Schwarzschild Definition and 319 Threads

In 1916 Schwarzschild wrote down his famous metric to solve (or re-solve using a polar coordinate system) the precession of the perihelion of Mercury. The curvature of spacetime described by the Metric is for any non-rotating spherically symmetric mass. ds^2 = -(1-\frac{2M}{r})dt^2 +...

Schwarzschild example: Two observers orbit around the same central point mass at different radii. They measure that the radial separation between them is greater than their orbital circumference / 2pi. They conclude that there is negative (parabolic) spatial curvature in the radial direction...

I have written a report on the Schwarzschild Metric, where I derive a version of it that I have never seen before in the literature. I have no idea whether it is correct or not. I would like to submit it for publication except that I would first like someone much more competent than I to...

Homework Statement This question is very simple, but it is driving me mad. Show that the Schwarzschild metric in Kruskal coordinates takes the form ds2 = (32M3/r)e-r/2M(-dv2+du2) +r2(d(theta)2 + sin2(theta)*d(phi)2)Homework Equations The equations are just those defining the Kruskal...

A black hole is an object so heavy that neither matter nor even light can escape the influence of its gravitational field. Since no light can escape from it, it appears black. Suppose a mass approximately the size of the Earth’s mass 7.22 × 1024 kg is packed into a small uniform sphere of radius...

As is well known, the relationship between the Schwarzschild radial coordinate (defined by the proper area of a spherical surface) and the proper distance in the radial direction is very different for the exterior and interior solutions. This makes it difficult to visualize what happens if we...

Hi there. I am trying to plot the fabric of spacetime caused by an object using the schwarzchild solution. The idea is to replace one of the basis of space with time. I have computed R_{\mu\nu}, R and T_{\mu\nu} but I'm stuck here. How do I get to the equation of the surface from here? Any help...

Consider the Schwarzschild black hole vacuum solution. Now let a test particle drop from "coordinate rest" at a finite r, and watch it fall in. Is there a coordinate transformation in which we go to a rotating frame where the black hole is now a Kerr black hole and the test particle follows...

I'm creating this thread to discuss some issues raised by kev in the Understanding maximally extended Schwarzschild solution[/color] thread, to avoid diverting that thread from its original question. As any fule kno, the problem with Schwarzschild coordinates is their coordinate singularity...

Given that the Newtonian 'radius of escape' for light is given by the relation \frac{1}{2}v^2_{esc}=\frac{GM}{R}<\frac{1}{2}c^2 from which we get the same value as the Schwarzschild critical radius, R_{crit}=\frac{2GM}{c^2} why can't we identify R with the Schwarzschild coordinate r ? The...

I'm going to use the notation in this Wiki article, and refer to the diagram therein. I assume the information here is essentially correct, aside from the fact the axes on the diagram should be T and R. Firstly, I wonder what sort of uniqueness properties this space-time is supposed to have...

Looking for the Schwarzschild Solution for this equation: ds^2 = -A(r) / c^2 * dr^2 - r^2 / c^2 *(d\\theta^2 +(sin(\\theta))^2 *d\\phi^2) + B(r) * dt^2 where A(r) = 1 / (1-2*m/r) And B(r) = (1-2*m/r) From this can be calculated the co- and contra-varient metric tensors and...

hi, i am trying to figure out the Schwarzschild Radius of myself but i don't know how to find the gravitational constant in the equation. G=6.67 x 10-11N(M/kg)2. What do i plug in on the N(M/kg)2? is that my mass and KG? Earth's? not quite sure... please let me know. Thank you

When people appear to be getting very confused about the weird nature of black holes, I normally respond with answers based on standard black hole theory, but I sometimes feel I should also call attention to the point that some people now think that the "black hole" solutions to the...

I was looking into the geodesic equations for the Schwarzschild metric and I noticed a discrepancy between two sources: According to http://www.mathpages.com/rr/s5-05/5-05.htm (near the bottom) the second derivative of the azimuth angle is \frac {d^{2} \phi}{d \lambda ^2}=\frac {-2}{r}...

I've recently been wondering what the exact relationship is between apparent distances to objects as seen by an observer within a spherical gravitational potential well (described by the Schwarzschild solution) compared with distance as seen by an outside observer. I've decided that the...

Recently I read that from the perspective of a distant observer (r \gg r_s =\frac{2GM}{c^2}) the speed of a beam of light moving directly towards the center of a spherical (non-rotating, non-charged) object decreases because if we set ds^2=d\theta ^2 =d\phi ^2 = 0 then \frac...

We could imagine a rod moving fast enough to compress it within its own Schwarzschild radius. Should it collapse into a black hole? Or is the rod's own reference frame, where it isn't compressed, the one that makes decisions here?

From the Schwarzschild solution.This solution has two singularities,one at r = 0 and one at r = 2M.I have a questions 1.Every Mass has these singularities ? 2.For singularity at r = 0 it is the center of mass ? thank you

Considering the simple case of two observers O1 and O2 lying on the same radius at positions r=r1 and r=r2 respectively. Using a result from Stephani(1) I work out that the ratio of frequencies of light sent radially between these observers is given by this ratio, numerator and denominator...

Say, does anyone happen to know the non-zero components of the Riemann (curvature) tensor for the Schwarzschild metric using r,\phi,\theta and t? Thanks.

http://camoo.freeshell.org/30.5quest.pdf" Latex source below, please click on link above, though. I've been working through the exercises in the Penrose book "The Road to Reality". There's one that I'm really puzzled about. He's talking about an "eternal" black hole - never created...

Can a 4-dimensional manifold with the Schwarzschild metric be embedded into a flat manifold of 5 (or more if necessary) dimensions? In other words, are there functions of t,r,\theta , \phi and M such that if x_1 = f_1 (t,r,\theta ,\phi ,M) x_2 = f_2 (t,r,\theta ,\phi ,M) . . etc...

I've read Schwarzschild paper and I don't understand his conditions "The solution is spatially symmetric with respect to the origin of the co-ordinate system in the sense that one finds again the same solution when x,y,z are subjected to an orthogonal transformation(rotation)" Could...

Homework Statement Calculate the four velocity V^i , the four acceleration A^i and the scalar A^i A_i for an observer at r=r_0, \theta = \theta_0, \phi = \phi_0 in the Schwarzschild spacetime with r>2m. Homework Equations The Schwarzschild Metric ds^2 = -\displaystyle...

Hi; I am trying to find the geometry of a near-extremal D3 brane. I have been told that this geometry is the same as the 5D analog to the Schwarzschild metric with a negative cosmological constant. Trying to mimic Schutz (Ch 10) I tried plugging the metric...

According to Wikipedia, if the metric was vacuum, spherically symmetric and static the Schwarzschild metric may be written in the form: ds^2=((1-2GM/(c^2r))^-1)*dr^2+r^2*(dtheta^2+sin(theta)^2*dphi^2)-c^2*(1-2GM/(c^2r))*dt^2 I need someone to help me to derive an expression from the...

. They understand the classical Schwarzschild radius argument for black hole formation. They have bare rudiments of special and general rel. I sound like an idiot saying "there's this anti-gravity" force that kicks in when the collapsing system gets really big. Any help?

I have a problem with the formula for obtaining the Schwardzchild's radius. Karl Schwardzchild substituted the speed of light in the escape velocity's formula for a body to obtain the Rc(critical radius as he called it). He used this form the proven deduction that light is the speed limit for...

Hi, I am new to this forum so I apologise if a similar thread already exists. I am trying to resolve the implications on space and time as you approach a black hole event horizon with respect a distant observer and an onboard observer. My issue relates to combining the effects of both...

If one rewrites the Schwarzschild solution in terms of a radial coordinate R = r - 2GM where r is the Schwarzschild radial coordinate (as for example is done by Marcel Brillouin in his 1923 paper where he explains why he considers that r = 2GM is effectively the origin), then all of the factors...

Re-Poll: We are in a Schwarzschild black hole--T or F? Would I be correct to say that time can "run" either way? That is, in physics, time can be forward or backward. I realize that this language is loose bigtime. Here's my problem... Matter added to a black hole is added...

The solution for the Schwarzschild metric is stated from reference 1 as: ds^2=- \left(1-\frac{r_s}{r}\right) c^2 dt^2 + \left(1-\frac{r_s}{r}\right)^{-1}dr^2+r^2(d \theta^2 +\sin^2 \theta d \phi^2) The solution for the Schwarzschild metric is stated from references 2 as: ds^2 = \left(1 -...

Where can I find an elementary discussion of the orbits of particles and light rays in Schwarzschild de Sitter spacetime showing the effective radial potential, the rotational speed of circular orbits etc ? I'm sure I can derive everything mimicking Hartle's textbook treatment of...

Forgive a question from a mere piker in GR who has got interested in something he can't find the answer to: What is the metric and coordinates for a radial free-faller in Schwarschild? Let's specify we drop him radially from some r0 and he sets his clock to 0 and drops. I'm imagining...

We are in a Schwarzschild black hole--T or F? What I am wondering is WHO HERE THINKS WE ARE IN A SCHWARZSCHILD BLACK HOLE where the black hole event horizon coincides with one of the two well-known cosmology horizons? There are a couple of well-known horizon radii that we hear about a bunch...

i am trying to understand why dr/dTau must be negative for a future-directed (physical) observer in the Schwarzschild metric. it says "we also know (e.g. from the Kruskal picture) that the sign of dr/dTau must be negative for a "future-directed" (i.e. physical) observer" i am probably...

If you have two black holes separated by more than one Schwarzschild radii, given a location at: The event horizon of one of the black holes. A location between both black holes A location on the axis that passes the centers of both black holes. Wouldn't the potential there actually be less...

The Schwarzschild solution to the EFE has the (possibly not physical) 'two sided' view (aka wormhole). Anyone know what would happen in a thought experiment if you added mass to one side of the wormhole? So say mass was M (which is seen from both sides). If you add dM to one side, (say 50%)...

I need to write Schwarzschild Metric, that is in spherical coordinates, into the form that has the metric tensor. Now, if the first the term of the metric is: \Large (ds)^2=f(r)c^2dt^2-... and x0=ct, then the first component gij of the metric tensor g is supposed to be: \Large...

Hello, folks - here is a question that I have been pondering for about 20 years. As I understand it, the Schwarzschild radius can be thought of as a measure of how much mass can fit within a given space before that space warps from gravity to such an extent that it acquires an event horizon...

The Rindler geometry and its horizon can be obtained by a simple succession of Poincaré transformations to match the frame of an accelerated observer. By combining this SR result and the equivalence principle it follows that a uniform gravitational field is represented by the Rindler metric and...

Hi everyone! I was trying to solve this question following the Hartle's book (Gravity: an introduction to Einstein’s general relativity) , exercise 9.15, but I don't know how to do the expansion of (1-2GM/c^2r) in powers of 1/c^2... I know this sounds easy, but I couldn't get the expression...

I am a bit confused about the Schwarzschild radius perhaps someone can help me here. The Schwarzschild radius for a black hole is defined as the distance between the center of mass and the event horizon. Now in GR this distance should not be the arc length of the geodesic but the actual...

From an https://www.physicsforums.com/showthread.php?t=140501", a new question comes to me. Is there a known generalisation of the Schwarzschild geometry when the cosmological constant is positive? Are there still black-holes in this case? Are there small modifications to the Newtonian...

Today, as I guess, there are good indications that black-holes are a reality. But let us go back in time and pretend we are physicists in 1916 or a few years later. Schwarzschild lectures us about its static and spherical solution to the Einstein's equation. The consequence is striking: any...

Dear all, I would like to know about a possible plane Schwarzschild geometry. This would be the analog of a uniform and infinite gravitational field, or a uniform acceleration. I would like to compare it with the solution of the uniformly accelerated motion in SR. Thanks,

My Java applet gravity simulator http://www.gaugegravity.com/testapplet/SweetGravity.html draws beautiful orbits, however the GR simulation is very badly broken as one can tell when comparing it with Newton at long distances. The source code is at...

Hi. I've got a quick question on Penrose diagrams for the Schwarzschild space-time that I'd appreciate some comments on. In standard (t,r,\theta,\phi) coordinates the Schwarzschild metric is ds^2 = -\left(1-\frac{2M}{r}\right)dt^2 + \left(1-\frac{2M}{r}\right)^{-1}dr^2 + r^2 d\Omega^2. The...

I posted a thread in the Homework section on my attempt to find the Schwarzschild solution using Cartan's method instead of the orthodox Christoffel symbol method. Unfortunately I wasn't getting any help :redface: Then I was asked to move the thread to this section because I may get more...