A large family of new black hole solutions in $2+1$-dimensional Einstein-power-Maxwell gravity with prescribed physical properties is derived. We show with particular examples that according to the power parameter $k$ of the Maxwell field, the obtained solutions may be asymptotically flat for $1/2<k<1$ or nonflat for $k>1$ in the vanishing cosmological constant limit. We study the thermodynamic properties of the solution with two different models, and it is shown that thermodynamic quantities satisfy the first law. The behavior of the heat capacity indicates that by employing the $1+1$-dimensional dilaton analogy the local thermodynamic stability is satisfied.

• Received 9 February 2012

DOI:https://doi.org/10.1103/PhysRevD.85.104004