2025/01/22 by Abhinove Nagarajan Seenivasan, Seenivasan, Abhinove N., Sam R. Dolan +1
Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.2501.13176
openalex publication_date 2025/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
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.