What is Schwarzschild: Definition and 324 Discussions

Schwarzschild ([ˈʃvaʁtsʃɪlt]) is a German surname meaning "black sign" or "black shield".
Those bearing the name include:

Karl Schwarzschild (1873–1916), physicist and astronomer
Steven Schwarzschild (1924–1989), philosopher and rabbi
Henry Schwarzschild (1926–1996), civil rights activist
Martin Schwarzschild (1912–1997), astronomer
Shimon Schwarzschild (1925–), environmental activist
Luise Hercus (née Schwarzschild) (1926–), linguist

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  1. P

    D'Inverno derivation of Schwarzschild solution

    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...
  2. G

    Inverse coefficients of dt & dr in Schwarzschild

    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...
  3. P

    Understanding proper distance in Schwarzschild solution.

    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...
  4. PeterDonis

    Family of nested spheres in Schwarzschild spacetime

    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...
  5. A

    Schwarzschild Circular Orbits Problem

    Homework Statement Find the linear velocity of a particle in a circular orbit of radius R in the Schwarzschild geometry as would be measured as by a stationary observer stationed at one point on the orbit. (It's problem 10 in chapter 9 of Hartle, if that helps) Homework Equations The...
  6. A

    Schwarzschild Metric - Rindler coordinates

    Hello, well I just read a paper by Atish Dabholkar and Ashoke Sen, titled "Quantum Black Holes", pp. 4-5 as shown below and I tried to find d\xi^{2}\frac{2GM}{\xi}=d\rho^{2} like this which is different from the eq. in the paper. So, could somebody please help me to find my...
  7. P

    Towards a Generic Integral for Tau in Schwarzschild Radial Motion

    I am trying to formulate an integral representing Tau between two r-values for radial motion in the Schwarzschild solution. There are a few possibilities: 1. Free fall from infinity with zero initial local velocity (v0=0 and r0 -> infinity) 2. Free fall from infinity with a given local...
  8. L

    When the Schwarzschild radius is inside the star

    What happens to the Schwarzschild metric for an isolated non-rotating body when the horizon radius is inside the body? As I remember from classical physics all of the gravitational pull on an object inside a shell cancels out so it would seem that the horizon radius can not include any mass...
  9. J

    Deriving the Schwarzschild Metric

    I've worked through a common-sense argumenthttp://www.mathpages.com/rr/s8-09/8-09.htm" showing the time-time component of the Schwarzschild metric g_{tt} = \left (\frac{\partial \tau}{\partial r} \right )^2\approx 1-\frac{2 G M}{r c^2} On the other hand, I've not worked through any...
  10. C

    Black Holes Schwarzschild radius

    Is Schwarzschild radius trying to state the gravitational field on the event horizon of a black hole? If not, what is it trying to state? Can you give me a example using his formula to figure out the gravitational force of a black hole in the event horizon? Do you have any links I can...
  11. TrickyDicky

    Schwarzschild radius and curvature

    In the Schwarzschild spacetime setting we have a vacuum solution of the Einstein field equations, that is an idealized universe without any matter at the geodesics that are solutions of the equations. This spacetime has however a curvature in both the temporal and spatial component that comes...
  12. L

    Schwarzschild Metric - Need help understanding

    Alright, first things first, I'm a grade 12 student residing in Ontario, Canada and I'm relatively new to these forums and to the world of physics. I'm doing my grade 12 ISU and I've taught myself how to work around spherical coordinate systems, however, the schwarzschild metric confuses me...
  13. E

    The Schwarzschild (Exterior) Solution

    This might be a silly question to people who are have more practice in this subject, but how does the Schwarzschild Solution/metric have a singularity at r=0 if it is only valid outside the gravitational mass (black hole)? wouldn't that be in the interior solution, describing the inside of a...
  14. K

    Schwarzschild radius question.

    An object is accelerated close to c. Does the relativistic mass contribute to the sch. radius as seen by an observer? Is it simultaneously a black hole and not a black hole?
  15. L

    Solving the Radius of a Collapsing Star in Schwarzschild Geometry

    I have that \left( \frac{dR}{d \tau} \right)^2 = ( 1 - \epsilon)^2 ( \frac{R_{\text{max}}}{R}-1) describes the radius of the surface of a collapsing star in Schwarzschild geometry. I need to show it falls to R=0 in time \tau = \frac{\pi M}{(1-\epsilon)^{3/2}} So far I have rearranged to get...
  16. jfy4

    What Are the Killing Vectors of the Schwarzschild Metric?

    Hi, Does anyone know the explicit form the the killing vector fields for the Schwarzschild metric, specifically in the basis ##\partial_{\alpha}##? On that note, Is the Schwarzschild geometry a space of constant curvature? does it admit 10 killing vectors?
  17. P

    Schwarzschild vs Gullstrand–Painleve and event horizons

    Now my question is about these two systems is how they handle time at the event horizon. Now if I understand correctly the Schwarzschild coordinates states that as you reach the event horizon of a black hole that time reaches infinity thus time has stopped using this system. Now with the...
  18. A

    The Schwarzschild Solution and how it led to the discovery of Black Holes

    I'm currently researching for the term paper of my class on black holes and the topic I selected is the one in the title. I've found some good information so far, but I don't feel like I have enough to get an A without a bit more. I'm curious if anyone has any resources that would aid this...
  19. L

    Is the Schwarzschild spacetime with negative mass geodesically complete?

    Hi, If you look at the Schwarzschild geodesics for negative mass, I believe that radial null rays can hit the naked singularity in finite value of affine parameter? but if L <>0 then the null rays get repelled away from r=0 no matter what their energy? does this mean the spacetime is null...
  20. Demon117

    What is the Lagrangian for geodesics in Schwarzschild coordinates?

    For pure interest I have been trying to solve for the geodesics of the Schwarzschild metric. To do so I know I need to find the explicit Lagrangian for the variational principle for geodesics in this spacetime in Schwarzschild coordinates. How do I derive this lagrangian? I know that the...
  21. L

    Why is r treated as a time coordinate in region 2 of the Kruskal manifold?

    Show that in region 2 of the Kruskal manifold, one may regard r as a time coordinate and introduce a new set of spatial coordinates x such that ds^2=-\frac{dr^2}{(\frac{2M}{r}-1)} + ( \frac{2M}{r}-1) dx^2 + r^2 d \Omega^2 Hence show that every timelike curve in region 2 intersects the...
  22. WannabeNewton

    General Question on Schwarzschild Metric

    Hi guys I have a quick question on the Schwarzschild Metric: Since the metric is a solution to the EFEs does it intrinsically have the curvature of the gravitational field embedded in the metric? If so is it represented by the time and spatial components of the metric? If not could you please...
  23. D

    Timelike geodesic equations for the Schwarzschild metric

    I'm following a slightly confusing set of notes in which I can't tell what exactly the timelike geodesic equations for the Schwarzschild metric are (seems to have about 3 different equations for them). How are these derived, or alternatively, does anyone have a link to a site in which they...
  24. D

    Deriving the Schwarzschild solution

    Right so there's this part in my notes where we begin to derive the schwarzchild solution. There's a substitution part I don't understand fully (I think) but I'll start from the beginning...The Schwarzschild Solution. The solution corresponds to the metric corresponding to a static, spherically...
  25. V

    Eddington Finkelstein coordinates in the Schwarzschild spacetime

    Do the Eddington-Finkelstein coordinates allow to cover the maximal analytic extension of the Schwarzschild spacetime? ans if not what region do they cover?
  26. Z

    Schwarzschild metric in 3-dimensional space-time

    I'm trying to find Schwarzschild solution for 3-dimensional space-time (i.e. time\otimes space^2). The problem is, I can't take the 4-dimensional solution \[ds^2=\left(1-\frac{r_g}{r}\right) dt^2-\left(1-\frac{r_g}{r}\right)^{-1} dr^2-r^2\left(d\theta^2+sin^2\theta d\phi^2\right)\] and...
  27. nomadreid

    Entropy of Schwarzschild black holes

    I am trying to reconcile three things: (1) The entropy of a black hole is proportional to the logarithm of the number of possible states of that object to give the same event horizon. (2) The only parameter for a S. black hole is its mass, since its electric charge and angular momentum are...
  28. M

    Negative Schwarzschild mass parameter?

    I know that a Schwarzschild metric cannot have negative mass parameter. But what about regions? It is possible to have negative mass parameter between two spherical shells? If not, what is the argument?
  29. P

    The Schwarzschild Metric - A Simple Case

    The Schwarzschild Metric - A Simple Case of How to Calculate! There is thread open at https://www.physicsforums.com/showthread.php?t=431407 about tidal effects but there may be too many question or the chunk asked is simply to large to handle. At any rate, perhaps it is better to have a very...
  30. P

    Tidal Effects in the Schwarzschild Metric

    Assume we have a non rigid ball. When this ball is radially free falling in a Schwarzschild metric the height increases while the width decreases due to tidal effects. How do we calculate the ruler width and height in terms of R and m? When we have two of those balls radially free falling...
  31. bcrowell

    Schwarzschild metric not stationary inside the horizon?

    The Schwarzschild metric, described in Schwarzschild coordinates, has a Killing vector \partial_t. This vector is timelike outside the horizon, but spacelike inside it. Therefore I would think that a Schwarzschild spacetime should not be considered stationary (which also means it can't be...
  32. P

    Schwarzschild solution without matter

    Is it theoretically possible that the metric in the whole universe would be described by Kruskal extension of Schwarzschild solution of Einstein equation and in the universe would be no matter at all (vaccum solution everywhere). What's the interpretation of parameter m characterising...
  33. O

    Schwarzschild Radius, Constantcy of Light speed, and Time Dialation

    First off, I'd like to point out that I am by no means an expert in this area, and I am only doing some casual research as a personal interest topic, and have some further unanswered questions that I'm unable to find reasonable answers for. These questions are all inter-related, so I'll post...
  34. P

    Schwarzschild metric as induced metric

    According to Nash theorem http://en.wikipedia.org/wiki/Nash_embedding_theorem" every Riemannian manifold can be isometrically embedded into some Euclidean space. I wonder if it's true also in case of pseudoremanninan manifolds. In particular is it possible to find a submanifold in...
  35. P

    Schwarzschild and Newton potential

    Expressing the Schwarzschild in the Weyl form allows one to use the Newton potential. The Newton potential here is, perhaps surprisingly, equivalent with a rod of length 2M and mass M. Also the rod is exactly positioned where r = 2M. Furthermore if we decrease the length of the rod to the...
  36. Jonathan Scott

    Local curvature of surface just outside Schwarzschild radius

    Suppose one had a solid sphere just slightly larger than its Schwarzschild radius. What would the curvature of the surface look like to a local observer? Would it curve downwards, or appear flat, or curve upwards? If my brain was working a bit better today, I'd calculate it myself from the...
  37. P

    Heuristic approach to the Schwarzschild geometry - Accident of deeper meaning?

    The Schwarzschild solution can be obtained by using Newton for the weak field. However it turns out that this in fact is the exact solution. Is this coincidence or is there more to it? Opinions? http://arxiv.org/pdf/gr-qc/0309072v3
  38. stevebd1

    Energy in Schwarzschild geometry

    From In Wheeler and Taylor's 'Exploring Black Holes', on pages 3-12, the equation for energy in Schwarzschild geometry for an object in free fall is- \frac{E}{m}=\left(1-\frac{2M}{r}\right)\frac{dt}{d\tau}=1 where \tau is proper time conventionally expressed in Schwarzschild geometry as...
  39. H

    Deriving the Schwarzschild metric just by using the equivalence principle

    I've read a few papers about derivation of the Schwarzschild metric by using the equivalence principle ( http://cdsweb.cern.ch/record/1000100/files/0611104.pdf" )... but I couldn't understand them completely they assume , According to Einstein’s equivalence principle, that the influence of...
  40. J

    Understanding the 3 coordinate systems for a Schwarzschild geometry

    Hello, There are 3 main coordinate systems for a Schwarzschild geometry : Lemaitre-Rylov (LR), Eddington-Finkelstein (EF), Kruskal-Szekeres (KS). Thanks to my readings, I know thaht KS coordinates are better than EF coordinates and that EF coordinates are better than LR coordinates. But, I...
  41. E

    Schwarzschild Proton: Thoughts & Paper Review

    What are everyones thoughts? Just google the paper if you havn't read it yet.
  42. Z

    Question about Schwarzschild radius

    Okay, correct me if I am wrong but Schwarzschild radius of an object if it squeezed to a radius of that point it will collapse into a gravitational singularity and become a black hole. For example, if the sun has a Schwarzschild radius of about 3 kilometers. If we were to be squeezed the sun to...
  43. D

    Physical meanings of universal coordinates in schwarzschild metric

    The metric due to the gravitational field of a spherical mass is described by the schwarzschild metric ds2 = c2 (1 - R/r) dt2 - (1 - R/r)-1 dr2 - r2 d\Omega 2 Where \Omega is the solid angle, and R is the schwarzschild radius. What are the physical meanings of the coordinates t and r...
  44. A

    Schwarzschild affine connection

    Hi all! Anyone knows where to find, online or on a book, the affine connection for the schwarzschild metric? Thanks
  45. Orion1

    Schwarzschild and Reissner–Nordström metrics

    A non-rotating J = 0 and charge neutral Q = 0 spherically symmetric metric is defined by the Schwarzschild metric: c^2 {d \tau}^{2} = \left(1 - \frac{r_s}{r} \right) c^2 dt^2 - \frac{dr^2}{1 - \frac{r_s}{r}} - r^2 d\theta^2 - r^2 \sin^2 \theta \, d\phi^2 \right) The next metric form for a...
  46. J

    Schwarzschild & Kerr black holes geometries

    Hello Let's consider a Schwarzschild BH. A photon (or a massive particle) crossing the event horizon cannot be static : the r (radial) coordinate becomes a temporal coordinate. Therefore, the photon falls towards the central singularity (r=0). There is no way for him to escape : the...
  47. N

    Light ray paths near schwarzschild blackhole

    hey there, I'm interested in (eventually) simulating light ray paths near black holes, starting with schwarzschild black holes and working my way to kerr-newman black holes. I have a good understanding of the nature of black holes but have trouble when it comes to the equations. My background...
  48. A

    Solving the Transformation to Eddington-Finkelstein in Schwarzschild Geometry

    Homework Statement I'm having problems seeing how the transformation to Eddington-Finkelstein in the Schwarzschild geometry works. Any help would be great! Homework Equations So we have the Schwarzschild Geometry given by: ds^2 = -(1-2M/r)dt^2 + (1-2M/r)^-^1 dr^2 +...
  49. D

    Schwarzschild solution and velocity of stationary observer

    Hey all, I suddenly find myself very confused about velocity and coordinate systems. I have a feeling this is very simple, but sometimes the mind just curls up, you know? ;) When you ask what an observer observe, you need to see things from his point of view - his reference frame. And his...
  50. N

    Does Schwarzschild Solution work inside a massive body?

    The Schwarzschild Solution to Einstein's Field Equations for gravity are said to be exact when outside a spherically symmetric massive body. My question is, can the Schwarzschild Solution also be used inside the massive body, such as a neutron star. In Newtonian gravity we can find the...
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