore divides sharply into two domains. One concerns intrinsic magnetic monopole charge, whether in Einstein–Maxwell, string-inspired, or NLED form. The other concerns electrically charged or neutral black holes embedded in magnetic environments. Both domains are relevant for strong-field phenomenology, but only the first corresponds to a magnetically charged black hole in the literal sense.