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<p>The intricacy of the gravitational field poses a central challenge for quantum gravity, since a full nonperturbative quantization of the spacetime metric remains analytically intractable. The Kantowski-Sachs minisuperspace model, widely used for the black hole interior, offers a useful simplification but may overly constrain the quantum dynamics near the classical singularity. We therefore propose in this paper an enlarged minisuperspace model that extends the Kantowski-Sachs framework by incorporating an additional metric degree of freedom. This minimal extension enriches the dynamical structure of the model and allows for a more nuanced exploration of the quantum geometry in the black hole interior while maintaining analytical tractability. Applying canonical quantization to this enlarged minisuperspace, we obtain the corresponding Wheeler-DeWitt equation. Remarkably, we find that this model is amenable to <i>exact analytical solution</i>, yielding the wave function of the black hole interior. The resulting wave function <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Psi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Ψ</mi> </math></EquationSource> </InlineEquation> is regular across the entire interior region of the black hole and it approaches zero in the region where the classical singularity would occur. Thus the wave function complies with the <i>DeWitt criterion</i> for singularity resolution, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\Psi \rightarrow 0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Ψ</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>, upon approaching the classical singularity. This limit implies that the probability of the geometry attaining the singular configuration is zero in quantum gravity. Physically, this outcome suggests that the classical singularity is replaced by a quantum region where the geometry remains regular. The exact solvability of the enlarged minisuperspace model thus offers a valuable analytical implementation in providing higher assurance and greater confidence in quantum resolution of the black hole singularity.</p>

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Enlarged minisuperspace quantization and black hole singularity resolution

  • 期刊论文

  • 发表日期：

    2025年11月2日

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  • Harpreet Singh,
  • Malay K. Nandy

摘要

The intricacy of the gravitational field poses a central challenge for quantum gravity, since a full nonperturbative quantization of the spacetime metric remains analytically intractable. The Kantowski-Sachs minisuperspace model, widely used for the black hole interior, offers a useful simplification but may overly constrain the quantum dynamics near the classical singularity. We therefore propose in this paper an enlarged minisuperspace model that extends the Kantowski-Sachs framework by incorporating an additional metric degree of freedom. This minimal extension enriches the dynamical structure of the model and allows for a more nuanced exploration of the quantum geometry in the black hole interior while maintaining analytical tractability. Applying canonical quantization to this enlarged minisuperspace, we obtain the corresponding Wheeler-DeWitt equation. Remarkably, we find that this model is amenable to exact analytical solution, yielding the wave function of the black hole interior. The resulting wave function \(\Psi \) Ψ is regular across the entire interior region of the black hole and it approaches zero in the region where the classical singularity would occur. Thus the wave function complies with the DeWitt criterion for singularity resolution, \(\Psi \rightarrow 0\) Ψ → 0 , upon approaching the classical singularity. This limit implies that the probability of the geometry attaining the singular configuration is zero in quantum gravity. Physically, this outcome suggests that the classical singularity is replaced by a quantum region where the geometry remains regular. The exact solvability of the enlarged minisuperspace model thus offers a valuable analytical implementation in providing higher assurance and greater confidence in quantum resolution of the black hole singularity.