# Anti-de Sitter-Space/Conformal-Field-Theory Casimir Energy for Rotating Black Holes

## Abstract

We show that, if one chooses the Einstein static universe as the metric on the conformal boundary of Kerr-anti-de Sitter spacetime, then the Casimir energy of the boundary conformal field theory can easily be determined. The result is independent of the rotation parameters, and the total boundary energy then straightforwardly obeys the first law of thermodynamics. Other choices for the metric on the conformal boundary will give different, more complicated, results. As an application, we calculate the Casimir energy for free self-dual tensor multiplets in six dimensions and compare it with that of the seven-dimensional supergravity dual. They differ by a factor of 5/4.

- Authors:

- DAMTP, Centre for Mathematical Sciences, Cambridge University, Wilberforce Road, Cambridge CB3 OWA (United Kingdom)
- George P. and Cynthia W. Mitchell Institute for Fundamental Physics, Texas A and M University, College Station, Texas 77843-4242 (United States)

- Publication Date:

- OSTI Identifier:
- 20699638

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review Letters; Journal Volume: 95; Journal Issue: 23; Other Information: DOI: 10.1103/PhysRevLett.95.231601; (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; BLACK HOLES; CASIMIR EFFECT; CONFORMAL INVARIANCE; COSMOLOGY; DE SITTER GROUP; MANY-DIMENSIONAL CALCULATIONS; QUANTUM FIELD THEORY; SPACE-TIME; SUPERGRAVITY; TENSORS; THERMODYNAMICS; UNIVERSE

### Citation Formats

```
Gibbons, G.W., Perry, M.J., and Pope, C.N.
```*Anti-de Sitter-Space/Conformal-Field-Theory Casimir Energy for Rotating Black Holes*. United States: N. p., 2005.
Web. doi:10.1103/PhysRevLett.95.231601.

```
Gibbons, G.W., Perry, M.J., & Pope, C.N.
```*Anti-de Sitter-Space/Conformal-Field-Theory Casimir Energy for Rotating Black Holes*. United States. doi:10.1103/PhysRevLett.95.231601.

```
Gibbons, G.W., Perry, M.J., and Pope, C.N. Fri .
"Anti-de Sitter-Space/Conformal-Field-Theory Casimir Energy for Rotating Black Holes". United States.
doi:10.1103/PhysRevLett.95.231601.
```

```
@article{osti_20699638,
```

title = {Anti-de Sitter-Space/Conformal-Field-Theory Casimir Energy for Rotating Black Holes},

author = {Gibbons, G.W. and Perry, M.J. and Pope, C.N.},

abstractNote = {We show that, if one chooses the Einstein static universe as the metric on the conformal boundary of Kerr-anti-de Sitter spacetime, then the Casimir energy of the boundary conformal field theory can easily be determined. The result is independent of the rotation parameters, and the total boundary energy then straightforwardly obeys the first law of thermodynamics. Other choices for the metric on the conformal boundary will give different, more complicated, results. As an application, we calculate the Casimir energy for free self-dual tensor multiplets in six dimensions and compare it with that of the seven-dimensional supergravity dual. They differ by a factor of 5/4.},

doi = {10.1103/PhysRevLett.95.231601},

journal = {Physical Review Letters},

number = 23,

volume = 95,

place = {United States},

year = {Fri Dec 02 00:00:00 EST 2005},

month = {Fri Dec 02 00:00:00 EST 2005}

}

Other availability

Save to My Library

You must Sign In or Create an Account in order to save documents to your library.