# The Non-BPS Black Hole Attractor Equation

## Abstract

We study the attractor mechanism for extremal non-BPS black holes with an infinite throat near horizon geometry, developing, as we do so, a physical argument as to why such a mechanism does not exist in non-extremal cases. We present a detailed derivation of the non-supersymmetric attractor equation. This equation defines the stabilization of moduli near the black hole horizon: the fixed moduli take values specified by electric and magnetic charges corresponding to the fluxes in a Calabi Yau compactification of string theory. They also define the so-called double-extremal solutions. In some examples, studied previously by Tripathy and Trivedi, we solve the equation and show that the moduli are fixed at values which may also be derived from the critical points of the black hole potential.

- Authors:

- Publication Date:

- Research Org.:
- Stanford Linear Accelerator Center (SLAC)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 876040

- Report Number(s):
- SLAC-PUB-11660

TRN: US200604%%430

- DOE Contract Number:
- AC02-76SF00515

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ATTRACTORS; BLACK HOLES; COMPACTIFICATION; GEOMETRY; STABILIZATION; HEPTH

### Citation Formats

```
Kollosh, R.
```*The Non-BPS Black Hole Attractor Equation*. United States: N. p., 2006.
Web. doi:10.2172/876040.

```
Kollosh, R.
```*The Non-BPS Black Hole Attractor Equation*. United States. doi:10.2172/876040.

```
Kollosh, R. Wed .
"The Non-BPS Black Hole Attractor Equation". United States.
doi:10.2172/876040. https://www.osti.gov/servlets/purl/876040.
```

```
@article{osti_876040,
```

title = {The Non-BPS Black Hole Attractor Equation},

author = {Kollosh, R},

abstractNote = {We study the attractor mechanism for extremal non-BPS black holes with an infinite throat near horizon geometry, developing, as we do so, a physical argument as to why such a mechanism does not exist in non-extremal cases. We present a detailed derivation of the non-supersymmetric attractor equation. This equation defines the stabilization of moduli near the black hole horizon: the fixed moduli take values specified by electric and magnetic charges corresponding to the fluxes in a Calabi Yau compactification of string theory. They also define the so-called double-extremal solutions. In some examples, studied previously by Tripathy and Trivedi, we solve the equation and show that the moduli are fixed at values which may also be derived from the critical points of the black hole potential.},

doi = {10.2172/876040},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Wed Feb 08 00:00:00 EST 2006},

month = {Wed Feb 08 00:00:00 EST 2006}

}