Solutions to the mode equation for a quantized massless scalar field outside a black hole that forms from the collapse of a null shell: Late-time behaviors and computation of the stress-energy tensor
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arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912158922571776 |
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| author | Siahmazgi, Shohreh Gholizadeh |
| author_facet | Siahmazgi, Shohreh Gholizadeh |
| contents | The late-time behaviors of the modes in the Unruh state for various eternal two-dimensional black holes are discussed. The Unruh state is designed to be a state that mimics the late-time behaviors of quantized fields that Hawking predicted for the black holes that form from collapse. Evidence is provided that the late-time behaviors of some of the modes of the quantum fields and the symmetric two-point function are determined by infrared effects. In four dimensions, a spacetime is considered in which a black hole forms from the collapse of a spherically symmetric null shell. A method is developed to compute the semi-classical stress-energy tensor for a massless minimally-coupled scalar field in the $in$ vacuum state outside the event horizon of the black hole. The computation of the stress-energy tensor involves finding the mode solutions of the scalar field and renormalizing the stress-energy tensor. The former has been done by expanding the modes of the scalar field in terms of a complete set of modes for an eternal Schwarzschild black hole. The latter is done by subtracting the stress-energy tensor for the scalar field in the Unruh state. The computation of the mode solutions of the scalar field in the $in$ vacuum state is discussed. The results are shown for three cases. They are the continuity of the modes for the scalar field across the null shell surface, their high-frequency behaviors for a fixed spacetime point, and their late-time behaviors for a fixed frequency and a fixed spatial point. The preliminary results for the contribution to the stress-energy tensor from the part of the scalar field modes that are ingoing inside the null shell are presented and an approximation for the contribution to the stress-energy tensor from the part of the modes that are outgoing inside the null shell is discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_11848 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Solutions to the mode equation for a quantized massless scalar field outside a black hole that forms from the collapse of a null shell: Late-time behaviors and computation of the stress-energy tensor Siahmazgi, Shohreh Gholizadeh General Relativity and Quantum Cosmology The late-time behaviors of the modes in the Unruh state for various eternal two-dimensional black holes are discussed. The Unruh state is designed to be a state that mimics the late-time behaviors of quantized fields that Hawking predicted for the black holes that form from collapse. Evidence is provided that the late-time behaviors of some of the modes of the quantum fields and the symmetric two-point function are determined by infrared effects. In four dimensions, a spacetime is considered in which a black hole forms from the collapse of a spherically symmetric null shell. A method is developed to compute the semi-classical stress-energy tensor for a massless minimally-coupled scalar field in the $in$ vacuum state outside the event horizon of the black hole. The computation of the stress-energy tensor involves finding the mode solutions of the scalar field and renormalizing the stress-energy tensor. The former has been done by expanding the modes of the scalar field in terms of a complete set of modes for an eternal Schwarzschild black hole. The latter is done by subtracting the stress-energy tensor for the scalar field in the Unruh state. The computation of the mode solutions of the scalar field in the $in$ vacuum state is discussed. The results are shown for three cases. They are the continuity of the modes for the scalar field across the null shell surface, their high-frequency behaviors for a fixed spacetime point, and their late-time behaviors for a fixed frequency and a fixed spatial point. The preliminary results for the contribution to the stress-energy tensor from the part of the scalar field modes that are ingoing inside the null shell are presented and an approximation for the contribution to the stress-energy tensor from the part of the modes that are outgoing inside the null shell is discussed. |
| title | Solutions to the mode equation for a quantized massless scalar field outside a black hole that forms from the collapse of a null shell: Late-time behaviors and computation of the stress-energy tensor |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2412.11848 |