Black hole horizon around a relativistic star

A star surrounded by a black hole generated by it is analyzed. For an outer static observer the black hole mass (and radius) depends on his position in the gravitational field of the star. In spite of the black hole presence, the geometry remains that of Schwarzschild. For an inner observer the black hole mass is constant and depends on the star's mass $m$ and radius $R$. The entropy for $r > R$ is one quarter of the area and is constant for $r < R$.