Second-order gravitational self-force

Abstract

We derive an expression for the second-order gravitational self-force that acts on a self-gravitating compact-object moving in a curved background spacetime. First we develop a new method of derivation and apply it to the derivation of the first-order gravitational self-force. Here we find that our result conforms with the previously derived expression. Next we generalize our method and derive a new expression for the second-order gravitational self-force. This study also has a practical motivation: The data analysis for the planned gravitational wave detector LISA requires construction of waveforms templates for the expected gravitational waves. Calculation of the two leading orders of the gravitational self-force will enable one to construct highly accurate waveform templates, which are needed for the data analysis of gravitational-waves that are emitted from extreme mass-ratio binaries.

35 pages

References in corpus (12)

• LISA Capture Sources: Approximate Waveforms, Signal-to-Noise Ratios, and Parameter Estimation Accuracy
• Gravitational Radiation Reaction to a Particle Motion
• An axiomatic approach to electromagnetic and gravitational radiation reaction of particles in curved spacetime
• The motion of point particles in curved spacetime
• Self-force via a Green's function decomposition
• Gravitational self force and gauge transformations
• Construction of the second-order gravitational perturbations produced by a compact object
• Self-forces on extended bodies in electrodynamics
• Quasi-local contribution to the gravitational self-force
• Universal Self Force from an Extended-Object Approach
• Calculation of the Self Force using the Extended-Object Approach
• Regularization of the second-order gravitational perturbations produced by a compact object

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