Apparent horizons of an expanding Schwarzschild-like spacetime
We define an expanding Schwarzschild-like spacetime by attaching a scaling function a(t) to the spatial components of the Schwarzschild metric. By imposing McVittie's no accretion condition -- asserting an absence of radially flowing cosmic fluid -- the modified Schwarzschild metric is then used to describe a black hole embedded in an anisotropic universe. Expressions for the radii of the black hole and cosmological apparent horizons are calculated by locating the regions where the expansion scalars of ingoing and outgoing null geodesic congruences vanish. Results show that while the black hole horizon always exists, the duration of the existence of the cosmological horizon is bounded by a critical time tc and the time interval of its existence depends on how the cosmic flow parameter H(t) is defined.