[论文解读] Quantum dust cores of rotating black holes

Tommaso Bambagiotti, Roberto Casadio|arXiv (Cornell University)|Jan 4, 2026

Quantum Electrodynamics and Casimir Effect被引用 0

一句话总结

This paper quantises the geodesic motion of dust in rotating (Kerr) black hole interiors to construct quantum rotating dust cores, revealing how angular momentum shapes core size and interior geometry and leading to an integrable singularity without a Cauchy horizon.

ABSTRACT

Black holes are spacetimes that should describe the end state of the gravitational collapse of huge amounts of quantum matter. A quantum description of dust cores for black hole geometries that accounts for the large number of matter constituents can be obtained by quantising the geodesic motion of dust particles and finding the corresponding many-body ground state. We here generalise previous works in spherical symmetry to rotating geometries and show the effect of angular momentum on the size of the core and effective interior geometry.

研究动机与目标

• Motivate a quantum description of black hole interiors via a dust core model.
• Generalise previous spherically symmetric quantum dust core results to rotating (Kerr) geometries.
• Investigate how angular momentum affects core size and the interior Misner-Sharp-Hernandez mass function.
• Identify configurations where the mass function and angular momentum grow linearly with radius, yielding an integrable singularity without a Cauchy horizon.

提出的方法

• Model dust as comoving layers in a generalised Kerr metric with mass function m(r) and specific angular momentum a(r).
• Derive geodesic equations for dust particles and obtain conserved quantities E/μ and j, then enforce j=0 for co-rotating surface layers.
• Quantise the radial motion of each layer via a Schrödinger-like equation for the layer coordinate R_i with effective potentials W_i^{ax} and W_i^{eq}.
• Analyze ground-state solutions (E^2=0) leading to Laguerre-type eigenfunctions and compute mean radii and uncertainties.
• Apply slow-rotation perturbation theory to estimate corrections to the radial potential and core size.
• Propose an ellipsoidal, linearly growing angular-momentum profile A_i ∝ R_i and M_i, yielding a horizon-free interior and quantised exterior Kerr parameter A.]
• research_questions":["How does rotation (Kerr geometry) modify the quantum dust-core description compared to the spherical case?","What is the impact of angular momentum on the core's size and the interior mass function?","Can a quantum rotating dust core avoid a Cauchy horizon and lead to an integrable singularity?","Under what conditions do the layer mass and angular momentum grow linearly with radius, and how does this affect the exterior Kerr horizon?","Is there a consistent quantisation condition that links interior angular momentum to the exterior Kerr parameters?"]
• key_findings":["Rotating dust cores form ellipsoidal layers elongated on the equator; rotation reduces layer radii along the axis and increases them at the equator.","Ground-state solutions yield a mass function M_i that grows approximately linearly with layer size when the angular momentum A_i scales with radius, consistent with an integrable singularity without a Cauchy horizon.","Assuming A_i ∝ R_i leads to a simple linear recursion M_{i+1} ≈ (4/3) M_i and a corresponding linear mass distribution within the core.","A linearly growing A_i implies a quantised exterior Kerr parameter A, linked to differences in axially vs equatorially quantised quantum numbers (N_i^{ax}−N_i^{eq}).","The effective interior metric can be constructed via the Gurses–Gursey algorithm from a spherically symmetric dust core, with Δ(r) confirming the absence of a Cauchy horizon in the slow-rotation regime.","Outer horizon area acquires a quantum correction term dependent on the angular-momentum parameter α, reflecting the underlying layer quantisation.

Figure 1: Core radii vs horizon radii for the whole range of classical Kerr black holes $A^{2}\leq G_{\rm N}^{2}\,M^{2}$ (left panel); right panel shows the region of near extremal rotation magnified.

实验结果

研究问题

• RQ1 How does rotation (Kerr geometry) modify the quantum dust-core description compared to the spherical case?
• RQ2 What is the impact of angular momentum on the core's size and the interior mass function?
• RQ3 Can a quantum rotating dust core avoid a Cauchy horizon and lead to an integrable singularity?
• RQ4 Under what conditions do the layer mass and angular momentum grow linearly with radius, and how does this affect the exterior Kerr horizon?
• RQ5 Is there a consistent quantisation condition that links interior angular momentum to the exterior Kerr parameters?

主要发现

• Rotating dust cores form ellipsoidal layers elongated on the equator; rotation reduces layer radii along the axis and increases them at the equator.
• Ground-state solutions yield a mass function M_i that grows approximately linearly with layer size when the angular momentum A_i scales with radius, consistent with an integrable singularity without a Cauchy horizon.
• Assuming A_i ∝ R_i leads to a simple linear recursion M_{i+1} ≈ (4/3) M_i and a corresponding linear mass distribution within the core.
• A linearly growing A_i implies a quantised exterior Kerr parameter A, linked to differences in axially vs equatorially quantised quantum numbers (N_i^{ax}−N_i^{eq}).
• The effective interior metric can be constructed via the Gurses–Gursey algorithm from a spherically symmetric dust core, with Δ(r) confirming the absence of a Cauchy horizon in the slow-rotation regime.
• Outer horizon area acquires a quantum correction term dependent on the angular-momentum parameter α, reflecting the underlying layer quantisation.

Figure 2: Function $\Delta$ in Eq. ( 2.3 ) for $m_{\rm int}$ (left panel) and $m_{\rm par}$ (right panel) for different values of $\delta=A/G_{\rm N}\,M$ , with $M=150\,m_{\rm p}$ . The dotted lines correspond to the maximum values $\delta_{\rm i}\simeq 0.867$ (left panel) and $\delta_{\rm p}\simeq