The size limit of an Earth-like planet, beyond which it would collapse under its own weight and potentially become a black hole, depends on several factors, including its mass, composition, and physical properties.
To understand this, we can consider the concept of the Chandrasekhar limit. The Chandrasekhar limit is the maximum mass that a stable white dwarf star, composed mostly of electron-degenerate matter, can sustain without collapsing further into a more compact object, such as a neutron star or a black hole. This limit is approximately 1.4 times the mass of the Sun (known as the solar mass).
Applying this concept to an Earth-like planet, which is composed primarily of solid and liquid matter rather than degenerate matter, we need to consider different physics. Earth-like planets are primarily held up by the mechanical strength of their materials rather than electron degeneracy pressure.
Based on current understanding, it is estimated that if an Earth-like planet were to accumulate significantly more mass, it would likely undergo a different type of collapse before reaching the black hole stage. At a certain point, the planet's internal pressures and forces would cause it to undergo gravitational compression, resulting in a transition to a different type of object such as a gas giant, a brown dwarf, or a star.
The exact threshold for this transition would depend on various factors, including the planet's composition, structure, and thermal properties. However, it is important to note that the size and mass limits for such transitions are still the subject of ongoing scientific research and investigation.
In summary, an Earth-like planet would not collapse under its own weight to form a black hole. Instead, it would likely undergo a different type of collapse or transformation before reaching such extreme conditions.