The Routh of the Attractor Mechanism
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866912939075698688 |
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| author | Chattopadhyay, Arghya Marrani, Alessio Roychowdhury, Sourav |
| author_facet | Chattopadhyay, Arghya Marrani, Alessio Roychowdhury, Sourav |
| contents | We investigate and clarify various aspects of the effective dynamics of Maxwell-Einstein-scalar theories in the background of static, spherically symmetric and asymptotically flat extremal black holes in four space-time dimensions. This rigorously places the one-dimensional effective radial dynamics governed by the Attractor Mechanism, through the critical points of the Ferrara-Gibbons-Kallosh effective black hole potential $V_{BH}$, into the Routhian formalism, a framework which is intermediate between the Lagrange and Hamilton ones, based on a partial Legendre transform, and especially relevant in presence of cyclic variables. We elucidate and analyze the interplay of a trio of effective functionals: the aforementioned $V_{BH}$, Sen's entropy functional $\mathcal{E}$, and the relevant effective Routhian functional $\mathcal{R}$. Through their critical values at the event horizon, such functionals determine the Bekenstein-Hawking and the Wald entropy of the extremal black hole. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_02559 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Routh of the Attractor Mechanism Chattopadhyay, Arghya Marrani, Alessio Roychowdhury, Sourav High Energy Physics - Theory General Relativity and Quantum Cosmology We investigate and clarify various aspects of the effective dynamics of Maxwell-Einstein-scalar theories in the background of static, spherically symmetric and asymptotically flat extremal black holes in four space-time dimensions. This rigorously places the one-dimensional effective radial dynamics governed by the Attractor Mechanism, through the critical points of the Ferrara-Gibbons-Kallosh effective black hole potential $V_{BH}$, into the Routhian formalism, a framework which is intermediate between the Lagrange and Hamilton ones, based on a partial Legendre transform, and especially relevant in presence of cyclic variables. We elucidate and analyze the interplay of a trio of effective functionals: the aforementioned $V_{BH}$, Sen's entropy functional $\mathcal{E}$, and the relevant effective Routhian functional $\mathcal{R}$. Through their critical values at the event horizon, such functionals determine the Bekenstein-Hawking and the Wald entropy of the extremal black hole. |
| title | The Routh of the Attractor Mechanism |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2603.02559 |