8.15 Black Holes

Consider a spherical body of mass \(M\) and radius \(R\). Suppose, due to some reason the volume goes on decreasing while the mass remains the same. The escape velocity \(\sqrt{\frac{2 G M}{R}}\) from such a dense material will be very high. Suppose the radius is so small that
\(
\sqrt{\frac{2 G M}{R}} \geq c
\)
where \(c=3 \times 10^8 \mathrm{~m} \mathrm{~s}^{-1}\) is the speed of light. The escape velocity for such an object is equal to or greater than the speed of light. This means, anything starting from the object with a speed less than the speed of light will return to the object (neglecting the effect of other objects in space). According to the theory of relativity, it is not possible to achieve a velocity greater than \(c\) for any material object. Thus, nothing can escape from such a dense material. Such objects are known as black holes. A number of such black holes exist in space. Even light cannot escape from a black hole.