Black dwarf

A black dwarf is what is theorized to remain after White dwarfs exhaust all their heat.

Existence
A white dwarf does not sustain thermonuclear reactions and so it slowly cools down. Given its small radius and large mass, the time needed for a white dwarf to cool down until it no longer emits visible light is longer then the estimated age of the Universe. If we found one today, it would mean that our knowledge about the age of the Universe is wrong, the formation processes are unknown, or the object was somehow created artificially faster.

If they exist, black dwarfs are very hard to detect. The only way to find them should be by their gravity interactions with another visible companion. However, they are theorized to exist in large numbers as the Universe gets older.

Basic properties
A black dwarf has the same mass and diameter of a white dwarf. That means, it has a diameter of 5000 to 10000 km (similar to a rocky planet) and a mass similar to a star (from 0.1 to 1.4 the mass of Sol, our sun). So, its gravitational effect on an orbiting planet is similar to that of a white dwarf.

Surface temperature is low, below 600K, even as low as 5 degrees kelvin. It emits no visible light, only a very faint infrared radiation, So, it cannot support light or heat an orbiting planet.

Because of its small size and high mass, its density is very high, over 1 million times that of the Sun. Also, its surface gravity is very high, millions of times higher then Earth's. As so, no spacecraft can land on its surface and no known material can resist under its own weight. This huge gravity is what keeps matter so compacted.

A white or black dwarf is made of what remained when its previous star remained without fuel. Small dwarfs might be made of helium (remnants of M - type stars), while others, heavier, contain carbon or other elements.

All white dwarfs are known to have a compacted atmosphere, made usually of lighter elements. The atmosphere is replenished by matter captured by their strong gravity (for example solar wind from a stellar companion). When the amount of hydrogen in the atmosphere reaches a certain limit, white dwarfs go nova (and the atmosphere explodes, while hydrogen undergoes nuclear fusion). In case of a black dwarf, since the required temperature for nuclear reactions is not achieved, there should be no nova and all matter should deposit on their surface, forming a larger atmosphere.

White dwarfs rotate fast (even faster then a second), generating strong magnetic fields. Since rotation speed is decreased by tidal forces, we can speculate that black dwarfs rotate much slower and don't have a strong magnetic field.