Regular Article - Theoretical Physics
Generalized (2+1) dimensional black hole by Noether symmetry
Center for Excellence in Astronomy and Astrophysics of IRAN (CEAAI-RIAAM), Maragha, 55134-441, Iran
2 Department of Physics, Azarbaijan Shahid Madani University, Tabriz, 53741-161, Iran
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Published online: 26 November 2013
We use the Noether symmetry approach to find f(R) theory of (2+1) dimensional gravity and (2+1) dimensional black hole solution consistent with this f(R) gravity and the associated symmetry. We obtain f(R)=D 1 R(n/n+1)(R/K)1/n +D 2 R+D 3, where the constant term D 3 plays no dynamical role. Then, we find general spherically symmetric solution for this f(R) gravity which is potentially capable of being as a black hole. Moreover, in the special case D 1=0,D 2=1, namely f(R)=R+D 3, we obtain a generalized BTZ black hole which, other than common conserved charges m and J, contains a new conserved charge Q. It is shown that this conserved charge corresponds to the freedom in the choice of the constant term D 3 and represents symmetry of the action under the transformation R→R′=R+D 3 along the killing vector ∂ R . The ordinary BTZ black hole is obtained as the special case where D 3 is fixed to be proportional to the infinitesimal cosmological constant and consequently the symmetry is broken via Q=0. We study the thermodynamics of the generalized BTZ black hole and show that its entropy can be described by the Cardy–Verlinde formula.
© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica, 2013