# What is Schwarzschild radius: Definition and 48 Discussions

The Schwarzschild radius (sometimes historically referred to as the gravitational radius) is a physical parameter that appears in the Schwarzschild solution to Einstein's field equations, corresponding to the radius defining the event horizon of a Schwarzschild black hole. It is a characteristic radius associated with any quantity of mass. The Schwarzschild radius was named after the German astronomer Karl Schwarzschild, who calculated this exact solution for the theory of general relativity in 1916.
The Schwarzschild radius is given as

r

s

=

2
G
M

c

2

,

{\displaystyle r_{s}={\frac {2GM}{c^{2}}},}
where G is the gravitational constant, M is the object mass, and c is the speed of light.

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1. ### B Black hole electromagnetic spectrum

Of course neither a single Schwarzschild nor a single Kerr black hole, nor a pair of these has an emission spectrum, other than the Hawking one. (Nordström and Newman holes must have it while in binaries, but they are not common). But not having emission spectrum does not rule out having...
2. ### I A mirror behind the event horizon

Thought experiment: What will happen if you place a mirror behind the event horizon and turn on the light in its direction?
3. ### 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...
4. ### 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?
5. ### 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?
6. ### 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...
7. ### 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?
8. ### 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...
9. ### 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...
10. ### I Coordinate singularity at Schwarzschild radius

I would like to ask how rigorous is the statement that Schwarzschild metric has coordinate singularity at Schwarzschild radius. The argument is that singularity at Schwarzschild radius appears because of bad choice of coordinates and can be removed by different choice of coordinates. However...
11. ### I Schwarzschild Radius: Calculating V(esc.) & R

Correct if I'm wrong. V(esc.)=(2GM/R)^1/2 that is equal to R=2GM/V^2 putting v=c,we get R=2GM/c^2 by putting the value of G,M,C we get schwarzschild radius=1.46*10^-27 m/kg
12. ### B Schwarzschild Radius: Compression Inside Black Holes

Learning about Schwarzschild radius from Wikipedia: Is it accurate to say any object of mass crossing the event horizon of a black hole is compressed sufficiently to have its own Schwarzschild radius, becoming a black hole itside of a black hole?
13. ### I Schwarzschild Radius of All Matter & Energy in Known Universe

Including dark matter but not including dark energy, what's the Schwarzschild radius of the known universe? Actually, let me put it another way. What's the SR of all the matter and energy thought to be created at the Big Bang? So that would include not just all the matter we see but also all the...
14. ### What Happens to Mass When Black Holes Move?

I've recently read a new article that said that the recent gravitational waves might have had 2 black holes in a star that gave me a question, because you need masses to move or accelerate to generate gravitational waves, what happens to the mass inside of the star? because black holes's space...

Is this the proper formula for calculating the Schwarzschild radius of a black hole? rs = 2GM / c2 If it is not, or if anyone has one that might work better, could you refer it to me?

I have read that the Schwarzschild radius of a black hole with the mass-energy of the observable universe is roughly equal to the actual Hubble radius of 13.8 billion light years. And I have read that contrary to some popular esoteric interpretations such as "the universe is a black hole", "we...
17. ### Schwarzschild Radius Derivation: Is it Possible Classically?

Is it possible to derive r=GM/c^2 classically(as in Newtonian gravity) without using eeinstein field equation?
18. ### Minimum Orbital Radius Around Black Holes

Hi there, I was reading one of my textbooks and I had a thought. For a black hole, there is minimum orbiting radius of ##R_{min}=3R_s## where ##R_s## is the Schwarzschild Radius. This minimum orbit is created by the fact that in order to obtain an orbit of that radius around a black hole, you...
19. ### 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...
20. ### 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...
21. ### 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?
22. ### 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...
23. ### 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...
24. ### (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...

Comment, discuss and explain please. Thanka
26. ### 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...

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...
28. ### 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...
29. ### 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...
30. ### 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...

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...
32. ### 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...
33. ### 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...
34. ### 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...
35. ### 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...
36. ### 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...
37. ### 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...

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?
39. ### 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...
40. ### 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...

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...
42. ### Calculate Schwarzschild Radius of Earth-Sized Mass

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...
43. ### Schwarzschild Radius and gravitational constant

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
44. ### Length contraction compression and Schwarzschild radius

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?
45. ### Exploring Black Hole Formation: Schwarzschild Radius and Relativity

. 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?
46. ### Understanding Schwarzschild Radius Formula & Escape Velocity Calculation

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...
47. ### Schwarzschild radius of a black hole

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...
48. ### Hawking Radiation: What it is and How it Relates to the Schwarzschild Radius

if schwarzschild radius is a pt. at which no information can come back after going in. Then what is Hawking radiation?