Quantum corrections for a Bañados-Teitelboim-Zanelli black hole via the 2D reduced model

Abstract

The one-loop quantum corrections for BTZ black hole are considered using the dimensionally reduced 2D model. Cases of 3D minimal and conformal coupling are analyzed. Two cases are considered: minimally coupled and conformally coupled 3D scalar matter. In the minimal case, the Hartle-Hawking and Unruh vacuum states are defined and the corresponding semiclassical corrections of the geometry are found. The calculations are done for the conformal case too, in order to make the comparison with the exact results obtained previously in the special case of spinless black hole. Beside that we find exact corrections for AdS 2 black hole for 2D minimally coupled scalar field in the Hatrle-Hawking and Boulware state.

Geometrical and hydrodynamic aspects of five-dimensional Schwarzschild black hole

“…Even though the (2+1)dimensional Bañados-Teitelboim-Zanelli (BTZ) black hole [4][5][6][7][8] is a toy model in some respects, the BTZ black hole has triggered significant interest due to its connections with some string theories [9,10] on ten-dimensional space-times, and with it roles in microscopic entropy derivations [11,12] and in quantum-corrected thermodynamics [13][14][15]. Specifically, a slightly modified solution for the BTZ black hole yields a solution to string theory, the so-called black string [16,17].…”

“…There have been tremendous progresses in lower dimensional black holes associated with the ten-dimensional string theory [1,2] since an exact conformal field theory describing a black hole in two-dimensional space-time was proposed [3]. Even though the (2+1) dimensional Bañados-Teitelboim-Zanelli (BTZ) black hole [4][5][6][7][8] is a toy model in some respect, the BTZ black hole has triggered significant interests due to its connections with some string theories [9,10] on ten-dimensional space-time, its role in microscopic entropy derivations [11,12] and quantum corrected thermodynamics [13][14][15]. Specifically, a slightly modified solution of the BTZ black hole yields an solution to the string theory, so-called the black string [16,17].…”

“…(A1) of Appendix A.For the steady-state flow of a perfect fluid of massive particles and photons, Eqs (15). and(16)yield 2π 2 nu r r 3 sin 2 α sin θ = A 0 ,…”

Hawking radiation from the charged and magnetized BTZ black hole via covariant anomaly

“…[17] On the other hand, the Bañados-Teitelboim-Zanelli (BTZ) black holes have attracted great attention recently, because the BTZ theory refers to special solutions of (2+1)-dimensional anti-de Sitter gravity and the charged BTZ black holes are simply the analogous solutions in (2+1)-dimensional anti-de Sitter-Maxwell gravity. Hence it can provide a simplified model for exploring some conceptual issues, such as the quantum corrected thermodynamics, [18,19] AdS/CFT correspondence, [20] string theory [21] and so on. To further understand the basic properties of BTZ black hole, in this paper, we concentrate on studying Hawking radiation from the charged and magnetized BTZ black hole from the anomaly point of view.…”

Note on cosmology of the dimensionally reduced gravitational Chern-Simons term

“…A three-dimensional Einstein-Hilbert action has been dimensionally reduced to two-dimensional lineal gravity theory [1], and three-dimensional rotating black hole can be studied in the reduced theory [2,3] (for a review, see [4]). On the other hand, there has been much attention to the gravitational Chern-Simons (GCS) term in the topologically massive gravity [5] as a higher derivative correction.…”