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Calculating the gravitational self-force in Schwarzschild spacetime
Leor Barack1, Yasushi Mino, Hiroyuki Nakano
1Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, Am Mühlenberg 1, D-14476 Golm, Germany.
Physical Review Letters
|February 28, 2002
Summary
We present a practical method for calculating the gravitational self-force for particles orbiting black holes. This study provides essential parameters for accurately computing this force in Schwarzschild spacetime.
Area of Science:
- Astrophysics
- General Relativity
- Computational Physics
Background:
- Calculating gravitational self-force is crucial for understanding particle dynamics near black holes.
- Previous methods for calculating gravitational self-force have limitations in practical application.
Purpose of the Study:
- To present a practical method for calculating the gravitational self-force for a pointlike particle orbiting a Schwarzschild black hole.
- To provide the necessary regularization parameters for implementing this method.
Main Methods:
- Implementation of the mode-sum regularization method.
- Calculation of finite contributions to the force from individual multipole modes.
- Application of a regularization procedure to the mode sum.
Main Results:
- A practical method for calculating gravitational self-force is presented.
- Values for all required regularization parameters are provided.
- The method is applicable to any geodesic orbit in Schwarzschild spacetime.
Conclusions:
- The presented method offers a practical approach to computing gravitational self-force.
- The provided regularization parameters enable accurate force calculations for orbiting particles.
- This work facilitates further research in gravitational dynamics around black holes.