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Do black holes really exist?

Welcome back,
Hey guys first of all I want to clarify that I am none to accept or deny about the existence or non existence of black holes.It is a huge topic and already many theories have been put regarding this by great scientists.I will just discuss about my views on existence of black hole.
Let's start..
Coming to the basic definition of black hole which states that a black hole is created by a dying star by collapsing under its own mass by getting reduced to nearly zero volume.When a huge mass shrinks in volume in space time fabric it gets penetrated inside it leading to so called hole.But the question is whether the star shrinks to zero volume.If it is so where will the mass exist?The mass can only exist at non zero volume.In my opinion,the black holes when created go deep inside a point,that is the point of singularity.The other case can be that the hole created goes to infinity and never stops at a point.
Thanks...

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