Timeline for Can a stress-energy tensor induce signature changes on the metric?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 5, 2020 at 18:02 | vote | accept | Anon21 | ||
| Jul 5, 2020 at 16:25 | comment | added | J. Murray | @AlexandreH.Tremblay Let's continue this in chat. | |
| Jul 5, 2020 at 16:19 | comment | added | Anon21 | I apologize if I am using the wrong terms. My understanding of General Relativity is that it recovers Special Relativity in the absence of matter/energy; that is when the stress-energy tensor is zero everywhere. Now imagine instead that we define an analog to General Relativity, called Euclidean gravity, that instead recovers a metric with signature (+,+,+,+) when the stress-energy tensor is zero. Now I ask, in Euclidean gravity, what is the stress-energy tensor whose corresponding metric is (+,-,-,-) everywhere? In this case, there is no change of metric signature in spacetime. | |
| Jul 5, 2020 at 16:05 | comment | added | J. Murray | @AlexandreH.Tremblay I don't understand what you mean when you say a metric initially has signature (++++) but also has signature (+---) everywhere. Everywhere means everywhere in spacetime - at all points, and at all times. | |
| Jul 5, 2020 at 16:01 | comment | added | Anon21 | Hello, I was more thinking of a case where, using your "toy" metric, $x=-1$. Thus, $x$ would not change. The metric would be $(+,-,-,-)$ everywhere and thus "unique". Is there a stress-energy tensor that can fix $x$ to $-1$ for metric initially defined as $(+,+,+,+)$? If I then define this stress-energy tensor as the "true vacua of space" then I do not need to worry about the possibility of my metric switching to a different signature. Does a stress-energy tensor that fixes $x$ to $-1$ change anything to your conclusion? In this case there would be no discontinuity nor degeneracy. | |
| Jul 5, 2020 at 15:13 | history | answered | J. Murray | CC BY-SA 4.0 |