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I want to know whether mass of the black hole which has born from a star is similar to its parent star or not. whether the born black hole will have high or low mass comparing to its parent star. Whether in its life time black hole will increase mass by eating neighboring stars?

Advance thanks for your help

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The mass of the black hole, neutron start or even white dwarf is typically much smaller than the original star. Neutron stars and (probably) black holes are formed from supernovae and much of the original mass of the star will be blasted away. See the Wikipedia article on neutron stars form more info.

Even for white dwarves the parent star will usually have been through a red giant phase and will have blown away a lot of matter as a planetary nebela.

Whether a black hole can grow depends on its enviroment. Remember that outside the event horizon the gravitational field of a black hole behaves just like a normal star. Normal stars collide only extremely rarely, so it would be a very rare event for a black hole to swallow another star. An exception to this would be if the black hole is part of a binary system, in which case it will eventually swallow its partner star.

The black holes in the centre of galaxies are different because star orbits near the galactic centre are frequently perturbed by other stars and collision with the central black hole is much more common.

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