What is Singularity: Definition and 428 Discussions
A gravitational singularity, spacetime singularity or simply singularity is a location in spacetime where the density and 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. The quantities used to measure gravitational field strength are the scalar invariant curvatures of spacetime, which includes a measure of the density of matter. Since such quantities become infinite at the singularity point, the laws of normal spacetime break down.Gravitational singularities are mainly considered in the context of general relativity, where density apparently becomes infinite at the center of a black hole, and within astrophysics and cosmology as the earliest state of the universe during the Big Bang/White Hole. Physicists are undecided whether the prediction of singularities means that they actually exist (or existed at the start of the Big Bang), or that current knowledge is insufficient to describe what happens at such extreme densities.General relativity predicts that any object collapsing beyond a certain point (for stars this is the Schwarzschild radius) would form a black hole, inside which a singularity (covered by an event horizon) would be formed. The Penrose–Hawking singularity theorems define a singularity to have geodesics that cannot be extended in a smooth manner. The termination of such a geodesic is considered to be the singularity.
The initial state of the universe, at the beginning of the Big Bang, is also predicted by modern theories to have been a singularity. In this case, the universe did not collapse into a black hole, because currently-known calculations and density limits for gravitational collapse are usually based upon objects of relatively constant size, such as stars, and do not necessarily apply in the same way to rapidly expanding space such as the Big Bang. Neither general relativity nor quantum mechanics can currently describe the earliest moments of the Big Bang, but in general, quantum mechanics does not permit particles to inhabit a space smaller than their wavelengths.
When looking at depictions of black holes, we often get illustrations of a two-dimensional space-time where everything spirals into a "hole". The hole then leads to a singularity usually depicted as a funnel shape. Then there are images of black holes shown as spherical with glowing rings...
Question: The idea of a continuum breaks down for a singularity when a geodesic become incomplete (the breaking of the idea that there was a continuous succession, where no part could be distinguished from neighboring parts, except by arbitrary division), and so with that does this indicate a...
Below is the description from the book. I thought that hyperbolas in the right quadrant are time-like and hyperbolas in the upper quadrant are space-like. If it were so, the surface ##r=0## would be space-like, but the book says otherwise. -- ?
Here's my reasoning.
The event horizon is the point where the escape velocity becomes greater than the speed of light.
This results in the event horizon spacetime boundary having infinite time dilation.
So, that must mean that inside the boundary of the event horizon, time dilation must...
Suppose the universe were to eventually collapse in a Big Crunch [1]. How closely could the universe's final moments resemble those at the beginning of the universe? Could the universe return to its original state exactly in some kind of "Big Crunch" or "Big Bounce" model?
[1]...
Setting: a plane with the standard Cartesian coordinate system. A particle is constrained to the x axis, with position x and moving at speed x dot. Another particle is constrained to the y axis, with position y and moving at speed y dot. The distance between them at any moment is s. It is...
a singularity is assume to be a point without dimensions. When 2 mass particles fall into a black hole in the direction of the centre and separated by small distance, the particle closest to the center will have an acceleration as seen from the other particle as I understood. so distance between...
Consider the FLRW metric.
We pick a specific definition for the scale factor as suggested bellow.
Suppose we have a hypothetical metric having the scale factor defined by
## a(t)=\sin(t) (1+ \text {sgn}(\sin(t)) +\epsilon ##
Does this make sense, mathematically (and physically)?
Like having...
In big bang theories where our universe begins from a singularity (ignoring other theories just now), what would happen if the universe didn't begin as a single point but rather began as energy in an uneven shape? Would we be able to tell from the way the universe is now? Do we know that if the...
Suppose we have a large sphere with thin non rotaring surface of floating iron particles (to prevent that they start a chain reaction making a star instead of a black hole) with a total mass sufficient to form a black hole. with an observer in the center of the sphere. This means the sphere...
I'm wondering about some aspects about black holes (BH) and singularities, but since all my questions have to do mostly with quantum mechanics, I placed this thread in here.
OK, let's assume there IS a singularity in the middle of a BH.
A) Pauli exclusion principle (PEP) says no two fermions...
This old nut is often dismissed as flawed thinking by a naive student. It’s been discussed here too, I know.
However, when you do the math in standard (Schwarzschild-like) coordinates:
Dustball collapse and evaporation in standard coordinates (Arxiv)
A. the (coordinate) speed of light...
Let's say you have two extremal black holes containing the maximum amount of possible charge. Now let's say they're orbiting each other such that they will eventually merge. As the black holes merge they are producing gravitational waves. Once the merger is complete the new black hole mass will...
Since my understanding of these geometries is wrong, I'll do this in numbered steps - the easier to correct my logic.
I think the big problem I have is with the time dimension. There seems to be a presumption that the time vector will drive a falling object into a central singularity. But how...
Assume a Schwarzschild black hole. Near the event horizon other than Hawking radiation the behavior of matter and energy are fairly accuratly described by general relativity. How close can one get to the center (the singularity based on GR) before one must switch to a quantum gravity theory...
Tad Williams’ Otherland series has a scene where the characters are drawn to a temple no matter which direction they try to walk, as if space itself is curved.
This is kind of the intuition I get when a physicist talks about the spacetime interval kind of flipping past an event horizon: if you...
When calculating the proper time along a timelike radial geodesic, with the initial condition that object the starts at rest at some Schwarzschild coordinate ##r_0>r_S##, i.e.
\frac{\mathrm{d}r}{\mathrm{d}\tau}\Bigg|_{r=r_0}=0\;,
after using the equations of motion one finds...
How does the Singularity produce all of the diverse matter and properties that we observe in the Universe today?
Although Theories like Quantum Gravity have somewhat produced indications about the existence of Graviton particles and allow some form of Gravity to operate within the laws of...
So, for this exercise I'm considering the removable singularity for ##x=2## to cause ##f(2)## to be different from ##\lim_{x \to 2}f(x)##.
But as soon as I write everything down, I get stuck here: ##\lim_{x \to 2}f(x)\neq\frac{4(a-4)}{0}##
How do I calculate ##a##?
Dear Everyone,
I am wondering how to use the integral formula for a holomorphic function at all points except a point that does not exist in function's analyticity. For instance, Let f be defined as $$f(z)=\frac{z}{e^z-i}$$. F is holomorphic everywhere except for $$z_n=i\pi/2+2ni\pi$$ for all...
A Paradox of the black hole is that GR states the stationary observer experiences time dilation, while the inflating observer experiences no time dilation. By the time the infalling observer reaches the event horizon, an infinite amount of time passes for the other frame of reference. But...
So I have been watching the latest edition of PBS Space Time ( I know, not a proper resource/guide,) and it seems to be a bit confusing as to whether you would hit the ring singularity at the center or not.
On the one side he claims that the geodesics end there but on the other he claims you...
The Big Bang is sometimes described as started from a singularity, which I have interpreted as meaning that its characteristics are undefineḍ. If that is the case, can we not even say that the Universe as a singularity was still infinite? Otherwise we are implying that the singularity was...
As I understand Penrose proved there must a be a singularity using certain assumption for black holes and something called a "trapped surface:. Can anyone give a lay person explanation of what this and "anti trapped surface" are? How were they used in the singularity theorems and what was new...
I have a question about the history of cosmology, hope its okay to ask here. Who was the first person since Einstein's Gr to point out a singularity in cosmology? I know Freidman talked of an expanding universe and Lematire a primeval atom. But were there any explicit mentions of the density of...
Since Planck length is a distance unit of space-time which cannot be further subdivided, would that not imply that an electron, or singularity, or any other point particle cannot actually be a “point”, but must rather be a spherical volume with a Planck length diameter?
i realize this may well...
Due to strong gravitational tidal forces, any living observer will die and any macroscopic measuring apparatus will be destroyed before it reaches the black hole singularity at the center of a macroscopic black hole. Hence the black hole singularity cannot be observed, so from an experimental...
Summary: different methods give different results. They are not consistent.
Summary: different methods give different results. They are not consistent.
I use two different methods to detect whether a matrix is singular. The result of calculating the determinant of a 9-order square matrix is...
NOTE: Was not sure where to post this as it is a math question, but a part of my "Theoretical Physics" course.
I have no idea where to start this and am probably doing this mathematically incorrect.
given the function f(z) = cos(z+1/z) there should exist a singular point at z=0 as at z = 0...
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...
In fact I'm working on a condensed matter physics paper, where I stumbled with an integral that I need to visualize.
The function, Ls I need to visualize is equal to:
$$Ls=4\nu^4 \dfrac{\int_{-1}^{1} \dfrac{( 1-u^2)}{(u+\sqrt{u^2-\nu^2})^3} \, du}{\int_{-1}^{1}-u \Big...
The potential of a dipole distribution at a point ##P## is:
##\psi=-k \int_{V'}
\dfrac{\vec{\nabla'}.\vec{M'}}{r}dV'
+k \oint_{S'}\dfrac{\vec{M'}.\hat{n}}{r}dS'##
If ##P\in V'##, the integrand is discontinuous (infinite) at the point ##r=0##. So we need to use improper integrals by removing...
##\mathbf{M'}## is a vector field in volume ##V'## and ##P## be any point on the surface of ##V'## with position vector ##\mathbf {r}##
Now by Gauss divergence theorem:
\begin{align}
\iiint_{V'} \left[ \nabla' . \left( \dfrac{\mathbf{M'}}{\left| \mathbf{r}-\mathbf{r'} \right|}...
Hello.
I'm trying to pin down something Stephen Hawking was referring to in his book, A Brief History of Time.
During the next few years I developed new mathematical techniques to remove this and other technical conditions from the theorems that proved that singularities must occur. The final...
First off, this is just an assumption. My knowledge of the field is extremely limited and I beg you to come and correct my mistakes, so I can learn.
So, I guess we all know how that space-time fabric is bended by gravity. When a star dies, all of the atoms are brought extremely close...
I came across a question on PSE. I am not sure its a violation to ask the same question here, but there's no answer to the question in there so I wanted to ask it here.
Quoting his question,"Since the universe has a positive cosmological constant, there is an upper limit on the mass of the...
OK so, I was wondering could the reason that our universe was in a hot dense state prior the the Big Bang Be because of it was actually a huge singularity that had no more mass to swallow up?
And what caused this is that a type of matter or subatomic particle interacted with a different...
Yes, I understand that this is all kind of hypothetical, there have been no black holes discovered with a naked singularity. A black hole which is spinning beyond the speed of light is said to expand its event horizon to drop below the speed of light again. When it does that, it creates a...
Hi,
I'm new on here and this is my first post, so forgive me if I don't master the threads instantly :) - right, now that's out of way:
I want to open a discussion on the singularity in Black Holes, namely in regards to the well known issue of Special Realitivity breaking down at the...
Homework Statement
Homework Equations
Singularity equations for beam deflection
$$\sum M_B=0=-M_0-R_AL-M_0$$
$$R_A=-\frac{2M_0}{L}$$
The Attempt at a Solution
I know how to use singularity equations and all that but my problem is calculating the force especially when moment is involved. For...
Hi! I have the following problem I don't really know how to approach. Could someone give me a hand?
The line element of a black hole is given by: ds^2=\Bigg(1-\frac{2m}{r}\Bigg)d\tau ^2+\Bigg(1-\frac{2m}{r}\Bigg)^{-1} dr^2+r^2\Big(d\theta ^2+\sin^2(\theta)d\phi ^2\Big)
It has an apparent...
Is there a fundamental difference between the (speculative) understanding of a singularity arising from the creation of a black hole and the singularity which we think may have been at the origin of the Big Bang?
Noteably, would there be two basic theoretical types of singularities...
Hello.
My question is based upon my (mis?)understanding of these two premises.
1.
General Relativity breaks down when trying to describe the extreme conditions that are inferred to have existed in the very early universe.
2.
According to this link...
Hi, I am working on a video, and I was wondering if any of you knew of some real-life demonstrations I can do about black holes? So far I have the gravity well, and the balloon covered by foil that you crush to show same mass but denser. My video is about the anatomy of a black hole, so I cover...