# Extreme throat initial data set and horizon area-angular momentum inequality for axisymmetric black holes

## Abstract

We present a formula that relates the variations of the area of extreme throat initial data with the variation of an appropriate defined mass functional. From this expression we deduce that the first variation, with fixed angular momentum, of the area is zero and the second variation is positive definite evaluated at the extreme Kerr throat initial data. This indicates that the area of the extreme Kerr throat initial data is a minimum among this class of data. And hence the area of generic throat initial data is bounded from below by the angular momentum. Also, this result strongly suggests that the inequality between area and angular momentum holds for generic asymptotically flat axially symmetric black holes. As an application, we prove this inequality in the nontrivial family of spinning Bowen-York initial data.

- Authors:

- Facultad de Matematica, Astronomia y Fisica, FaMAF, Universidad Nacional de Cordoba, Instituto de Fisica Enrique Gaviola, IFEG, CONICET, Ciudad Universitaria (5000) Cordoba (Argentina)
- (Albert Einstein Institute) Am Muehlenberg 1 D-14476 Potsdam (Germany)

- Publication Date:

- OSTI Identifier:
- 21509924

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 82; Journal Issue: 10; Other Information: DOI: 10.1103/PhysRevD.82.104010; (c) 2010 American Institute of Physics

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ANGULAR MOMENTUM; AXIAL SYMMETRY; BLACK HOLES; KERR FIELD; MASS; GRAVITATIONAL FIELDS; SYMMETRY

### Citation Formats

```
Dain, Sergio, and Max Planck Institute for Gravitational Physics.
```*Extreme throat initial data set and horizon area-angular momentum inequality for axisymmetric black holes*. United States: N. p., 2010.
Web. doi:10.1103/PHYSREVD.82.104010.

```
Dain, Sergio, & Max Planck Institute for Gravitational Physics.
```*Extreme throat initial data set and horizon area-angular momentum inequality for axisymmetric black holes*. United States. doi:10.1103/PHYSREVD.82.104010.

```
Dain, Sergio, and Max Planck Institute for Gravitational Physics. Mon .
"Extreme throat initial data set and horizon area-angular momentum inequality for axisymmetric black holes". United States. doi:10.1103/PHYSREVD.82.104010.
```

```
@article{osti_21509924,
```

title = {Extreme throat initial data set and horizon area-angular momentum inequality for axisymmetric black holes},

author = {Dain, Sergio and Max Planck Institute for Gravitational Physics},

abstractNote = {We present a formula that relates the variations of the area of extreme throat initial data with the variation of an appropriate defined mass functional. From this expression we deduce that the first variation, with fixed angular momentum, of the area is zero and the second variation is positive definite evaluated at the extreme Kerr throat initial data. This indicates that the area of the extreme Kerr throat initial data is a minimum among this class of data. And hence the area of generic throat initial data is bounded from below by the angular momentum. Also, this result strongly suggests that the inequality between area and angular momentum holds for generic asymptotically flat axially symmetric black holes. As an application, we prove this inequality in the nontrivial family of spinning Bowen-York initial data.},

doi = {10.1103/PHYSREVD.82.104010},

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

number = 10,

volume = 82,

place = {United States},

year = {Mon Nov 15 00:00:00 EST 2010},

month = {Mon Nov 15 00:00:00 EST 2010}

}