Quantum Effects Inside Rotating, Accreting Black Holes

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Abstract

Models of black holes in general relativity have a problem. Rotating spacetimes like the Kerr metric do incredibly well at predicting observed phenomena outside of the event horizon, despite the fact that these models assume that the spacetime is completely empty and stationary, or at the least that any added matter or radiation will not contribute any gravity of its own. However, if this matter or radiation falls below the event horizon into a black hole’s interior, counter-propagating streams will grow in energy and eventually diverge before they even reach the central singularity, at a special surface called the inner horizon. This divergence will trigger an inflationary instability that calls into question the self-consistency of the Kerr metric and the very stability of black holes as astrophysical (and especially as quantum mechanical) objects.

In this thesis, the astrophysically relevant effects of rotation and accretion are examined in detail to understand how they contribute self-consistently to the spacetime geometry of a black hole near its inner horizon. First, a model is developed (which I call the inflationary Kasner metric) that reproduces and generalizes the aforementioned inflationary instability within the framework of general relativity. Then, the effects of a quantum field near an inner horizon are explored. In particular, Hawking radiation emanating from the past horizon will accumulate and eventually diverge in temperature as the inner horizon is approached, and more numerically intensive calculations of the renormalized stress-energy tensor reveal that this diverging radiation plays a substantial role in modifying the black hole’s interior geometry and replacing the inner horizon with a strong, chaotic, spacelike singularity. By analyzing the effects of both classical and quantum fields within black holes, one can thus come to a closer understanding of how astrophysically realistic black holes should appear in the context of semiclassical gravity. 

Year of Publication
2024
Academic Department
Department of Physics
Degree
PhD
Number of Pages
297
Date Published
2024-07
University
University of Colorado Boulder
City
Boulder
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