# Time coordinate inside black hole horizon [duplicate]

I am new to physics and was trying to learn more especially about general relativity. The Schwarzschild metric, changes the sign of the time and radial parts of the metric once we cross the event horizon. Someone on stack exchange had noted that as a result inside the horizon the decrease in radius is the direction of increasing time.

My question is if radius (i.e space) becomes timelike due to change in metric sign, then does time also become spacelike. I mean can then inside the horizon one move freely in time?

NOTE: As far as my understanding of the linked question goes, that question is about cosmology of interiro of ablack hole (it asks about a spacetime originating form blackhole horizon). My question i think is different, its really more on the lines of time-travel.Since the signature of the time corrdinate is spacelike, it should behave like space and we should be able to move in it in the backward direction as we can in space. Some say that it is a coordinate artifact, but I think the other coordinates dont tend to have the physical interpretation of time.(I may have understood it incorrectly)

• Yes, time and space are "interchanged." As another feature, energy and momentum are interchanged. However, it is not good to say that we can move "freely," because it can be shown that we have a finite proper time during which we can be inside the horizon before we hit the singularity. Jan 7, 2015 at 3:07
• As the linked question explains, you're taking the space-time flip too literally. Time doesn't become space and we can't move both directions in time. Jan 8, 2015 at 7:25

• @CuriousOne: the transformation between Schwarzschild and KZ coordinates is different on the two sides of the event horizon. That's how $u$ remains spacelike and $v$ timelike everywhere. Jan 8, 2015 at 7:24