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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2604.05094 |
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| _version_ | 1866918524479340544 |
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| author | C., Jacobo Hernández |
| author_facet | C., Jacobo Hernández |
| contents | The KMOC (Kosower-Maybee-O'Connell) formalism establishes a bridge between quantum scattering amplitudes and classical observables in gravitational systems. In this work, we show how the weak-field limits of the four classical black hole metrics - Schwarzschild, Kerr, Reissner-Nordstrom, and Kerr-Newman - can be reproduced within this formalism. Starting from three-point amplitudes with exponential spin structure for both gravitational and electromagnetic interactions, we compute four-point scattering amplitudes and extract the momentum impulse via the KMOC formula. Matching these results with geodesic motion in a general metric allows us to reconstruct the metric components to leading order in G, a, and Q^2. For the Kerr-Newman case, we include interference terms between gravitational and electromagnetic interactions, which produce a Q^2 a/r^3 contribution to g_{tϕ} that does not appear in the Kerr or Reissner-Nordstrom weak-field limits separately. Our results are consistent with those of arXiv:1907.00431 [hep-th], where the Kerr-Newman metric is derived from minimal coupling amplitudes using the KMOC formalism arXiv:1908.04342 [hep-th]. All results are verified through their consistency with the well-known full metrics, though we emphasize that the KMOC formalism as applied here reproduces only the weak-field expansions, not the complete non-linear solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05094 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Weak-Field Limits of Black Hole Metrics from the KMOC formalism: Schwarzschild, Kerr, Reissner-Nordström, and Kerr-Newman C., Jacobo Hernández High Energy Physics - Theory General Relativity and Quantum Cosmology The KMOC (Kosower-Maybee-O'Connell) formalism establishes a bridge between quantum scattering amplitudes and classical observables in gravitational systems. In this work, we show how the weak-field limits of the four classical black hole metrics - Schwarzschild, Kerr, Reissner-Nordstrom, and Kerr-Newman - can be reproduced within this formalism. Starting from three-point amplitudes with exponential spin structure for both gravitational and electromagnetic interactions, we compute four-point scattering amplitudes and extract the momentum impulse via the KMOC formula. Matching these results with geodesic motion in a general metric allows us to reconstruct the metric components to leading order in G, a, and Q^2. For the Kerr-Newman case, we include interference terms between gravitational and electromagnetic interactions, which produce a Q^2 a/r^3 contribution to g_{tϕ} that does not appear in the Kerr or Reissner-Nordstrom weak-field limits separately. Our results are consistent with those of arXiv:1907.00431 [hep-th], where the Kerr-Newman metric is derived from minimal coupling amplitudes using the KMOC formalism arXiv:1908.04342 [hep-th]. All results are verified through their consistency with the well-known full metrics, though we emphasize that the KMOC formalism as applied here reproduces only the weak-field expansions, not the complete non-linear solutions. |
| title | Weak-Field Limits of Black Hole Metrics from the KMOC formalism: Schwarzschild, Kerr, Reissner-Nordström, and Kerr-Newman |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2604.05094 |