No, the Earth's inner core cannot be made out of a black hole. The Earth's core is primarily composed of solid iron and nickel, and it is not possible for a black hole to exist at the center of the Earth.
A black hole is a region of spacetime where gravity is so strong that nothing, including light, can escape its gravitational pull. Black holes are formed from the remnants of massive stars that have undergone gravitational collapse. They have extremely high density and a singularity at their core, where matter is compressed to an infinitely small point.
The Earth's core, on the other hand, is thought to consist of solid and liquid materials due to the high pressures and temperatures found in that region. It is not dense enough nor does it possess the conditions required for a black hole to form.
Furthermore, the presence of a black hole at the center of the Earth would have significant and observable effects on the surrounding environment. The strong gravitational effects of a black hole would disrupt the orbits of nearby planets and objects, causing noticeable disturbances in the motion of celestial bodies within the solar system. We do not observe such effects, indicating that a black hole does not exist at the Earth's core.
In summary, the Earth's inner core is not composed of a black hole. It is primarily made up of solid iron and nickel, consistent with our current understanding of its composition based on seismic and other geophysical data.