Asymptotic Generation of Kerr Geometry from Schwarzschild via BMS Supertranslations
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| Format: | Preprint |
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2025
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| author | Ghosh, Nihar Ranjan Nandy, Malay K. |
| author_facet | Ghosh, Nihar Ranjan Nandy, Malay K. |
| contents | The Bondi-van der Burg-Metzner-Sachs (BMS) group, as the asymptotic symmetry group of asymptotically flat spacetimes, plays a central role in connecting infrared structures of gravity with soft theorems and gravitational memory. In this work, we investigate the extent to which BMS supertranslations can relate physically distinct black hole geometries. Focusing on the Schwarzschild and Kerr solutions, we show that the asymptotic structure of the Kerr spacetime can be generated from the Schwarzschild geometry via two successive supertranslations. These transformations yield a Kerr-like geometry at null infinity and reveal two distinct classes of supertranslation functions. The first, composed of $l=1$ spherical harmonics, corresponds to center-of-mass displacements and encodes the translational sector of the BMS group. The second, characterized by an infinite series of even-parity Legendre polynomials ($l \geq 2$), captures the intrinsic mass multipole structure of the Kerr spacetime. Our result illustrates how BMS supertranslations can act as symmetry transformations linking asymptotically flat black hole geometries, and that they encode physically meaningful soft hair consistent with the multipole structure of rotating black holes. This work supports a unified description of soft degrees of freedom in black hole spacetimes and underscores the role of infinite-dimensional asymptotic symmetries in gravitational physics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_01203 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotic Generation of Kerr Geometry from Schwarzschild via BMS Supertranslations Ghosh, Nihar Ranjan Nandy, Malay K. General Relativity and Quantum Cosmology The Bondi-van der Burg-Metzner-Sachs (BMS) group, as the asymptotic symmetry group of asymptotically flat spacetimes, plays a central role in connecting infrared structures of gravity with soft theorems and gravitational memory. In this work, we investigate the extent to which BMS supertranslations can relate physically distinct black hole geometries. Focusing on the Schwarzschild and Kerr solutions, we show that the asymptotic structure of the Kerr spacetime can be generated from the Schwarzschild geometry via two successive supertranslations. These transformations yield a Kerr-like geometry at null infinity and reveal two distinct classes of supertranslation functions. The first, composed of $l=1$ spherical harmonics, corresponds to center-of-mass displacements and encodes the translational sector of the BMS group. The second, characterized by an infinite series of even-parity Legendre polynomials ($l \geq 2$), captures the intrinsic mass multipole structure of the Kerr spacetime. Our result illustrates how BMS supertranslations can act as symmetry transformations linking asymptotically flat black hole geometries, and that they encode physically meaningful soft hair consistent with the multipole structure of rotating black holes. This work supports a unified description of soft degrees of freedom in black hole spacetimes and underscores the role of infinite-dimensional asymptotic symmetries in gravitational physics. |
| title | Asymptotic Generation of Kerr Geometry from Schwarzschild via BMS Supertranslations |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2509.01203 |