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Examples of Space-Times
| Content Provider | Scilit |
|---|---|
| Author | Date, Ghanashyam |
| Copyright Year | 2014 |
| Description | We will take a specification of a space-time as a set of coordinates xµ with a non-singular metric gµν(x) with Lorentzian signature, given as an infinitesimal invariant interval, also known as line element, and study some of its properties1. Specifically, we consider, Minkowski (No gravity) ∆s2 = −∆t2 + ∆x2 + ∆y2 + ∆z2 Rindler (Uniform) ∆s2 = −g20z2∆t2 + ∆x2 + ∆y2 + ∆z2, z > 0 Rotating Disk (Centrifugal) ∆s2 = −f(ρ)∆t2 + 2h(ρ)∆t∆φ+ g(ρ)∆φ2 + ∆ρ2 + ∆z2 f(ρ) := e−ω 2ρ2 − ρ2ω2e+ρ2ω2 , h(ρ) := −ωg(ρ) , g(ρ) := ρ2e+ρ2ω2 Schwarzschild (Spherical) ∆s2 = − (1− 2GMr )∆t2 + (1− 2GMr )−1 ∆r2 + r2∆Ω2 FRW (Cosmological) ∆s2 = −∆t2 + a2(t) { 1−κr2 + r 2∆Ω2 } where, ∆Ω2 := ( ∆θ2 + sin2θ∆φ2 ) Plane wave ∆s2 = (ηµν + hµν)∆x µ∆xν , where, (Undulating) hµν(x) = µν(k)e ik·x + ¯(k)µνe−ik·x and ηµν = diag (-1, 1, 1, 1) . Book Name: General Relativity |
| Related Links | https://content.taylorfrancis.com/books/download?dac=C2012-0-00567-5&isbn=9780429088742&doi=10.1201/b17759-5&format=pdf |
| Ending Page | 40 |
| Page Count | 18 |
| Starting Page | 23 |
| DOI | 10.1201/b17759-5 |
| Language | English |
| Publisher | Informa UK Limited |
| Publisher Date | 2014-12-03 |
| Access Restriction | Open |
| Subject Keyword | Book Name: General Relativity History and Philosophy of Science |
| Content Type | Text |
| Resource Type | Chapter |
