Generic effective sources for first-order in mass-ratio gravitational self-force calculations in Schwarzschild spacetime

2025/05/26 by Zhang, Chao, Cai, Rong-gen, Fu, Guoyang +3 · 1 citation
#FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)

paper · doi:10.48550/arxiv.2505.19732

Abstract

The numerical calculation of gravitational self-force in extreme mass ratio inspiral systems is fundamentally challenging due to the singular nature of point-particle sources. To overcome these difficulties, the effective source method offers an innovative alternative by replacing traditional regularization techniques with a reformulation of the problem. In this paper, we present the first fully analytic framework for constructing effective sources to compute the gravitational self-force for generic orbits in Schwarzschild spacetime. By reformulating the singular field through angular modulation in terms of a tetrad decomposition, the effective source can be constructed with the linear combination of scalar modes. The derived effective source is continuous across the particle's worldline, enabling efficient numerical implementation in 1+1 dimensions.

Citations

• Toward Second-Order Self-Force for Eccentric Extreme-Mass Ratio Inspirals in Schwarzschild Spacetime
• Gravitational self-force with hyperboloidal slicing and spectral methods
• Sourced metric perturbations of Kerr spacetime in Lorenz gauge
• Parameterized Non-circular Deviation from the Kerr Paradigm and Its Observational Signatures: Extreme Mass Ratio Inspirals and Lense-Thirring Effect
• Second-order perturbations of the Schwarzschild spacetime: practical, covariant and gauge-invariant formalisms
• Detecting vector charge with extreme mass ratio inspirals onto Kerr black holes
• TianQin: a space-borne gravitational wave detector
• 3+1 Formalism and Bases of Numerical Relativity
• The motion of point particles in curved spacetime
• LISA - an ESA cornerstone mission for a gravitational wave observatory

Cited by

• Quasinormal modes of scalar, electromagnetic, and gravitational perturbations in slowly rotating Kalb-Ramond black holes
• Toward Second-Order Self-Force for Eccentric Extreme-Mass Ratio Inspirals in Schwarzschild Spacetime

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