Static-fluid black hole and wormhole in three-dimensions

Abstract

Abstract We introduce the so-called static-fluid solutions in 2+1-dimensional spacetime. We assume the spacetime to be static and circular symmetric and for the perfect fluid we consider an equation of state (EoS) of the form p r = − 1 3 ρ r where r is the radial coordinate. Since, unlike the 3+1-dimensions, in 2+1-dimensions there is no vacuum solution other than the flat spacetime, our approach is not exactly the same as the 3+1-dimensions such that the static-fluid is accompanied by a cosmological constant. In addition to that, at first, we present a static solution supported by a static-fluid of constant energy-momentum tensor with a general EoS. Then, in the nonconstant energy-momentum tensor case, we introduce a large class of solutions. Depending on the values of the integration constants it implies black holes, wormholes, or cosmological solutions. Some of these solutions are closed in two-space which are considered for the first time in 2+1-dimensions. In both cases i.e. the constant and nonconstant energy-momentum tensor we imposed the satisfaction of conservation of the energy-momentum i.e. ∇ μ T μ ν = 0 .