# Geometrically motivated hyperbolic coordinate conditions for numerical relativity: Analysis, issues and implementations

## Abstract

We study the implications of adopting hyperbolic-driver coordinate conditions motivated by geometrical considerations. In particular, conditions that minimize the rate of change of the metric variables. We analyze the properties of the resulting system of equations and their effect when implementing excision techniques. We find that commonly used coordinate conditions lead to a characteristic structure at the excision surface where some modes are not of outflow type with respect to any excision boundary chosen inside the horizon. Thus, boundary conditions are required for these modes. Unfortunately, the specification of these conditions is a delicate issue as the outflow modes involve both gauge and main variables. As an alternative to these driver equations, we examine conditions derived from extremizing a scalar constructed from Killing's equation and present specific numerical examples.

- Authors:

- Departament de Fisica, Universitat de les Illes Balears, Palma de Mallorca (Spain)
- Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803-4001 (United States)

- Publication Date:

- OSTI Identifier:
- 20711562

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 72; Journal Issue: 10; Other Information: DOI: 10.1103/PhysRevD.72.104009; (c) 2005 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; BOUNDARY CONDITIONS; COORDINATES; COSMOLOGY; GENERAL RELATIVITY THEORY; GEOMETRY; SCALARS

### Citation Formats

```
Bona, Carles, Lehner, Luis, and Palenzuela-Luque, Carlos.
```*Geometrically motivated hyperbolic coordinate conditions for numerical relativity: Analysis, issues and implementations*. United States: N. p., 2005.
Web. doi:10.1103/PhysRevD.72.104009.

```
Bona, Carles, Lehner, Luis, & Palenzuela-Luque, Carlos.
```*Geometrically motivated hyperbolic coordinate conditions for numerical relativity: Analysis, issues and implementations*. United States. doi:10.1103/PhysRevD.72.104009.

```
Bona, Carles, Lehner, Luis, and Palenzuela-Luque, Carlos. Tue .
"Geometrically motivated hyperbolic coordinate conditions for numerical relativity: Analysis, issues and implementations". United States.
doi:10.1103/PhysRevD.72.104009.
```

```
@article{osti_20711562,
```

title = {Geometrically motivated hyperbolic coordinate conditions for numerical relativity: Analysis, issues and implementations},

author = {Bona, Carles and Lehner, Luis and Palenzuela-Luque, Carlos},

abstractNote = {We study the implications of adopting hyperbolic-driver coordinate conditions motivated by geometrical considerations. In particular, conditions that minimize the rate of change of the metric variables. We analyze the properties of the resulting system of equations and their effect when implementing excision techniques. We find that commonly used coordinate conditions lead to a characteristic structure at the excision surface where some modes are not of outflow type with respect to any excision boundary chosen inside the horizon. Thus, boundary conditions are required for these modes. Unfortunately, the specification of these conditions is a delicate issue as the outflow modes involve both gauge and main variables. As an alternative to these driver equations, we examine conditions derived from extremizing a scalar constructed from Killing's equation and present specific numerical examples.},

doi = {10.1103/PhysRevD.72.104009},

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

number = 10,

volume = 72,

place = {United States},

year = {Tue Nov 15 00:00:00 EST 2005},

month = {Tue Nov 15 00:00:00 EST 2005}

}