1. ### A Orbit velocity in Schwarzschild metric?

Hi, I'm trying to deduce orbit velocity of a particle with mass from Schwarzschild metric. I know for Newtonian gravity it is: $$v^2=GM\left(\frac{2}{r}-\frac{1}{a}\right)$$ The so called vis-viva equation. Where ##a## is the length of the semi-major axis of the orbit. For Schwarzschild metric...
2. ### I Maximally extended Schwarzschild spacetime

I have a very quick question about the maximally extended Schwarzschild spacetime. I know you can't reach regions III and IV from I and II, and vice versa. But can you see in? If I'm in region I and I look down, the null paths reaching me originated in the white hole singularity. Likewise in...
3. ### I Does gravitational field strength cause time dilation?

Hi I have 2 questions. There are 2 planets and one clock on each of them. One of them has a bigger gravitational field strength. And two clock have same distance from the core. 1-) Does time dilation occur between two? Which clock ticks slower? 2-) If time dilation occurs, which formula...
4. ### Volume of a sphere in Schwarzschild metric

Homework Statement Calculate the volume of a sphere of radius ##r## in the Schwarzschild metric. Homework Equations I know that \begin{align} dV&=\sqrt{g_\text{11}g_\text{22}g_\text{33}}dx^1dx^2dx^3 \nonumber \\ &= \sqrt{(1-r_s/r)^{-1}(r^2)(r^2\sin^2\theta)} \nonumber \end{align} in the...
5. ### Insights The Schwarzschild Metric: Part 3, A Newtonian Comparison - Comments

Greg Bernhardt submitted a new PF Insights post The Schwarzschild Metric: Part 3, A Newtonian Comparison Continue reading the Original PF Insights Post.
6. ### Insights The Schwarzschild Metric: Part 2, The Photon Sphere - Comments

Greg Bernhardt submitted a new PF Insights post The Schwarzschild Metric: Part 2, The Photon Sphere Continue reading the Original PF Insights Post.
7. ### Insights The Schwarzschild Metric: Part 1, GPS Satellites - Comments

Greg Bernhardt submitted a new PF Insights post The Schwarzschild Metric: Part 1, GPS Satellites Continue reading the Original PF Insights Post.
8. ### A Pressure dependence in interior Schwarzschild metric

I'm looking influence of pressure on the general interior Schwarzschild metric (see for example the book by Weinberg, eq. 11.1.11 and 11.1.16. The radial component of the metric (usually called A(r)) depends only on the mass included up to radius r A(r) = \left(1-\frac{ 2G M(r)}{r}\right)^{-1}...
9. ### I How to derive weak-field Schwarzschild metric from LEFE's?

I am trying to derive weak-field Schwarzschild metric using Linearized Einstein's field equations of gravity: []hμν – 1/2 ημν []hγγ = -16πG/ c4 Tμν For static, spherically symmetrical case, the Energy- momentum tensor: Tμν = diag { ρc2 , 0, 0, 0 } Corresponding metric perturbations for...
10. ### I Null geodesics in Schwarzschild spacetime

I was looking at null geodesics in Schwarzschild spacetime. Carroll's lecture notes cover them here: https://preposterousuniverse.com/wp-content/uploads/grnotes-seven.pdf He notes (and justifies) that orbits lie in a plane and chooses coordinates so it's the equatorial plane, then uses Killing...
11. ### I Ricci tensor for Schwarzschild metric

Hello I am little bit confused about calculating Ricci tensor for schwarzschild metric: So we have Ricci flow equation,∂tgμν=-2Rμν. And we have metric tensor for schwarzschild metric: Diag((1-rs/r),(1-rs]/r)-1,(r2),(sin2Θ) and ∂tgμν=0 so 0=-2Rμν and we get that Rμν=0.But Rμν should not equal to...
12. ### I Moving Schwarzschild Black Hole

The Schwarzschild Metric (with ##c=1##), $$ds^2 = -\Big(1-\frac{2GM}{r}\Big)dt^2+\Big(1-\frac{2GM}{r}\Big)^{-1}dr^2+r^2d\Omega^2$$ can be adjusted to a form involving three rectangular coordinates ##x##, ##y##, and ##z##: ds^2 =...
13. ### B Schwarzschild Metric Derivation?

Hi, I was wondering if anybody could help me understand the derivation of the Schwarzschild metric developed by the author of mathpages website. Rather than reproduce all the equations via latex, I have attached a 2-page pdf summary that also points to the mathpages article and explains my...
14. ### I Schwarzschild equation of motion: initial conditions

The Schwarzschild equation of motion, where coordinate length is differentiated by proper time is as far as I know r''(t) = -\frac{G\cdot M}{r(t)^2} + r(t)\cdot{\theta}'(t)^2 - \frac{3\cdot G\cdot M\cdot{\theta}'(t)^2}{c^2} {\theta}''(t) = -2\cdot r'(t)/r(t)\cdot{\theta}'(t) Now the question...
15. ### Momentum of a photon heading towards a spherical mass

Homework Statement A distant observer is at rest relative to a spherical mass and at a distance where the effects of gravity are negligible. The distant observer sends a photon radially towards the mass. At the distant observer, the photon's frequency is f. What is the momentum relative to...
16. ### A Assumptions of the Schwarzschild solution to the EFE

Given that no assumption is of a point energy is necessary to derive the vacuum (Schwarzschild) solution to the EFE, why is the solution assumed to apply to spacetime surrounding a point energy?
17. ### Stellar-mass black hole formation sequence

I feel like this could go in quite a few of the Physics subforums (Quantum Physics, Beyond the Standard Model, Special and General Relativity, or High Energy, Nuclear, Particle Physics) instead of Astronomy and Cosmology, but hopefully this will work. This is my first question I've posed here...