Covariant Carrollian Electric and Magnetic Limits of General Relativity
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| Format: | Preprint |
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2025
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| author | Patil, Tanmay Shankaranarayanan, S. |
| author_facet | Patil, Tanmay Shankaranarayanan, S. |
| contents | The Carrollian limit ($c \to 0$) of General Relativity provides the geometric language for describing null hypersurfaces, such as black hole event horizons and null infinity. Motivated by the well-established electric and magnetic limits of Galilean electromagnetism, we perform a systematic analysis of the low-velocity limit of linearized gravity to derive its Carrollian counterparts. Using a 1+3 covariant decomposition, we study the transformation properties of linear tensor perturbations (gravitational waves) on a Friedmann-Lemaitre-Robertson-Walker background under Carrollian boosts. We demonstrate that, analogous to the electromagnetic case, the full set of linearized Einstein's equations is not Carrollian-invariant. Instead, the theory bifurcates into two distinct and consistent frameworks: a Carrollian Electric Limit and a Carrollian Magnetic Limit. In the electric limit, dynamics are frozen, leaving a static theory of tidal forces ($E_{ab}$) constrained by the matter distribution. In contrast, the Magnetic Limit yields a consistent dynamical theory where the magnetic part of the Weyl tensor ($H_{ab}$), which governs gravito-magnetic and radiative effects, remains well-defined and is sourced by the spacetime shear. This framework resolves ambiguities in defining Carrollian gravity and provides a robust theory for gravito-magnetic dynamics in ultra-relativistic regimes. Our results have direct implications for the study of black hole horizons, gravitational memory, and the holographic principle. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_07601 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Covariant Carrollian Electric and Magnetic Limits of General Relativity Patil, Tanmay Shankaranarayanan, S. General Relativity and Quantum Cosmology High Energy Physics - Theory The Carrollian limit ($c \to 0$) of General Relativity provides the geometric language for describing null hypersurfaces, such as black hole event horizons and null infinity. Motivated by the well-established electric and magnetic limits of Galilean electromagnetism, we perform a systematic analysis of the low-velocity limit of linearized gravity to derive its Carrollian counterparts. Using a 1+3 covariant decomposition, we study the transformation properties of linear tensor perturbations (gravitational waves) on a Friedmann-Lemaitre-Robertson-Walker background under Carrollian boosts. We demonstrate that, analogous to the electromagnetic case, the full set of linearized Einstein's equations is not Carrollian-invariant. Instead, the theory bifurcates into two distinct and consistent frameworks: a Carrollian Electric Limit and a Carrollian Magnetic Limit. In the electric limit, dynamics are frozen, leaving a static theory of tidal forces ($E_{ab}$) constrained by the matter distribution. In contrast, the Magnetic Limit yields a consistent dynamical theory where the magnetic part of the Weyl tensor ($H_{ab}$), which governs gravito-magnetic and radiative effects, remains well-defined and is sourced by the spacetime shear. This framework resolves ambiguities in defining Carrollian gravity and provides a robust theory for gravito-magnetic dynamics in ultra-relativistic regimes. Our results have direct implications for the study of black hole horizons, gravitational memory, and the holographic principle. |
| title | Covariant Carrollian Electric and Magnetic Limits of General Relativity |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2509.07601 |