A very simple minisuperspace describing the Oppenheimer-Snyder collapsing star is found. The semi... more A very simple minisuperspace describing the Oppenheimer-Snyder collapsing star is found. The semiclasical wave function of that model turn out to describe a bound state. For fixed initial radius of the collapsing star, the corrssponding Bohr-Sommerfeld quantization condition implies mass quantization. An extension of this model, and some consequences, are considered.
By analysing the infinite dimensional midisuperspace of spherically symmetric dust universes, and... more By analysing the infinite dimensional midisuperspace of spherically symmetric dust universes, and aply it to collapsing dust stars, one finds that the general quantum state is a bound state. This leads to discrete spectrum. In the case of a Schwarzschild black hole, the discrete spectrum implies Bekenstein area quantization: the area of the horizon is an integer multiple of the Planck area. Knowing the microscopic (quantum) states, we suggest a microscopic interpretation of the thermodynamics of black holes: the degeneracy of the quantum states forming a black hole, gives the Bekenstein- Hawking entropy. All other thermodynamical quantities can be derived by using the standard definitions.
The picture of S-wave scattering from a 4-D extremal dilatonic black hole is examined. Classicall... more The picture of S-wave scattering from a 4-D extremal dilatonic black hole is examined. Classically, a small matter shock wave will form a non-extremal black hole. In the “throat region” the r-t geometry is exactly that of a collapsing 2-D black hole. The 4-D Hawking radiation (in this classical background) gives the 2-D Hawking radiation exactly in the throat region. The 4-D geometry outside the throat region is almost the extremal one, and the deviations can be calculated using a linear approximation. Inclusion of the back-reaction changes this picture: the linear approximation is valid only at the beginning of the evaporating process. We give (explicitly) that linear 4-D solution. The linear approximation breaks down even before an apparent horizon is formed, which suggests that the 4-D semiclassical solution may be quite different from the 2-D one.
A very simple minisuperspace describing the Oppenheimer-Snyder collapsing star is found. The semi... more A very simple minisuperspace describing the Oppenheimer-Snyder collapsing star is found. The semiclasical wave function of that model turn out to describe a bound state. For fixed initial radius of the collapsing star, the corrssponding Bohr-Sommerfeld quantization condition implies mass quantization. An extension of this model, and some consequences, are considered.
By analysing the infinite dimensional midisuperspace of spherically symmetric dust universes, and... more By analysing the infinite dimensional midisuperspace of spherically symmetric dust universes, and aply it to collapsing dust stars, one finds that the general quantum state is a bound state. This leads to discrete spectrum. In the case of a Schwarzschild black hole, the discrete spectrum implies Bekenstein area quantization: the area of the horizon is an integer multiple of the Planck area. Knowing the microscopic (quantum) states, we suggest a microscopic interpretation of the thermodynamics of black holes: the degeneracy of the quantum states forming a black hole, gives the Bekenstein- Hawking entropy. All other thermodynamical quantities can be derived by using the standard definitions.
The picture of S-wave scattering from a 4-D extremal dilatonic black hole is examined. Classicall... more The picture of S-wave scattering from a 4-D extremal dilatonic black hole is examined. Classically, a small matter shock wave will form a non-extremal black hole. In the “throat region” the r-t geometry is exactly that of a collapsing 2-D black hole. The 4-D Hawking radiation (in this classical background) gives the 2-D Hawking radiation exactly in the throat region. The 4-D geometry outside the throat region is almost the extremal one, and the deviations can be calculated using a linear approximation. Inclusion of the back-reaction changes this picture: the linear approximation is valid only at the beginning of the evaporating process. We give (explicitly) that linear 4-D solution. The linear approximation breaks down even before an apparent horizon is formed, which suggests that the 4-D semiclassical solution may be quite different from the 2-D one.
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Papers by Yoav Peleg