If a singularity slows time. How long was the first second after big bang?
The first second, was by definition, one second long.
A second by my watch is different from a second next to a singularity. Are you saying it would be the time it took light (if it had existed) to travel 186000 miles (in which case it would have been a really long second)? Just trying to get this concept right in my head before I launch into more study.
No, it is not. It looks different to a remote observer but that's a different story.
Yes, It would have been the time it took light to travel 186000 miles along a spacetime geodesic, assuming there was nothing to get in its way.
How do you measure that "first second"?
;)Aleksandr Solzhenitsyn: "Who could act rationally on the first morning of Creation?" (Cancer Ward)
If you're thinking of a black hole, this applies to an observer "hovering" near the horizon, not the singularity (you can't "hover" near the singularity since you'd be inside the horizon and everything inside the horizon has to fall inward), and, as phinds says, it refers to a second by that observer's clock as seen by a remote observer.
None of this applies to the initial singularity in the Big Bang model. First, that singularity is a past singularity, not a future singularity (like a black hole's); second, you can't "hover" near the Big Bang, since it's really a moment of time, not a place in space (it would be like trying to "hover" near last Tuesday); and third, the concept of "gravitational time dilation" such as occurs near a black hole's horizon is not applicable to the universe as a whole, since it only works in a stationary spacetime and the universe is not stationary.
So the only real answer to your question is Matterwave's: a second is a second by definition.
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