Ladder Symmetry: The Necessary and Sufficient Condition for Vanishing Love Numbers
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| Format: | Preprint |
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2025
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| _version_ | 1866918339311304704 |
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| author | Sharma, Chanchal Roy, Shuvayu Sarkar, Sudipta |
| author_facet | Sharma, Chanchal Roy, Shuvayu Sarkar, Sudipta |
| contents | Black holes in four-dimensional, asymptotically flat general relativity have vanishing static tidal Love numbers (TLNs), a property tied to a hidden symmetry of the perturbation equations. Within the Konoplya-Rezzolla-Zhidenko (KRZ) parametrization, a subclass of spacetimes was previously shown to admit such Ladder symmetry, which enforces the absence of static scalar TLNs. In this work, we introduce parametric deformations to such Ladder-symmetric spacetimes and analyze the resultant linear tidal response. Using the parametrized formalism for TLNs, we show that any deviation from a Ladder-symmetric background leads to non-zero static scalar TLNs. This establishes Ladder symmetry as a necessary, as well as sufficient condition, for the vanishing of static TLNs in static, spherically symmetric black holes and in rotating black holes of the KRZ class. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_09670 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ladder Symmetry: The Necessary and Sufficient Condition for Vanishing Love Numbers Sharma, Chanchal Roy, Shuvayu Sarkar, Sudipta General Relativity and Quantum Cosmology High Energy Physics - Theory Black holes in four-dimensional, asymptotically flat general relativity have vanishing static tidal Love numbers (TLNs), a property tied to a hidden symmetry of the perturbation equations. Within the Konoplya-Rezzolla-Zhidenko (KRZ) parametrization, a subclass of spacetimes was previously shown to admit such Ladder symmetry, which enforces the absence of static scalar TLNs. In this work, we introduce parametric deformations to such Ladder-symmetric spacetimes and analyze the resultant linear tidal response. Using the parametrized formalism for TLNs, we show that any deviation from a Ladder-symmetric background leads to non-zero static scalar TLNs. This establishes Ladder symmetry as a necessary, as well as sufficient condition, for the vanishing of static TLNs in static, spherically symmetric black holes and in rotating black holes of the KRZ class. |
| title | Ladder Symmetry: The Necessary and Sufficient Condition for Vanishing Love Numbers |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2511.09670 |