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| Main Authors: | , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2604.13975 |
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| _version_ | 1866913035438784512 |
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| author | Becattini, F. Palli, F. |
| author_facet | Becattini, F. Palli, F. |
| contents | The mean value of the stress-energy tensor of a given quantum field theory at global thermodynamic equilibrium in a curved space-time can be expressed in terms of the derivatives of the Killing four-temperature field and the derivatives of the metric tensor. Its asymptotic expansion about zero includes an analytic part made of integer powers of these derivatives - corresponding to the so-called gradient expansion - as well as non-perturbative corrections. By using available exact solutions for the free real massless scalar field, we show that in the case of Minkowski, de Sitter, anti-de Sitter, and closed Einstein universe, the analytic part - obtained through the procedure of analytic distillation - has a finite number of terms and it is the same once expressed in a covariant form. On the other hand, non-universal terms are non-analytic in these derivatives and correspond to boundary conditions or to specific global properties of the space-time. We argue that the universality of the analytic part extends to any quantum field theory on a curved background. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_13975 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Universal analytic dependence of the stress-energy tensor at thermodynamic equilibrium in curved space-time Becattini, F. Palli, F. High Energy Physics - Theory General Relativity and Quantum Cosmology The mean value of the stress-energy tensor of a given quantum field theory at global thermodynamic equilibrium in a curved space-time can be expressed in terms of the derivatives of the Killing four-temperature field and the derivatives of the metric tensor. Its asymptotic expansion about zero includes an analytic part made of integer powers of these derivatives - corresponding to the so-called gradient expansion - as well as non-perturbative corrections. By using available exact solutions for the free real massless scalar field, we show that in the case of Minkowski, de Sitter, anti-de Sitter, and closed Einstein universe, the analytic part - obtained through the procedure of analytic distillation - has a finite number of terms and it is the same once expressed in a covariant form. On the other hand, non-universal terms are non-analytic in these derivatives and correspond to boundary conditions or to specific global properties of the space-time. We argue that the universality of the analytic part extends to any quantum field theory on a curved background. |
| title | Universal analytic dependence of the stress-energy tensor at thermodynamic equilibrium in curved space-time |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2604.13975 |