A theory that describes how matter interacts dynamically with the geometry of space and time. It was first published by Einstein in 1915 and is currently used to study the structure and evolution of the universe, as well as having practical applications like GPS.

learn more… | top users | synonyms (1)

37
votes
4answers
6k views

Are black holes very dense matter or empty?

The popular description of black holes, especially outside the academia, is that they are highly dense objects; so dense that even light (as particle or as waves) cannot escape it once it falls inside ...
4
votes
1answer
107 views

Do gravitational waves travelling through a medium produce sound?

Say Alice decided to orbit dangerously close to a couple of black holes circling each other. She is in a heavily enclosed astronaut suit, as is Bob, who is floating much further away. Assuming Alice ...
2
votes
0answers
62 views

Einstein equations from the Palatini action [closed]

I am trying to obtain the usual form of vacuum Einstein's equations $$ R_{\mu \nu} - \frac{1}{2} R g_{\mu \nu} + \Lambda g_{\mu \nu} = 0 $$ from the first-order (Palatini) tetradic action $$ ...
1
vote
1answer
69 views

If we could perfectly control gravitational waves, could we play music with them? [closed]

Sound is just a kinetic wave propagating through a medium, right? In that case, if we had the ability to make gravitational waves exactly as we want them, could we play music to an observer some ...
1
vote
1answer
36 views

Function to model deformed spacetime in 2D visualization of an Alcubierre drive

In the Wikipedia article on Alcubierre drive there is a top image. It is 2D visualization of an Alcubierre drive, showing the opposing regions of expanding and contracting space-time that displace the ...
4
votes
1answer
92 views

Why do we need connections, if we have the Lie derivative?

When I learned about the covariant derivative, it was motivated as a way of defining a good differentiation operation on tensors. To do this, we had to define a connection on the manifold, which was a ...
3
votes
2answers
314 views

Gravitational imaging

Gravitational Imaging So as we know from the famous theory and equations of Einstein is it possible to track the individual gravitational pull?
3
votes
2answers
185 views

If space can expand faster than light why can't gravitational wave?

I heard that gravitational wave is the measure of stretchiness of space time, so since there is no limit to how fast space can stretch what about gravitational wave?
1
vote
1answer
93 views

Why is the speed of gravity the same as that of photons? [duplicate]

Why is it that the speed of massless particles in space is the same as propagating disturbances of space? We can´t send human information (with photons) faster than the speed of light. But we can ...
1
vote
1answer
66 views

Derivation of the relativistic equation of energy conservation for a perfect fluid

I'm currently attempting to struggle through the first chapter of Sean M. Carrol's spacetime and geometry. I'm a bit stuck, most likely because of not understanding the mathematical operation. ...
0
votes
0answers
68 views

What is the explicit form of $\tau^{\alpha\beta}$ in the linearized Einstein field equations $\Box h^{\alpha\beta}=-16\pi\tau^{\alpha\beta}$?

If we let $h^{\alpha\beta}=\eta^{\alpha\beta}-g^{\alpha\beta}\sqrt{|det(g)|}$ then, according to wikipedia, the Einstein Field Equations become $$\Box h^{\alpha\beta}=-16\pi\tau^{\alpha\beta},$$ where ...
3
votes
2answers
95 views

Why does an evaporating black hole always stay a black hole?

Stars can only collaps and form black holes if their masses are above the Chandrasekhar limit, $M>M_{\rm Pl}^3/M_{\rm hydrogen}^2$. When the universe eventually cools down enough, the black holes ...
0
votes
0answers
18 views

Gibbons-Hawking-York boundary term expanded at second order in the fluctuation

Does anyone know a general form for the Gibbons-Hawking-York boundary term expanded at quadratic order in the fluctuation of the metric? Assume to define the fluctuation of the metric $g_{\mu \nu}$ ...
0
votes
2answers
74 views

The influence of gravity on the energy levels of atoms

There´s an ongoing debate if gravity waves (or gravity?) contains energy. But what if a very strong wave of gravity hits an atom. Let´s for simplicity say a hydrogen atom. Not a wave that is ...
2
votes
0answers
55 views

Closed timelike curves in the Kerr metric

I just read in Landau-Lifshitz that the Kerr metric admits closed timelike curves in the region $r \in (0, r_{hor})$ where $r_{hor}$ is the event-horizon ( I am talking about the case $|M|>|a|$ ...
1
vote
0answers
22 views

Hidden character in EPR paradox [duplicate]

I am a beginner in Quantum Mechanics so i am pretty new to the EPR paradox although i have heard about it a long time ago but finally studying in detail. And came across a doubt: Why the hidden ...
-1
votes
2answers
37 views

Curvy space in and around massive objects [closed]

If space curves around massive objects, what happens to the space within the massive objects?
4
votes
1answer
107 views

Why is Newtonian cosmology correct for curved space?

The Newtonian model of an expanding Universe gives Friedmann's equation exactly for non-zero spatial curvature $k$ (see http://hyperphysics.phy-astr.gsu.edu/hbase/astro/expuni.html). Instead of using ...
0
votes
0answers
42 views

Can a lightlike singularity have nonzero mass?

The effective mass of the Schwarzschild solution is valid at $r=0$. For $m>0$, we have a spacelike singularity, while for $m<0$ we have a timelike singularity. Suppose, instead of a spacetime ...
4
votes
2answers
84 views

What's the metric of the Standard Non-Time-Orientable Spacetime

If you've read any spacetime topology, you know that spacetime. It is the amazing rotating lightcone identified after half a rotation. And outside of De Sitter space with some identifications, it is ...
2
votes
0answers
67 views

Should we consider space and time as separate entity?

In general relativity, we think of space and time in spacetime framework. As some people say, metric tensor sign difference, along with our inability to go backward in time suggests that space and ...
4
votes
1answer
78 views

Negative mass thin shell collapse

Suppose we have a collapsing light-like (ingoing) shell with negative mass and decreasing further. The shell is radiating and so the exterior region is that of the outgoing Vaidya solution. $$ds^2 = ...
1
vote
0answers
135 views

The integration of Einstein's equations [closed]

Einstein's equation is $$G_{\mu\nu} + \Lambda g_{\mu\nu} = {8 \pi G \over c^4} T_{\mu\nu}$$ where $G_{\mu\nu} = R_{\mu\nu} - (1/2)g_{\mu\nu}\,R$ is the Einstein tensor, which combines the Ricci ...
1
vote
0answers
33 views

Can we distinguish between two mass distributions in spacetime having the same effect over a test partlicle [duplicate]

Einstein's equation is $$8πT_{ab}=G_{ab}$$ where the left side contains the stress-energy tensor and the right side contains the Einstein tensor. Is there exactly one unique stress-energy tensor ...
0
votes
1answer
34 views

Elementary question about non-Euclidean geometry in general relativity: “cannot move about without changing shape”

One basic result of general geometry (from math) in curved spaces or on curved surfaces is that if you are in a surface of variable curvature, things like the Euclidean congruence postulates and ...
2
votes
1answer
129 views

Is every solution of Einstein field equations unique?

Einstein's equation is $$8 \pi T_{ab} = G_{ab},$$ where the left side contains the stress-energy tensor and the right side contains the Einstein tensor. Is there exactly one unique stress-energy ...
4
votes
2answers
157 views

When does causal separation imply no spacelike separation?

(See here for notation.) In Minkowski space, if $p\prec q$, then there is no spacelike curve $c:[0,1]\to \mathbb{R}^{n-1,1}$ with $c(0)=p$ and $c(1)=q$. This is obvious from a spacetime diagram. Here ...
3
votes
2answers
151 views

Is curvature space-time has impact on the object geometry

When we have e.g. metallic cube of dimensions 1x1x1m and we put it on the space without gravitational force the cube has equal 1x1x1m and we can use Euclidean geometry. But when this cube move on ...
3
votes
1answer
67 views

S-duality of Einstein-Maxwell-Dilaton theory

Consider theory with action $$S = \int d^D x \sqrt{-g} (R - \frac{1}{2} \partial_\mu \phi \partial^\mu \phi - \frac{1}{2k!} e^{a \phi} F^2 _{[k]} ) $$ where $\phi$ is dilaton and $F_{[k]}$ is ...
4
votes
2answers
89 views

Path Integral Quantization in General Relativity

In Ref. 1 I have seen that the action must contain only the first derivative of the metric as required by the path integral approach. I don't understand why. I mean why the path integral approach of ...
0
votes
0answers
16 views

How does curved space make an obejct move toward Earth? [duplicate]

I think I understand how the equivalence principle shows how light can bend and therefore space must be curved. What I do not understand is how curved space makes an object move directly toward the ...
4
votes
0answers
204 views

How does one determine if a spacetime is globally hyperbolic?

A spacetime $M$ is said to be globally hyperbolic if it is strongly causal and if the sets $J^+(p)\cap J^-(q)$, for all $p,q\in M$, are compact. (For more information, see the Wiki article on causal ...
1
vote
0answers
57 views

Why are symmetrical structures highly stable?

What makes symmetrical structures(geometry) highly stable? It is perfect to say that the forces acting on a symmetrical structure is balanced and hence stable. But why is it so? To be more specific, ...
6
votes
2answers
2k views

Does the existence of “gravitational waves” (assuming they exist) imply that time exists as a 4th dimension in the universe? [closed]

I'm new to thinking about special and general relativity and I have no formal training as a physicist. However, I've been doing a bit of thinking about spacetime recently. I was wondering if ...
4
votes
1answer
48 views

Frame dragging resulting in an orbital plane?

In astrophysics today we talked about spinning black holes, ring singularities, and frame dragging. Is this also (to some degree) the cause of the milky way being as flat as it is? Does the spin of ...
1
vote
0answers
64 views

What is the metric at the center of a star? [duplicate]

If there is only one star in the universe then is the metric at the center of the star flat?
1
vote
1answer
41 views

Vierbeins in General Relativty; degrees of freedom?

I am self-learning GR. I want to ask if vierbeins $e^b_{\ \ \nu}$ need to satisfy any relations or if I am free to choose any type of vierbein I like So I have been looking into tetrads again. I ...
0
votes
0answers
23 views

Relativistic mass increment [duplicate]

Is the mass increment with an increase absolute velocity of a body, a direct consequence of energy to mass conversion
2
votes
1answer
137 views

Quotient space in the book The Large scale structure of space-time

On page 79, the author states One is thus concerned only with $\mathbf{Z}$ modulo a component parallel to $\mathbf{V}$, i.e. only with the projection of $\mathbf{Z}$ at each point $q$ into the ...
0
votes
3answers
145 views

Is time unidirectional because of 4th spatial dimension? [closed]

We heard about an expanding universe. Consider an expanding sphere. Consider the surface of the sphere as our 3 dimensional universe. Can time dimension be the radius $R$ of this sphere? And because ...
0
votes
2answers
117 views

In what other fields of physics does “math break down”? [closed]

I've heard numerous articles and videos state that when it comes to black holes and singularities our "math breaks down". Is there any other areas in physics where math similarly "breaks down", where ...
1
vote
2answers
80 views

What are world lines as opposed to arbitrary curves in spacetime?

In GR the spacetime manifold is equipped with a metric which makes it a Lorentzian manifold. It is the metric that is doing the separation of space and time (so that we end up with three dimensions of ...
1
vote
1answer
46 views

Einstein's Principle of Equivalence - Infinite Acceleration/Energy?

Hello and thank you for your time. I've been wondering about Einstein's Equivalence Principle core idea. That is, from experiment alone, one cannot differentiate between a gravitational field and a ...
1
vote
0answers
22 views

A star starts at rest at infinity, how do you calculate the kinetic energy of the star when it crosses the event horizon of a black hole? [duplicate]

A star that begins very, very far away from a black hole (infinity) is brought in by the black hole's gravitational pull. How do you calculate the kinetic energy of the star as it passes the point ...
1
vote
1answer
55 views

Killing equation manipulation

Why does the killing equation $$K_{\mu;\nu}+ K_{\nu;\mu} = 0$$ equal $$K_{\mu,\nu}+ K_{\nu,\mu} -2\Gamma^{\rho}_{\mu\nu}K_{\rho} = 0 $$ when in general a covariant derivative $V_{\beta;\alpha} = ...
3
votes
1answer
141 views

Fermi-Propagated Jacobi equation in the book The Large scale structure of space-time

On page 81, equation (4.6), the author use the Fermi derivative to write the Jacobi equation \begin{equation} \tag{4.6} \frac{{D^2}_\text{F}}{\partial s^2} {}_{\bot}Z^a = ...
0
votes
0answers
25 views

Equation of state for a radiation fluid

Can anyone give me (point me to a reference of) a derivation of the equation of state for a radiation fluid: pressure = energy/3 Much thanks.
0
votes
1answer
96 views

The Lie derivative of the metric $g_{ab}$ and index notation

I don't quite know where to start this question. I'm essentially not understanding how to compute the Lie derivative of a given metric and vector. So I have the following definition: $$ ...
12
votes
3answers
1k views

How does gravity truly work? [duplicate]

I Am only 12 years old and I'm constantly wondering and trying understand how gravity really works. On YouTube everyone always talks about objects wrapping space time around themselves and uses the ...
1
vote
1answer
80 views

Extrinsic curvature components

I'm trying to understand how to derive the extrinsic curvature (in order to understand some calculation on fluid/gravity dynamics). But I hit a wall in my progress. I stuck at trying to verify the ...