# 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 waveform 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.

- Authors:

- Department of Physics, University of Guelph, Guelph, Ontario N1G 2W1 (Canada)

- Publication Date:

- OSTI Identifier:
- 20871410

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 74; Journal Issue: 8; Other Information: DOI: 10.1103/PhysRevD.74.084018; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; COSMOLOGY; DATA ANALYSIS; EMISSION; GRAVITATIONAL WAVE DETECTORS; GRAVITATIONAL WAVES; MASS; SPACE-TIME; WAVE FORMS

### Citation Formats

```
Rosenthal, Eran.
```*Second-order gravitational self-force*. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVD.74.084018.

```
Rosenthal, Eran.
```*Second-order gravitational self-force*. United States. doi:10.1103/PHYSREVD.74.084018.

```
Rosenthal, Eran. Sun .
"Second-order gravitational self-force". United States.
doi:10.1103/PHYSREVD.74.084018.
```

```
@article{osti_20871410,
```

title = {Second-order gravitational self-force},

author = {Rosenthal, Eran},

abstractNote = {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 waveform 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.},

doi = {10.1103/PHYSREVD.74.084018},

journal = {Physical Review. D, Particles Fields},

number = 8,

volume = 74,

place = {United States},

year = {Sun Oct 15 00:00:00 EDT 2006},

month = {Sun Oct 15 00:00:00 EDT 2006}

}