More science fiction: Larry Niven wrote about Jack Brennan, a human turned Pak Protector who set up a small environment around a micro black hole to provide gravity in the outer solar system. I don't think it was earth-mass size though, more likely a singularity
A sub-Moon-mass singularity of 1e22 kg provides an acceleration of 9.8 m/s^2 at a radius of 261 km, while having a Schwarzchild radius of 1.5e-5 m.
The combined system of that singularity plus a hard spherical shell at radius 261 km (anchored by some sci-fi means that does not contribute significant mass) has a density of 134 g/mL, 6 times as dense as pure osmium, but being mostly empty space inside. And having a surface area of 856000 km^2, 0.6% the land area of Earth. Such a body could retain an atmosphere and sustain ecological cycles.
I had the question "how much mass does it take for a black hole to have 1G at the same radius as its event horizon" and the answer appears to be about 10^12 times that of the Sun.
Further science fiction tangent: Asimov wrote a novel called Nemesis that (among other things) discussed the concept of a red or brown star hidden in the outer solar system. That concept was a strange hypothesis debated back to at least the 80s.
