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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2604.27449 |
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| _version_ | 1866909016054038528 |
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| author | Xu, Yingnan Chu, Shuangshuang |
| author_facet | Xu, Yingnan Chu, Shuangshuang |
| contents | We study Carrollian limits of Schwarzschild-AdS black-hole thermodynamics using covariant phase space. Allowing the cosmological constant to vary, we derive the extended Iyer-Wald identity and identify the renormalized bulk term proportional to $δΛ$ with the generator-normalized thermodynamic volume contribution $V_ξ\,δP$. We show that the Carroll limit contracts the full thermodynamic phase space together with the metric. For fixed Newton constant, the Lorentzian generator $\partial_t$ collapses to a zero-norm direction as $c\to0$, yielding a degenerate sector with vanishing Hamiltonian variation, temperature and volume. Introducing $ξ_λ=c^{-α}\partial_t$ and $G=c^γG_C$, we find that the extended first law scales as $c^{1-α-γ}$, so finite phase-space contractions require $α+γ=1$. The endpoint $(α,γ)=(1,0)$, obtained by $τ=ct$, is the ordinary non-degenerate Lorentzian finite-clock normalization. Carrollian finite first laws lie on the segment $α<1$, hence $γ=1-α>0$, and give $T\to0$, $S\to\infty$, with finite $T\,δS$ and $V_ξ\,δP$. We test the scaling principle for fixed-charge and fixed-rotation AdS black holes, and extend it to arbitrary spacetime dimension within the Schwarzschild-AdS family. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27449 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Phase-Space Contractions of Carrollian Black-Hole Thermodynamics Xu, Yingnan Chu, Shuangshuang High Energy Physics - Theory We study Carrollian limits of Schwarzschild-AdS black-hole thermodynamics using covariant phase space. Allowing the cosmological constant to vary, we derive the extended Iyer-Wald identity and identify the renormalized bulk term proportional to $δΛ$ with the generator-normalized thermodynamic volume contribution $V_ξ\,δP$. We show that the Carroll limit contracts the full thermodynamic phase space together with the metric. For fixed Newton constant, the Lorentzian generator $\partial_t$ collapses to a zero-norm direction as $c\to0$, yielding a degenerate sector with vanishing Hamiltonian variation, temperature and volume. Introducing $ξ_λ=c^{-α}\partial_t$ and $G=c^γG_C$, we find that the extended first law scales as $c^{1-α-γ}$, so finite phase-space contractions require $α+γ=1$. The endpoint $(α,γ)=(1,0)$, obtained by $τ=ct$, is the ordinary non-degenerate Lorentzian finite-clock normalization. Carrollian finite first laws lie on the segment $α<1$, hence $γ=1-α>0$, and give $T\to0$, $S\to\infty$, with finite $T\,δS$ and $V_ξ\,δP$. We test the scaling principle for fixed-charge and fixed-rotation AdS black holes, and extend it to arbitrary spacetime dimension within the Schwarzschild-AdS family. |
| title | Phase-Space Contractions of Carrollian Black-Hole Thermodynamics |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2604.27449 |