Black hole dark monopole system

This paper investigates a system of electric charges from visible and dark matter sectors near magnetic poles, revealing that such stationary charges possess intrinsic angular momentum and, when placed outside a magnetically charged black hole in dark photon theory, cause the spacetime to appear as a stationary axisymmetric black hole at large distances.

The Gist

The Big Picture: A Cosmic Dance of Invisible Partners

Imagine the universe has two different "rooms." One room is the Visible Sector, where we live, containing normal light, electricity, and magnets. The other room is the Dark Sector, filled with "dark matter" and invisible forces we can't see directly.

Usually, these two rooms are separated by a thick, soundproof wall. However, this paper explores a tiny, secret "leak" in that wall called kinetic mixing. It's like a very thin, invisible thread connecting the two rooms. Through this thread, things in the dark room can slightly influence things in our visible room, and vice versa.

The author investigates what happens when you bring together three specific ingredients near a Black Hole:

1. A Magnetic Monopole (a magnet with only a North pole, no South pole).
2. An Electric Charge (like a static shock).
3. The Dark Sector connection (the invisible thread).

The Main Discovery: The "Ghost" Spin

The most surprising finding in the paper is about angular momentum (spin).

The Analogy of the Ice Skater:
Imagine an ice skater standing perfectly still on the ice. They are holding a heavy, invisible backpack. If they suddenly put the backpack on, they might start spinning.

In this paper, the author looks at a black hole that is sitting perfectly still (not spinning). He then places a stationary electric charge near a magnetic monopole. In normal physics, if nothing is moving, nothing should spin.

However, the paper claims that even though the charge and the magnet are sitting still, the space around them creates a "hidden spin." It's as if the electric charge and the magnetic pole are holding hands across a distance, creating a swirling vortex of invisible energy between them. This energy has its own "spin," even though the objects themselves aren't moving.

The "Dark" Twist

Now, let's add the Dark Sector (the dark matter room).

The paper suggests that because of the "leak" (kinetic mixing) between the visible and dark worlds, the black hole doesn't just see the normal magnetic pole; it sees a mixture of the visible pole and a dark pole.

The Metaphor of the Blended Smoothie:
Think of the black hole's environment as a blender.

• Normal Physics: You put in a visible electric charge and a visible magnet. The blender makes a specific kind of "spin smoothie."
• Dark Photon Theory: You put in the same ingredients, but you also add a splash of "dark matter juice" through the invisible thread.

The result? The "spin smoothie" changes flavor. The black hole ends up spinning slightly faster or differently than it would have if the dark matter didn't exist. The paper calculates exactly how much extra "spin" is added by this dark connection.

The "Hair" on the Black Hole

There is a famous rule in physics called the "No-Hair Theorem." It says that once a black hole swallows something, it forgets all the details about what it ate. It only remembers three things: its mass, its electric charge, and its spin.

The Paper's Claim:
The author argues that if you slowly bring an electric charge toward a magnetic black hole, the "exotic" details of that charge (its specific location, its weird quantum properties) act like "hair" growing on the black hole. But as the charge gets closer and eventually falls in, that "hair" disappears.

Instead of the charge staying outside as a weird, stationary object, the "spin" it created gets transferred entirely into the black hole itself. The black hole absorbs the charge, and suddenly, the black hole starts spinning.

The Analogy:
Imagine a calm, round pond (the black hole). You drop a spinning top into the water. At first, the top spins on its own. But as it sinks and merges with the water, the water itself starts to swirl. The "spin" of the top is no longer a separate object; it has become the spin of the pond.

Why This Matters (According to the Paper)

The paper suggests that this process could explain why some black holes are spinning. Maybe, in the history of the universe, many "dark magnetic monopoles" fell into black holes. We can't see the monopoles anymore because they are inside the black hole, but we can see the spin they left behind.

The author also mentions that if we could measure the spin of a black hole with extreme precision, we might find a tiny "extra" spin that doesn't match our normal laws of physics. This extra spin would be the fingerprint of the dark sector, proving that dark matter exists and interacts with our world through this invisible thread.

Summary in One Sentence

This paper proposes that when electric charges and magnetic poles interact near a black hole, they create a hidden spin, and if "dark matter" is involved, it tweaks that spin in a way that could eventually be detected as a black hole spinning faster than expected.

Technical Summary

Technical Summary: Black Hole Dark Monopole System

Problem Statement
The paper investigates the interaction between electrical charges from both the visible (Standard Model) and hidden (dark) sectors and magnetically charged black holes within the framework of dark photon theory. Specifically, it addresses how the presence of kinetic mixing between the visible Maxwell field and the dark photon field modifies the angular momentum properties of a system comprising static electric charges and magnetic monopoles. The study focuses on whether such a system, initially static, can induce a rotation in a magnetically charged black hole, effectively "spinning it up," and how this process alters the observable properties of the black hole compared to standard Maxwell theory.

Methodology
The author employs a theoretical framework based on Einstein-Maxwell-dark photon gravity. The methodology proceeds through several distinct steps:

1. Field Redefinition: To handle the kinetic mixing term ($\alpha F_{\mu\nu}B^{\mu\nu}$) in the action, the author performs a linear transformation of the gauge fields ($A_\mu$ and $B_\mu$) into new fields ($\tilde{A}_\mu$ and $\tilde{B}_\mu$). This transformation diagonalizes the kinetic terms, effectively removing the mixing parameter $\alpha$ from the equations of motion but redefining the coupling constants for the electric charges ($e$ and $e_d$) and magnetic monopoles ($g_E$ and $g_B$).
2. Angular Momentum Calculation: The paper calculates the total angular momentum ($J_z$) stored in the electromagnetic fields of the visible and dark sectors. This is done by integrating the Poynting vector-like terms over a spatial volume bounded by spheres, utilizing the definitions of the transformed electric and magnetic fields.
3. Quantization Conditions: The derived angular momentum is used to establish generalized Dirac quantization conditions for the dark sector, relating the charges and monopole strengths.
4. Black Hole Dynamics: The study considers a static, spherically symmetric, magnetically charged black hole solution in dark photon theory. It then analyzes the system when electric charges are placed at rest near this black hole. By applying the uniqueness theorem for stationary axisymmetric black holes in this theory (previously established by the author), the paper argues that as charges approach the event horizon, the "hair" (exotic field configurations) fades, and the system must settle into a stationary, rotating (Kerr-Newman-like) black hole solution.
5. Observational Proxies: The paper explores potential observational signatures, including Aharonov-Bohm (AB) phase shifts for charges circling monopoles and flux changes in SQUID devices, as well as modifications to the black hole's rotation parameter.

Key Contributions and Results

• Generalized Angular Momentum: The study demonstrates that a system of static electric charges (visible and dark) and magnetic monopoles (visible and dark) possesses a non-zero angular momentum, even when the charges are at rest. The total angular momentum is given by $J_z = \tilde{e}\tilde{g}_E + \tilde{e}_d\tilde{g}_B$, where the tilded variables represent the redefined charges and monopole strengths incorporating the kinetic mixing parameter $\alpha$.
• Generalized Dirac Quantization: The paper derives a modified quantization condition: $\frac{2}{\hbar}(\tilde{e}\tilde{g}_E + \tilde{e}_d\tilde{g}_B) \in \mathbb{Z}$. In the limit where dark sector contributions vanish ($\alpha=0, e_d=0, g_B=0$), this reduces to the standard Dirac quantization condition.
• Black Hole Spin-Up Mechanism: A central result is the conclusion that a static, magnetically charged black hole can acquire rotation when electric charges from both sectors are brought near its event horizon. As the charges approach the horizon, the angular momentum stored in the external fields is transferred to the black hole. Upon crossing the horizon, the black hole transitions from a static, spherically symmetric state to a stationary, axisymmetric (rotating) state.
• Anomalous Rotation Parameter: The paper calculates the specific angular momentum per unit mass ($a$) of the resulting black hole. It finds that the rotation parameter is modified by the kinetic mixing. Specifically, if $g_E = g_B$, the rotation parameter is given by $-ma = e g_E (1 + \alpha/2)$. This implies that the black hole rotates slightly faster than it would in a pure Maxwell theory scenario, with the difference proportional to the kinetic mixing parameter $\alpha$.
• Observational Consequences:
  • Aharonov-Bohm Effect: The phase shift in an AB-like experiment involving charges circling monopoles is modified by the dark sector contributions.
  • SQUID Detection: The passage of a dark monopole through a SQUID junction could induce a change in magnetic flux proportional to $(1 + \alpha/4)$, assuming specific charge ratios.
  • Black Hole Signatures: The existence of dark monopoles could be inferred by detecting black holes with anomalous rotation parameters that exceed predictions from standard Maxwell theory.

Significance and Claims
The paper claims that the interaction between visible and dark sector charges and monopoles in the vicinity of a black hole provides a mechanism for "spinning up" static black holes. This process is governed by the conservation of angular momentum and the uniqueness theorems of stationary axisymmetric black holes in dark photon gravity.

The author posits that the lack of experimental detection of dark monopoles might be explained by this mechanism: such exotic objects may have been "devoured" by black holes in the history of the universe, transferring their angular momentum to the black holes and thereby erasing their own "hair" (exotic field configurations) from the exterior spacetime. Consequently, the presence of dark monopoles could be indirectly detected through the observation of black holes with rotation parameters that deviate from standard theoretical expectations, or through subtle modifications in quantum interference experiments (AB effect) and magnetic flux measurements (SQUIDs). The paper emphasizes that while the kinetic mixing parameter $\alpha$ is small, making these effects subtle, they represent a distinct theoretical imprint of the dark sector on black hole physics.