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| Main Authors: | , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.13176 |
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| _version_ | 1866909912555061248 |
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| author | Seenivasan, Abhinove N. Dolan, Sam R. |
| author_facet | Seenivasan, Abhinove N. Dolan, Sam R. |
| contents | We consider the self-force acting on a pointlike (electromagnetic or conformal-scalar) charge held fixed on a spacetime with a spherically-symmetric mass distribution of constant density (the Schwarzschild star). The Schwarzschild interior is shown to be conformal to a three-sphere geometry; we use this conformal symmetry to obtain closed-form expressions for mode solutions. We calculate the self-force with two complementary regularization methods, direct and difference regularization, showing agreement. For the first time, we show that difference regularization can be applied in the non-vacuum interior region, due to the vanishing of certain regularized mode sums. The new results for the self-force come in three forms: series expansions for the self-force near the centre of the star and in the far field; a new approximation that describes the divergence in the self-force near the star's boundary; and numerical data presented in a selection of plots. We conclude with a discussion of the logarithmic divergence in the self-force in the approach to the star's surface, and the effect of boundaries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_13176 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Self-force and the Schwarzschild star Seenivasan, Abhinove N. Dolan, Sam R. General Relativity and Quantum Cosmology We consider the self-force acting on a pointlike (electromagnetic or conformal-scalar) charge held fixed on a spacetime with a spherically-symmetric mass distribution of constant density (the Schwarzschild star). The Schwarzschild interior is shown to be conformal to a three-sphere geometry; we use this conformal symmetry to obtain closed-form expressions for mode solutions. We calculate the self-force with two complementary regularization methods, direct and difference regularization, showing agreement. For the first time, we show that difference regularization can be applied in the non-vacuum interior region, due to the vanishing of certain regularized mode sums. The new results for the self-force come in three forms: series expansions for the self-force near the centre of the star and in the far field; a new approximation that describes the divergence in the self-force near the star's boundary; and numerical data presented in a selection of plots. We conclude with a discussion of the logarithmic divergence in the self-force in the approach to the star's surface, and the effect of boundaries. |
| title | Self-force and the Schwarzschild star |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2501.13176 |