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. S

    Schwarzschild Light Anisotropy: Explained

    I was just reading an article on wikipedia about the Schwarzschild metric and I've red that these coordinates imply that the coordinate speed of light is anisotropical in some way. Can somebody explain to me when does this occur and how does it exactly occur, in which directions etc.? Thank you.
  2. Matterwave

    Proper mass vs Schwarzschild Mass

    Hello guys, I am reading through Wald chapter 6 section 2 on the interior Schwarzschild solution. In it he states that matching the interior solution to the exterior (Schwarzschild) solution gives a Schwarzschild mass of $$M=4\pi\int_0^R \rho(r)r^2 d$$ This would presumably be the same mass...
  3. P

    Ricci tensor of schwarzschild metric

    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...
  4. B

    Gravitational red- or rather blue-shift when approaching Schwarzschild radius

    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...
  5. C

    Schwarzschild Spacetime: Ellipsoidal for Moving Observers?

    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...
  6. K

    Orbital period around Schwarzschild radius

    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...
  7. avito009

    If the sun becomes a black hole will its schwarzschild radius change?

    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?
  8. B

    Photon that "fits" into its schwarzschild radius

    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...
  9. F

    Schwarzschild Radius of Masses Other Than Black Holes

    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...
  10. N

    (What is) Schwarzschild Radius and Potential Energy

    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...
  11. ChrisVer

    Understand Degeneracy of Metric at Schwarzschild Singularity

    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...
  12. H

    Einsteins-Rosen bridge different from schwarzschild black hole 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...
  13. V

    Killing vecotrs of Schwarzschild metric

    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...
  14. V

    Understanding the Schwarzschild Coordinate r in Spherical Symmetric Spacetime

    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)}...
  15. TrickyDicky

    Is Schwarzschild spacetime parallelizable?

    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...
  16. Y

    Fuel conservation near a Schwarzschild black hole

    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...
  17. ryanuser

    Is schwarzschild radius, where the whormholes could be made?

    Comment, discuss and explain please. Thanka
  18. Philosophaie

    Schwarzschild Solution for Planetary Motion: Find x'i from xi

    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}##...
  19. G

    Derivation of Schwarzschild radius from escape velocity

    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...
  20. Y

    Schwarzschild metric in terms of refractive index

    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...
  21. S

    Schwarzschild Radius Explanation?

    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...
  22. darida

    Hawking Mass in Schwarzschild Spacetime

    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...
  23. tom.stoer

    Radial Schwarzschild geodesics - again

    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...
  24. M

    Is Schwarzschild metric more intuitive?

    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...
  25. A

    Energy left of body falling down to Schwarzschild radius

    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...
  26. K

    Schwarzschild radial light rays

    Homework Statement Consider Schwarzschild spacetime. A) Show that the equation for ingoing/outgoing radial light rays is dt/dr = +-r/(r-2m) in t,r coordinates and dt*/dr = -1, dt*/dr=(r+2m)/(r-2m) in t*,r coordinates B) Sketch the local light cones in t,r and t*,r coordinates C) Explain...
  27. E

    Do Schwarzschild Black Holes exist?

    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?
  28. A

    Meaning of Schwarzschild solution in isotropic/anisotropic coordinates

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

    Schwarzschild conservation of angular momentum

    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...
  30. liometopum

    Definiton of Schwarzschild radius clarification request

    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...
  31. G

    Exploring the Schwarzschild and Reissner-Nordstrom Metrics

    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...
  32. T

    Schwarzschild radius of a proton

    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...
  33. A

    Black hole event horizon radius = Schwarzschild radius?

    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...
  34. J

    Life below the Schwarzschild radius

    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...
  35. N

    Questions about the Schwarzschild metric

    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...
  36. H

    Shape Operator for Schwarzschild spacetime in 2-dim

    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...
  37. H

    Is the Schwarzschild metric dimensionless?

    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...
  38. grav-universe

    Problem with Schwarzschild metric derivation

    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...
  39. grav-universe

    Schwarzschild metric and spherical symmetry

    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.
  40. E

    Solve Schwarzschild Metric: Transformation & Acceleration

    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...
  41. N

    Calculating Proper Time of "A" in Schwarzschild Geometry

    "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".
  42. L

    Bodies of mass near the Schwarzschild Radius

    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...
  43. M

    How Is the Komar Mass of a Schwarzschild Geometry Calculated?

    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...
  44. C

    Star Cluster Within Self Schwarzschild Radius

    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...
  45. N

    Proper time in Schwarzschild Space

    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?
  46. S

    Deriving Schwarzschild Metric: A Simple Method?

    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?
  47. Z

    What are the Christoffel symbols for the Schwarzschild metric?

    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...
  48. B

    General Relativity - Schwarzschild Metric

    Homework Statement A spaceship is moving without power in a circular orbit about an object with mass M. The radius of the orbit is R = 7GM/c^2 (1) Find the relation between the rate of change of angular position of the spaceship and the proper time and radius of the orbit. Homework...
  49. S

    Derive Schwarzschild Eq. without 4D Space/Tensors

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

    Timelike geodesics in Schwarzschild Metric.

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