Simple black holes with anisotropic fluid

We study a spherically symmetric spacetime made of an anisotropic fluid whose radial equation-of-state is given by p ₁ = -p. This case allows analytic solutions and is a good example for studying the static configuration of a black hole plus matter. For a given equation-of-state parameter w ₂ = p ₂ / p for angular directions, we find the exact solutions of the Einstein equation described by two parameters. We classify the solutions into six types based on the behavior of the metric function. Depending on the parameters, the solutions can have event and cosmological horizons. One of the solution types corresponds to a generalization of the Reissner-Nordstrm black hole, the thermodynamic properties for which are obtained in a simple form. The solutions are stable under radial perturbations.