# 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. ### I Orbital Period In General Relativity

What is the orbital period in General Relativity using the Schwarzschild metric? In classical mechanics, it is something like T=2pi(GnM/a3). Where a is the semi-major axis, this is for a small body orbiting a larger one. I think I have an idea but I am not 100% sure. I am interested in an...

9. ### Schwarzschild radius of the Universe

https://www.msn.com/en-us/news/technology/the-astonishing-scientific-theory-that-says-the-universe-might-be-inside-a-black-hole/ar-AA17lxtF?ocid=msedgdhp&pc=U531&cvid=272cb184de9c48fbbd3b321120e37dac Michio Kaku has often joked, "If you want to know what it looks like inside of a black hole...
10. ### I Karl Schwarzschild: Solving GR on the Eastern Front

Read the bio / fiction chapter on Karl Schwarzschild in Benjamin Labatut’s great Book, and curious on a little color on how he developed the solution - I had thought finding an exact solution in GR was just math chops, but actually any Lorentzian metric is an exact solution, so the difficulty...
11. ### A Connectedness of Boundary Points in Schwarzschild Penrose Chart

In the Penrose chart for Schwarzschild spacetime, the boundary "at infinity" appears to be connected all the way around. I want to explore what that means physically and whether particular boundary points that appear to be connected on the chart actually are. I am using the following notes as a...
12. ### A Schwarzschild Geometry: Evaluating Proper Distance

Schwarzschild Geometry-proper distance. From what I have studied when the Schwarzschild line element is evaluated at constant time and at a constant radius , proper distance becomes a Euclidean distance on the surface of a sphere. What I don't understand is how to evaluate the integral...
13. ### I Schwarzschild Metric & Particle Absorption

The Schwarzschild metric implies a potential different from that of Newtonian gravity. Is there a relationship between it and the process by which particles can be absorbed by other particles? (I haven't studied QFT yet)
14. ### I Differences b/w Schwarzschild Radius & Event Horizon

I understood that the event horizon is a null surface and not a place in space, what is the relationship between it and the Schwarzschild radius? Also, what does the Schwarzschild radius physically represent for example for an object such as a star?
15. ### I Equations of motion for the Schwarzschild metric (nonlinear PDE)

I'm working through some things with general relativity, and am trying to solve for my equations of motion from the Schwarzschild Metric. I'm new to nonlinear pde, so am not really sure what things to try. I have 2 out of my 3 equations, for t and r (theta taken to be constant). At first glance...
16. ### I Adapting Schwarzschild Metric for Nonzero Λ

So, there are a fair amount of metrics designed with a zero value for the cosmological constant in mind. I was wondering if there was some method to modify metrics to account for a nonzero cosmological constant. Say, for instance, the Schwarzschild metric due to its relative simplicity. A...
17. ### I Schwarzschild Radius vs Event Horizon: Black Hole?

Real quick, are the terms "Schwarzschild Radius" and "Event Horizon" for a black hole interchangeable or is there some subtle difference between the two? Just looking for a ballpark answer here
18. ### I Coord. Time Vector Field: Schwarzschild vs Gullstrand-Painleve

Hi, I was reading this insight schwarzschild-geometry-part-1 about the transformation employed to rescale the Schwarzschild coordinate time ##t## to reflect the proper time ##T## of radially infalling objects (Gullstrand-Painleve coordinate time ##T##). As far as I understand it, the vector...
19. ### Space-like trajectory in Schwarzschild spacetime

I'm not sure how to approach this question. So I start off with the fact the path taken is space-like, $$ds^2>0$$ Input the Schwarzschild metric, $$−(1−\frac{2GM}{r})dt^2+(1−\frac{2GM}{r})^{−1}dr^2>0$$ Where I assume the mass doesn't move in angular direction. How should I continue?

32. ### A GR: Is Schwarzschild Spacetime Time-Independent?

I'm a bit confused about GR : what is more significant about the considered spacetime, the metric, which is time-independent, or the embedding (there are already some posts on PF about it), which describes the shape of a manifold, but is time-dependent ?
33. ### I The Schwarzschild Radius: Mass vs. Energy

When calculating the Schwarzschild radius are we supposed to be using the rest mass of the object or its total energy?
34. ### I Energy in the Schwarzschild spacetime

I had a thought that I wanted to share in another thread, but it wandered way off track and quite properly was closed. But I thought the separate idea that I had spawned from the old thread was worthy of posting in a new thread. I do not want to re-open the old thread, though! In flat...
35. ### B Exploring Time Inside a Schwarzschild Black Hole

I notice that in a Schwarzschild black hole, at r=r_{s}/2, the c dt and dr terms are exactly the opposite of what they are in external, normal flat space (Minkowski metric). That is, one gets them by multiplying both terms by negative one. I'm having trouble grasping what this means. An...
36. ### I Calculating Surface Area of Schwarzschild Black Hole w/Weyl Coordinates

Recently, I was tasked to find the surface area of the Schwarzschild Black Hole. I have managed to do so using spherical and prolate spheroidal coordinates. However, my lecturer insists on only using Weyl canonical coordinates to directly calculate the surface area. The apparent problem arises...
37. ### A poor man's way to Schwarzschild Geometry

Can anyone help me get started with this problem? What should I use for Gni? I've tried to produce Tni by working out Rni (using methods developed in an earlier chapter) but the results don't lead me anywhere. I'm really stuck for a way forward on this problem so if anyone can help, it...
38. ### I The proper Schwarzschild radial distance between two spherical shells

For the purpose of this thread the metric is ds2 = - (1-rs/r) c2 dt2 + dr2 / (1-rs/r) where rs = 2GM/c2. (I modified the above from https://jila.colorado.edu/~ajsh/bh/schwp.html .) I assume that the two spherical shells are stationary. Therefore dt = 0. The r coordinate for the radii of the...
39. ### I Study After Schwarzschild Spacetime: What's Next?

For someone who have just finished the study of the (fundamentals) of Schwarzschild spacetime, what would be the next natural topic to study?
40. ### I Solving Confusion About Black Holes, Schwarzschild Radius & Time Dilation

According to the theory, every mass has a Schwarzschild radius associated. Any object whose radius is smaller than its Schwarzschild radius is called a black hole. So in principle is possible to create mini-black holes, it is just a fact of matter condensed. Those mini black holes have their...
41. ### I Strongest Evidence for Trapping Light in Schwarzschild Radius

The concept of that when a photon's trajectory intersects with the Schwarzschild Radius/event horizon, said photon will never exit the Schwarzschild Radius/event horizon. Or any other object besides a photon for that matter. So far what has been the strongest evidence for this prediction?
42. ### Schwarzschild coordinate time integral

I have tried integration by parts where, ##c dt = -\frac{1}{\sqrt{r*}} \frac{r^{3/2} dr}{r - r*} = \frac{1}{\sqrt{(r*)^3}} \frac{r^{3/2} dr}{1 - \Big(\sqrt{\frac{r}{r*}} \Big)^2}## ##u = r^{3/2} \quad \quad dv = \frac{dr}{1 - \Big(\sqrt{\frac{r}{r*}} \Big)^2}## ##du = \frac{3}{2} r^{1/2} dr...
43. ### A Schwarzschild Metric Geodesic Eq: Qs & Answers

I have no idea if this is an “A” level question, but I will put that down. From the Schwarzschild metric, and with the help of the Maxima program, one of the geodesic equations is: (I will have to attach a pdf for the equations...) I believe this integrates to the following, with ...
44. ### I with an exercise about Energy and Schwarzschild Black Holes

The thing is that this is an exercise that I have to show my teacher but I don´t know how to get the answer.The exercise says: "A body of mass m moving in the Keplerian field V = −M/r (in G = 1 units) has a total conserved energy, Etot = 1 /2( m r˙^2 + r ^2ϕ˙ ^2 )− mM/r. Show that the...
45. ### I Active Diffeomorphisms of Schwarzschild Metric

I am trying to understand active diffeomorphism by looking at Schwarzschild metric as an example. Consider the Schwarzschild metric given by the metric $$g(r,t) = (1-\frac{r_s}{r}) dt^2 - \frac{1}{(1-\frac{r_s}{r})} dr^2 - r^2 d\Omega^2$$ We identify the metric new metric at r with the old...
46. ### B Schwarzschild radius of an object is smaller than Planck length

I had this idea when some people said that LHC can produce black hole. Based on the calculation of Schwarzschild Radius, any mass than 9.375×10^7 kg have a Schwarzschild radius smaller than the plank length. Particles inside LHC or other particle accelerator have clearly radii smaller than that...
47. ### I Coordinate time between spatially separated events in Schwarzschild spacetime

Edit: I'm leaving the original post as is, but after discussion I'm not confused over coordinate time having a physical meaning. I was confused over a particular use of a coordinate time difference to solve a problem, in which a particular coordinate time interval for a particular choice of...
48. ### I The Singularity and the Schwarzschild radius

A singularity would be: a location in spacetime where the gravitational field of a celestial body is predicted to become infinite by general relativity in a way that does not depend on the coordinate system. (wiki) If the threshold to get a singularity is reached then space-time curvature...
49. ### I Radius in Schwarzschild Metric: Definition Explained

Hello! I am a bit confused about the definition of the radius in Schwarzschild metric. In the Schutz book on GR (pg. 264, General rules for integrating the equations) he says: "A tiny sphere of radius ##r = \epsilon## has circumference ##2\pi\epsilon##, and proper radius...