Black hole solution of three-dimensional Einstein-scalar gravity

Simple three-dimensional Einstein-scalar gravity is constructed in the present work, its black hole solution is found on condition of ϕ= 2αφ(α is a constant). Further analysis reveals some similarities of this black hole to Reissner-Nordstrom black hole, but the mass of this black hole could be negative with α>2e. Further, the Hawking temperature and Bekenstein-Hawking entropy of this black hole satisfy the laws of the rmodynamics, and defines the internal energy of this black hole with a well-defined zero temperature limit. A comparison of the metric of this black solution with Reissner-Nordstrom metric reveals that α2 and 1/l correspond to the mass and charge of the Reissner-Nordstrom black hole respectively.