Cuspy black hole shadows correspond to swallowtail thermodynamic free energy, with boundary self-intersections marking geometric phase transitions whose critical exponents fall in the mean-field class.
Intrinsic curvature and topology of shadows in Kerr spacetime
2 Pith papers cite this work, alongside 76 external citations. Polarity classification is still indexing.
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abstract
From the viewpoint of differential geometry and topology, we investigate the characterization of the shadows in a Kerr spacetime. Two new quantities, the length of the shadow boundary and the local curvature radius are introduced. Each shadow can be uniquely determined by these two quantities. For the black hole case, the result shows that we can constrain the black hole spin and the angular coordinate of the observer only by measuring the maximum and minimum of the curvature radius. While for the naked singularity case, we adopt the length parameter and the maximum of the curvature radius. This technique is completely independent of the coordinate system and the location of the shadow, and is expected to uniquely determine the parameters of the spacetime. Moreover, we propose a topological covariant quantity to measure and distinguish different topological structures of the shadows.
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Extends intrinsic curvature criteria for massive particle surfaces to stationary spacetimes and demonstrates application to black hole shadows in Kerr-family and Einstein-Maxwell-dilaton solutions.
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Gravity/thermodynamics correspondence via black hole shadows
Cuspy black hole shadows correspond to swallowtail thermodynamic free energy, with boundary self-intersections marking geometric phase transitions whose critical exponents fall in the mean-field class.
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Massive particle surfaces and black hole shadows from intrinsic curvature
Extends intrinsic curvature criteria for massive particle surfaces to stationary spacetimes and demonstrates application to black hole shadows in Kerr-family and Einstein-Maxwell-dilaton solutions.