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Critical Phenomenon inside Asymptotically Flat Black Holes with Spontaneous Scalarization
Li Li1,2,3, Ze Sun1,2,3, Fu-Guo Yang3,4
1School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS, Hangzhou 310024, China.
Physical Review Letters
|July 10, 2026
Summary
Spontaneously scalarized black holes lack a smooth inner Cauchy horizon, collapsing into a spacelike Kasner singularity. This finding reveals critical phenomena and scaling relations in hairy black hole interiors.
Area of Science:
- General Relativity
- Black Hole Physics
- Theoretical Cosmology
Background:
- Einstein-Maxwell-scalar theory describes black holes with scalar fields.
- Spontaneous scalarization can lead to 'hairy' black holes, deviating from standard solutions.
- The interior dynamics and singularity structure of these black holes are not fully understood.
Purpose of the Study:
- Investigate the nonlinear interior dynamics of spontaneously scalarized black holes.
- Explore critical phenomena and singularity formation in these black holes.
- Analyze the role of scalar hair in black hole interior evolution.
Main Methods:
- Numerical simulations of black hole evolution in Einstein-Maxwell-scalar theory.
- Analysis of the inner Cauchy horizon and singularity structure.
- Examination of critical phenomena near bifurcation points.
Main Results:
- Scalarized black holes, for many couplings, lack a smooth inner Cauchy horizon.
- These black holes evolve into a spacelike Kasner singularity.
- The Einstein-Rosen bridge collapses rapidly due to scalar hair.
- A scaling relation between the Kasner exponent and charge-to-mass ratio was found near critical points.
Conclusions:
- Scalar hair fundamentally alters black hole interior dynamics, preventing smooth horizons.
- The formation of Kasner singularities is a key feature of these hairy black holes.
- The discovered scaling relation offers insights into the simplicity of black hole interiors.
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