Can time dilation happen in a higher dimensional space or inside a wormhole?

A wormhole usually helps us to create a shortcut to a distant object through a higher dimensional space. Can the time factor in that higher dimensional space differ from our three-dimensional space? I mean that for example staying in a wormhole for a second (higher dimensional space) may cost a year in our three-dimensional space. Can such a time dilation happen in higher dimensions? If there could be more, please answer in detail.

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Can time dilation happen in a higher dimensional space or inside a wormhole?

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