I am studying Hawking's area theorem from the book the large scale structure of spacetime by Hawking and Ellis. At the end of page#318, it said: null geodesic generators of future infinity have no future end-points. I just don't understand why is that ? Please give some explanation.
$\begingroup$
$\endgroup$
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
2
In simple terms, if you imagine tracing the paths of light rays or gravitational waves as they propagate through spacetime, those paths never end in the future; they keep extending outwards towards future infinity $\mathcal{I}^+$.
To explain it better, since null geodesics (which are paths followed by photons that have no mass or objects moving at the speed of light) have zero length in spacetime and travel at the speed of light, they continue indefinitely into the future, never reaching a "final point" or "endpoint" in the future direction. In Penrose diagrams, $\mathcal{I}^+$ represents the "endpoint" or "boundary" of future-directed null geodesics, so it corresponds to where light rays or objects moving at the speed of light would ultimately end up if they traveled indefinitely into the future. In a sense, it represents the limit of spacetime at future times.
-
$\begingroup$ So does it mean future infinity have past end ? but i am wondering how ? $\endgroup$ Commented Mar 24 at 11:35
-
$\begingroup$ No, future infinity doesn't have a past end because it represents everything that can happen infinitely far into the future. It's like the endlessly distant horizon on a highway stretching forever, and the past has already happened. It's a separate concept with its own "infinitely far back" point, which we call past infinity. To explain it more easily, imagine a number line stretching infinitely in both directions: future infinity would be at positive infinity ($+\infty$) on that line, while past infinity would be at negative infinity ($-\infty$). They are separate concepts, not connected. $\endgroup$ Commented Mar 24 at 14:39