A 12-lecture mini-course providing an overview of advanced topics relevant to current research in General Relativity. The course will focus exclusively on classical aspects of gravity and, towards the end, on the quantum behaviour of particles/fields in gravitational backgrounds. The course will run from 20 March to 28 April 2023. Video recordings are available from the ICTS website for the series, https://www.icts.res.in/lectures/AGR2023
Saturday 15 April 2023
Notes updated to 15.04.2023
The course notes have been updated to 15.04.2023 in the shared folder.
I have one question. As in many cases and also in prompt path we reach same space-time point, as non prompt reaches but in some time earlier. Then we sit at that space point it for some time. Reached at same space- time point. My question I not directly linked to this case only. It's a general question that In all these cases we take same space for all time. That is space is same for all time. Or we separated out space and time notion. Or space is not changing with time. Is it happens or am I thinking wrong?
First of all, non-prompt definitely does not reach earlier. It reaches later. That's what the word "prompt" means. Second, we did not separate out space and time nor did we assume space is unchanging with time. On the contrary, we assumed a completely general, time-dependent, spacetime. I think you have in mind a case where a more prompt causal curve reaches a space point earlier and then "sits there". This is certainly possible for a timelike curve to do, it does not require the spacetime to be anything special. The timelike curve can simply be at a fixed coordinate point $x,y,z$ as time evolves. In a different coordinate system it would not be at a fixed point, but it would still be timelike, which is all we care about.
I have one question.
ReplyDeleteAs in many cases and also in prompt path we reach same space-time point, as non prompt reaches but in some time earlier. Then we sit at that space point it for some time. Reached at same space- time point. My question I not directly linked to this case only. It's a general question that In all these cases we take same space for all time. That is space is same for all time. Or we separated out space and time notion. Or space is not changing with time. Is it happens or am I thinking wrong?
First of all, non-prompt definitely does not reach earlier. It reaches later. That's what the word "prompt" means. Second, we did not separate out space and time nor did we assume space is unchanging with time. On the contrary, we assumed a completely general, time-dependent, spacetime. I think you have in mind a case where a more prompt causal curve reaches a space point earlier and then "sits there". This is certainly possible for a timelike curve to do, it does not require the spacetime to be anything special. The timelike curve can simply be at a fixed coordinate point $x,y,z$ as time evolves. In a different coordinate system it would not be at a fixed point, but it would still be timelike, which is all we care about.
ReplyDeleteThank you sir..
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