# Finite element computation of the gravitational radiation emitted by a pointlike object orbiting a nonrotating black hole

## Abstract

The description of extreme-mass-ratio binary systems in the inspiral phase is a challenging problem in gravitational wave physics with significant relevance for the space interferometer LISA. The main difficulty lies in the evaluation of the effects of the small body's gravitational field on itself. To that end, an accurate computation of the perturbations produced by the small body with respect the background geometry of the large object, a massive black hole, is required. In this paper we present a new computational approach based on finite element methods to solve the master equations describing perturbations of nonrotating black holes due to an orbiting pointlike object. The numerical computations are carried out in the time domain by using evolution algorithms for wave-type equations. We show the accuracy of the method by comparing our calculations with previous results in the literature. Finally, we discuss the relevance of this method for achieving accurate descriptions of extreme-mass-ratio binaries.

- Authors:

- Institute for Gravitational Physics and Geometry and Center for Gravitational Wave Physics, Department of Astronomy and Astrophysics, Pennsylvania State University, University Park, Pennsylvania 16802 (United States)
- (United States)

- Publication Date:

- OSTI Identifier:
- 20776766

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 73; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevD.73.044028; (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; ACCURACY; ALGORITHMS; BINARY STARS; BLACK HOLES; DISTURBANCES; EMISSION; FINITE ELEMENT METHOD; GEOMETRY; GRAVITATIONAL FIELDS; GRAVITATIONAL RADIATION; GRAVITATIONAL WAVES; INTERFEROMETERS; INTERFEROMETRY; MASS; SPACE-TIME

### Citation Formats

```
Sopuerta, Carlos F., Laguna, Pablo, and Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802.
```*Finite element computation of the gravitational radiation emitted by a pointlike object orbiting a nonrotating black hole*. United States: N. p., 2006.
Web. doi:10.1103/PhysRevD.73.044028.

```
Sopuerta, Carlos F., Laguna, Pablo, & Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802.
```*Finite element computation of the gravitational radiation emitted by a pointlike object orbiting a nonrotating black hole*. United States. doi:10.1103/PhysRevD.73.044028.

```
Sopuerta, Carlos F., Laguna, Pablo, and Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802. Wed .
"Finite element computation of the gravitational radiation emitted by a pointlike object orbiting a nonrotating black hole". United States.
doi:10.1103/PhysRevD.73.044028.
```

```
@article{osti_20776766,
```

title = {Finite element computation of the gravitational radiation emitted by a pointlike object orbiting a nonrotating black hole},

author = {Sopuerta, Carlos F. and Laguna, Pablo and Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802},

abstractNote = {The description of extreme-mass-ratio binary systems in the inspiral phase is a challenging problem in gravitational wave physics with significant relevance for the space interferometer LISA. The main difficulty lies in the evaluation of the effects of the small body's gravitational field on itself. To that end, an accurate computation of the perturbations produced by the small body with respect the background geometry of the large object, a massive black hole, is required. In this paper we present a new computational approach based on finite element methods to solve the master equations describing perturbations of nonrotating black holes due to an orbiting pointlike object. The numerical computations are carried out in the time domain by using evolution algorithms for wave-type equations. We show the accuracy of the method by comparing our calculations with previous results in the literature. Finally, we discuss the relevance of this method for achieving accurate descriptions of extreme-mass-ratio binaries.},

doi = {10.1103/PhysRevD.73.044028},

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

number = 4,

volume = 73,

place = {United States},

year = {Wed Feb 15 00:00:00 EST 2006},

month = {Wed Feb 15 00:00:00 EST 2006}

}