Critical gravity on AdS2 spacetimes
Abstract
We study the critical gravity in two-dimensional anti-de Sitter (AdS2) spacetimes, which was obtained from the cosmological topologically massive gravity (TMGΛ) in three dimensions by using the Kaluza-Klein dimensional reduction. We perform the perturbation analysis around AdS2, which may correspond to the near-horizon geometry of the extremal Banados, Teitelboim, and Zanelli (BTZ) black hole obtained from the TMGΛ with identification upon uplifting three dimensions. A massive propagating scalar mode δF satisfies the second-order differential equation away from the critical point of K=l, whose solution is given by the Bessel functions. On the other hand, δF satisfies the fourth-order equation at the critical point. We exactly solve the fourth-order equation, and compare it with the log gravity in two dimensions. Consequently, the critical gravity in two dimensions could not be described by a massless scalar δFml and its logarithmic partner δFlog4th.
- Publication:
-
Physical Review D
- Pub Date:
- September 2011
- DOI:
- 10.1103/PhysRevD.84.064042
- arXiv:
- arXiv:1106.0546
- Bibcode:
- 2011PhRvD..84f4042M
- Keywords:
-
- 04.70.Bw;
- 04.60.Kz;
- 04.60.Rt;
- Classical black holes;
- Lower dimensional models;
- minisuperspace models;
- High Energy Physics - Theory;
- General Relativity and Quantum Cosmology
- E-Print:
- 17 pages, 3 figures