Schwarzschild Definition and 319 Threads

In schwarzschild metric: $$ds^2 = e^{v}dt^2 - e^{u}dr^2 - r^2(d\theta^2 +sin^2\theta d\phi^2)$$ where v and u are functions of r only when we calculate the Ricci tensor $R_{\mu\nu}$ the non vanishing ones will only be $$R_{tt}$$,$$R_{rr}$$, $$R_{\theta\theta}$$,$$R_{\phi\phi}$$ But when u and v...

I found http://physicspages.com/2013/05/05/schwarzschild-metric-gravitational-redshift/: \frac{\lambda_R}{\lambda_E} = \sqrt{\frac{1-2GM/r_R}{1-2GM/r_E}} where the indexes R and E are for receiver and emitter respectively, and the speed of light is normalized to 1. Most other sources on the...

In special relativity a sphere in the rest frame for some observer looks like an ellipsoid for an observer with a relative velocity. Can we use the same reasoning for the Schwarzschild spacetime? Namely that a spherically symmetric spacetime produced by a spherical mass look ellipsoidal for an...

Homework Statement An observer is orbiting at a radius r = 3GM, \theta = \frac{\pi}{2} and \phi = \omega t where w is constant. The observer sends a photon around the circular orbit in the positive \phi direction. What is the proper time \Delta \tau for the photon to complete one orbit...

I know that the schwarzschild radius is proportional to the mass. But in case of black holes the mass remains the same only the size and density changes. So does the schwarzschild radius stay same when it is the sun and when it becomes a black hole?

Photons with smaller and smaller wave lengths have a higher and higher energy and these engeries have an increasing Schwarzschild radius r_s. Consequently i can ask when half the wave length \lambda/2 is equal to r_s, such that one wave length fits into the sphere of the Schwarzschild radius. I...

Recently I have been researching black holes, and came across the "Schwarzschild Radius". The wikipedia page on Schwarzschild radius's mentioned that the Sun has a radius of 3km. If that is so, then how can that be so, as that would mean that light cannot escape it. So when it said "3km", did...

I was thinking a bit earlier: What if you created a particle at infinity (ignore the normal particle rules for simplicity), and allowed it to fall towards a massive body? Ignoring other effects such as the other forces, would the particle ever gain enough energy to surpass the energy...

I am reading this paper http://arxiv.org/pdf/1111.4837.pdf and I came across under eq12 that the new metric is degenerate... How can someone see that from the metric's form? Degeneracy for a metric means that it has at least 2 same eigenvalues (but isn't that the same for the Minkowski metric...

Hello, if you could help, I will be glad. I am studying the Einsteins-Rosen bridge (a matematically solution of the black hole) and I thought that the Einsteins-Rosen bridge was what we found making the Schwarzschild metric a change in kruskal coordinates. But reading an scientific article it...

Hello, I have a question, whether is possible to looking for Killing Vectors (KV) in this way (I know about general solution): From Schwarzschild metric I can see two KV \frac{\partial}{\partial t} and \frac{\partial}{\partial\phi} . Then I see that other trivial KV arent there. Metric...

Schwarzschild coordinate "r" Hello, I am a newguy here, so if my question don't belong to this section, please let me know. My question: In spherical symmetric spacetime discrabed by Schwarzschild coordinate ds2=-a(r)dt2+b(r)dr2+r2(dΘ2+Sin2(Θ)d\varphi2), "r" is defined as r=\sqrt{A/(4\pi)}...

I was wondering since it is usually foliated into 2-spheres and these are not themselves parallelizable(only the n-spheres S1, S3 and S7 are). I know the timelike Killing vector field is not global, but is the a global basis of vector fields in Schwarzschild spacetime? I mean a basis in a...

In another thread we determined that the proper total force acting on an orbiting object in the Schwarzschild metric, is given by: ##f_{total} = \frac{Mm}{r^2\sqrt{1-2M/r}} - \frac{mv^2}{r}\left(\frac{1-3M/r}{(1 - v^2)\sqrt{1-M/r}}\right)## One interesting aspect of the equation is that when...

Comment, discuss and explain please. Thanka

Schwarzschild solution for Planetary Motion: ##g_{ij}= \left( \begin{array}{cccc} \frac{1}{(1-(\frac{2*m}{r}))} & 0 & 0 & 0 \\ 0 & r^2 & 0 & 0 \\ 0 & 0 & r^2*(sin\theta)^2 & 0 \\ 0 & 0 & 0 & c^2*(1-\frac{2*m}{r}) \end{array} \right) ## where ##m=\frac{G*(Mass of Sun)}{c^2}##...

Hi, Is it pure coincidence that if you put ##c=v_e=\sqrt{2GM/R}## in the escape velocity, you end up with the Schwarzschild radius ##R=2GM/c^2##? The derivation of the escape velocity is purely classical mechanics. It involves ##E_{kin}=mv^2/2## which is incorrect in special relativity...

This is a spin off from another thread: First there are a couple of mathpages http://mathpages.com/rr/s8-04/8-04.htm and http://mathpages.com/rr/s8-03/8-03.htm that discuss the refractive index model and highlights the differences. The first obvious objection is that the 'medium' must have...

Hello, First off, I'm not a physics student by any means, but it does intrigue me. I've been wondering about the Schwarzschild radius, and how the density of an object dictates the escape speed. Why is it, that the more you compress an object, the more gravity it "owns?" If you were able to...

Homework Statement Metric signature: - + + + Schwarzschild metric: dS^{2}=-(1-\frac{2M}{r})dt^{2}+(1-\frac{2M}{r})^{-1}dr^{2}+r^{2}d\theta^{2}+r^{2}(sin\theta)^{2}d\phi^{2} Second fundamental form: h_{ij}=g_{kl}\Gamma^{k}_{ij}n^{l} where: i=1,2 j=1,2...

Suppose there is a radially free falling object starting at r(t=0) = r0 > rS with some initial velocity v. And suppose there is a radial light ray starting at R(t=0) = R0 > r0. Suppose that both the object and the light ray reach the singularity at the same time. Question: is there a simple...

The textbooks claim that the weak field (Newtonian) metric is more intuitive than the Schwarzschild metric, but I don’t agree.The time correction factor for the weak field metric is the same as that for the Schwarzschild metric. But for the length correction factor for the weak field metric is...

Let us consider the case of a body falling down radially towards a Schwarzschild black hole. The velocity of the body is as high as it would be if it had been falling from standstill at infinity. When the body finally fuses with the black hole (get infinitely close to the Schwarzshild...

The title says it all. Do static black holes really exist, or do the ones we know about seem to be spinning? ISTM unlikely that there could be any non-rotating black holes, but I don't really know, hence the question. Do we have the means to determine with any certainty what the answer is?

According to the Schwarzschild solution in the most common anisotropic (Schwarzschild?) coordinates the proper time and the coordinate time are related as...

What is the definition of angular momentum that is to be conserved in the Schwarzschild solution of general relativity, expressed in coordinate time? I am trying to put together an expression for gravitational acceleration that is to emulate the Schwarzschild solution. I need to test whether...

I am looking for some input on the proper use of the definition of the Schwarzschild radius. Case 1: In the world of black holes, the Schwarzschild radius is used in reference to the distance from the center of a mass dense enough to not allow light to exit. It is a short distance compared to...

The Schwarzschild metric describes spacetime around a spherically symmetric neutral object and, as such, it is considered as a vacuum solution, with zero contribution from the energy-momentum tensor that otherwise influences the space in the region 0<r<2GM. The Schwarzschild metric can be...

1. Calculate the schwarzschild radius of a proton 2. R = (2MG)/c^2 3. I plugged in m= 1.67E-27, G=6.67E-11 and c=3E-8 and got out an answer of 2.5E-54. This seems ridiculously small, but I can't figure our if I'm doing something wrong or if it really is just that tiny. The next...

I am under the impression that the event horizon radius of a non-rotating black hole is equal to its Schwarzschild radius. Is this correct? If yes, then I have a mixed bag of questions: Is the event horizon radius always calculated using the Schwarzschild metric, no matter what model we are...

Note: I did not study psychics and only have a vague-ish conceptual understanding of stuff Seems to me one of these points must be wrong: * One can survive passing into the Schwarzschild radius of a black hole * The Schwarzschild radius of a black hole (or it's surface?) represents a...

Hello everybody! I have some questions concerning the structure of the Schwarzschild metric, which is given by $$ ds^2=-(1- \frac{2GM}{r})dt^2+(1-\frac{2GM}{r})^{-1}dr^2+ r^2(d\theta^2+ \sin^2(\theta) d\phi^2) $$ where we set $c=1$. I would like to know the following: \\ \\ 1. Why is it...

Hello: I would like to understand how to compute the shape operator (and eigenvalues etc) for a complex example like the Schwarzschild spacetime. It's easy for a submanifold in Euclidean space, but I don't know how to do it for the more advanced examples like the schwarzschild spacetime in...

Homework Statement The problem is I am wanting to know if the expression on the right hand side is dimensionless. Homework Equations ds^2 = (1 - \frac{2GM}{c^2 r})c^2 dt^2 The Attempt at a Solution Since the Schwarzschild radius is r = \frac{2GM}{c^2} would I be right in saying that...

In this Wiki link for the derivation of the Schwarzschild metric, in the section "simplifying the components", g_22 and g_33 are derived. The problem is that upon deriving them, they first set those local measurements of the components for the metric upon a 2_sphere (on the left side) equal to...

In deriving the Schwarzschild metric, the first assumption is that the transformation of r^2 (dθ^2 + sin^2 θ dψ) remains unchanged due to the spherical symmetry. What does that mean exactly? What is the logic behind it? Please apply any math involved in algebraic form. Thanks.

Hi! Given the schwarzschild metric ds^2=-e^{2\phi}dt^2+\frac{dr^2}{1-\frac{b}{r}} I can make this coordinate transformation \hat e_t'=e^{-\phi}\hat e_t \\ \hat e_r'=(1-b/r)^{1/2}\hat e_r and I will get a flat metric. Is this correct? Another thing I'm a lot confused about: if I am at...

"A" starts a journey from a massive body in Schwarzschild geometry in a radial path and returns back to the starting point while "B" stays at rest. Please explain how to find the proper time of "A".

What happens to bodies of mass as they approach and get near this value? If they don't actually reach the criteria, will their properties be vastly different from bodies that do reach the criteria? Will it expand instead of maintain it's radius? I'm also wondering how much energy it takes...

Homework Statement The Komar mass of a Schwarzschild geometry can be written as \frac{1}{4\pi}\int_{S}n^{\alpha}\sigma_{\beta} \nabla_{\alpha} \xi^{\beta}dA, where n^{\alpha} and \sigma_{\beta} are timelike and spacelike normal vectors respectively. How does one actually go about evaluating...

I have a qualitative question to ask: The Schwarzschild radius of matter is proportional to its mass. The actual radius of the matter, assuming it is spherical, is proportional to the cube root of its mass. This implies that the density required to form a Schwarzschild radius decreases as...

Please explain me how to find the proper time taken by one twin to travel around a massive body while his other twin stays on the Earth in Schwarzschild space?

Please suggest some simple method of deriving schwarzschild metric without using Einstein equations and tensors.I have learned somewhere that it is not possible.Is it so?

I needed some help with the Christoffel symbols for the Schwarzschild metric. I used the metric in wikipedia with signature (+---). For some reason, I get different Christoffel symbols when I use Mathimatica so I'm not sure if it's my calculations that are wrong or not. This isn't homework or...

Is it possible to derive Schwarzschild equation without using the concept of four dimensional space or tensors

Please explain me how to derive the Timelike geodesics in Schwarzschild Metric. Thank you.

If you happen to have D'Inverno's Introducing Einstein's Relativity, this is on page 187. He has reduced the metric to non-zero components: g_{00}= e^{h(t)}(1-2m/r) g_{11}=-(1-2m/r)^{-1} g_{22}=-r^2 g_{33}=-r^2\sin^2\theta The final step is a time coordinate transformation that reduces...

Awhile back A.T. & PeterDonis helped me through several basic confusions on my way to an intuitive understanding of geodesics in curved spacetime. I looked at http://www.relativitet.se/spacetime1.html http://www.adamtoons.de/physics/gravitation.swf...

I'm trying to understand the Schwarzschild solution concept of proper distance. Given the proper distance equation d\sigma=\frac{dr}{\left(1-\frac{R_{S}}{r}\right)^{1/2}} how would I calculate the coordinate distance. For example - assuming the distance from the Earth to the Sun is...

On the Wikipedia page on Schwarzschild coordinates... http://en.wikipedia.org/wiki/Schwarzschild_coordinates ...it talks about a "family of nested spheres": each surface of constant t and r is a 2-sphere (i.e., setting dt = dr = 0 and r = constant in the metric results in a Euclidean...