"There" Sentences

Hello! Please help me!!
I'm thinking of writing a graduation thesis on existential sentences("there"sentences).

It is generally claimed that the notional subject of existenial sentences must be indefinite, but there are some sentences which occur with the definite NPs:
a.There's the book of linguistics on the table.
b.There's the possibility for John to go abroad.

I don't know under what situations that kind of sentences are correct.
You may say "it depends on the situation, and it's impossible to determine when they are correct and when they are wrong."
But I have to draw one conclusion.

In my opinion, true to its name, existential sentences are used when you describe the existence of something, so if there is a locative word included in the sentence or shown implicitly in the sentence, the sentence is acceptable.
And especially, if you can point at the NP(with your finger), the sentence with the definite NP can be accepted:
a.There's the book of linguistics on the table.
If you were searching for the book and finally found it you could say this.
=(Pointing at the book)"Here it is! That's what I'm looking for !"
b.There's the possibility for John to go abroad.
If you came across a way that John could go abroad. For example, if he didn't have enough money, but you saw a part-time job advertised that would suit him.
=(Pointing at the ad)"Look here! This job will give you a high hourly wage! You'll be able to go abroad soon!"

What do you think of my idea?
Are there any exceptional instances?
I hope you understood my English...