Generalised focusing theorem and dynamical horizon entropy in diffeomorphism-invariant theories
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916927593512960 |
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| author | Yan, Zihan |
| author_facet | Yan, Zihan |
| contents | I summarise recent progress on light-ray focusing and horizon thermodynamics in general diffeomorphism-invariant theories of gravity coupled to bosonic matter. In pure gravity and with scalar or vector fields, the null-null gravitational equation of motion on a linearly perturbed Killing horizon generalises the Raychaudhuri equation, defining a generalised expansion that never increases under the null energy condition. This proves a generalised focusing theorem and defines an increasing horizon entropy (Wall entropy). When higher-spin fields are present, the generalised focusing theorem persists subject to a "higher-spin focusing condition", which I propose as a physical consistency constraint on higher-spin theories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_00628 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalised focusing theorem and dynamical horizon entropy in diffeomorphism-invariant theories Yan, Zihan General Relativity and Quantum Cosmology High Energy Physics - Theory I summarise recent progress on light-ray focusing and horizon thermodynamics in general diffeomorphism-invariant theories of gravity coupled to bosonic matter. In pure gravity and with scalar or vector fields, the null-null gravitational equation of motion on a linearly perturbed Killing horizon generalises the Raychaudhuri equation, defining a generalised expansion that never increases under the null energy condition. This proves a generalised focusing theorem and defines an increasing horizon entropy (Wall entropy). When higher-spin fields are present, the generalised focusing theorem persists subject to a "higher-spin focusing condition", which I propose as a physical consistency constraint on higher-spin theories. |
| title | Generalised focusing theorem and dynamical horizon entropy in diffeomorphism-invariant theories |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2509.00628 |