I am an Indian citizen. and i am flying to New York, US on 27th April 2015. my flight is from Lucknow to Mumbai and then my connecting flight is from Mumbai with a layover of 8 hrs. Do the airport authorities allow us to leave the airport for a few hours?
Let's tear this question apart because it's reasonably common. I will answer the generic question, the specific should be clear after:
You intend to leave the airport after stepping off a flight. If you have the legal right to stay in the country then this shouldn't be a problem. In most cases, if you are allowed inside the terminal you should be in the clear: you might simply be visa exempt or you have a visa that allows you into the country not just the airport. Citizens of countries needing Schengen airport transit visas, certain citizens who can transfer through a Canadian airport to the USA without a visa etc are exceptions. Also, if you fall under this, don't you worry, you will not be let out of the transit area. If you see a way to exit the transit area without passing a border guard / immigration officer, you are good to go.
You intend to reenter the secure area of the airport. You need a boarding pass (and in some countries, a government issued ID) for this. There are almost no exceptions to this rule.