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.

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5
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2answers
777 views

Is time going backwards beyond the event horizon of a black hole?

For an outside observer the time seems to stop at the event horizon. My intuition suggests, that if it stops there, then it must go backwards inside. Is this the case? This question is a followup ...
2
votes
1answer
2k views

Stress energy tensor of a perfect fluid and four-velocity

In the following demonstration, there is an error, but I cannot find where. (I explicitely put the $c^2$ to keep track of units). We consider a metric $g_{\mu\nu}$ with a signature $(-, +, +, +)$ : ...
11
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2answers
234 views

What is a sudden singularity?

I've seen references to some sort of black hole (or something) referred to as a sudden singularity, but I haven't seen a short clear definition of what this is for the layman.
3
votes
1answer
343 views

The most general form of the metric for a homogeneous, isotropic and static space-time

What is the most general form of the metric for a homogeneous, isotropic and static space-time? For the first 2 criteria, the Robertson-Walker metric springs to mind. (I shall adopt the (-+++) ...
3
votes
1answer
240 views

Sign crazyness on the stress energy tensor?

I would like to know on what depends the sign of the stress energy tensor in the following formula : $T_{\mu\nu}=\pm(\rho c^2+P)u_{\mu}u_{\nu} \pm P g_{\mu\nu}$ In my case the metric is equal to ...
6
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3answers
383 views

Are gravitational time dilation and the time dilation in special relativity independent?

There are two kinds of time dilation: One because the other clock moves fast relative to me (special relativity). Another one because the other clock is in a stronger gravitational field (general ...
4
votes
1answer
130 views

“WLOG” re Schwarzschild geodesics

Why, when studying geodesics in the Schwarzschild metric, one can WLOG set $$\theta=\frac{\pi}{2}$$ to be equatorial? I assume it is so because when digging around the internet, most references seem ...
1
vote
1answer
118 views

Gravitational time delay and contraction of matter [duplicate]

How can any matter contract to its Schwarzschild radius if gravitational time dilation clearly states that all clocks stop at that point. So any contraction any movement would stop. If that is so why ...
2
votes
0answers
187 views

Do we expect that the universe is simply-connected? [duplicate]

I heard recently that the universe is expected to be essentially flat. If this is true, I believe this means (by the 3d Poincare conjecture) that the universe cannot be simply-connected, since the ...
2
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1answer
829 views

General relativity and the conservation of momentum

I'm trying to understand the conservation of momentum in general relativity. Due to the curvature of space-time by matters and energy, the path of a linear motion appears to be distorted. Therefore ...
1
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0answers
63 views

Singularities in Schwarzchild space-time

Can anyone explain when a co-ordinate and geometric singularity arise in Schwarzschild space-time with the element $$ ...
6
votes
2answers
509 views

First and second fundamental forms

I'm writing notes about the 3+1 formalism in general relativity, for myself. Inevitably I came across the notions of first and second fundamental forms. Mathematically, it is clear how these objects ...
2
votes
0answers
135 views

Lecture Notes confusion: Constructing the Einstein Equation

This question is on the construction of the Einstein Field Equation. In my notes, it is said that The most general form of the Ricci tensor $R_{ab}$ is $$R_{ab}=AT_{ab}+Bg_{ab}+CRg_{ab}$$ ...
1
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0answers
637 views

How to calculate Riemann and Ricci tensors for a sphere? [closed]

Let's have the metric for a sphere: $$ dl^{2} = R^{2}\left(d\psi ^{2} + sin^{2}(\psi )(d \theta ^{2} + sin^{2}(\theta ) d \varphi^{2})\right). $$ I tried to calculate Riemann or Ricci tensor's ...
0
votes
1answer
620 views

Contraction of the metric tensor

This is perhaps a simple tensor calculus problem -- but I just can't see why... I have notes (in GR) that contains a proof of the statement In space of constant sectional curvature, $K$ is ...
2
votes
0answers
197 views

Stress-energy tensor of point particle when the trajectory is a transcendental equation?

I'm working through Carroll's GR book, and Problem 7.8 is not coming together. I'm missing something idiotically simple, but I'm not sure if I can cleanly write a stress-energy tensor for a point ...
4
votes
2answers
523 views

Is Earth's orbit around the sun affected by the ~8 minutes light delay?

Gravitational change occurs at the speed of light. As a consequence, we experience on Earth the gravitational attraction of the sun based on its position relative to us ~8 minutes ago. How does this ...
1
vote
1answer
125 views

A physical sense of an Inertial frame

Definition clarification needed, please: I am hoping to get physical sense of an "inertial frame". Do inertial reference frames all have zero curvature for their spacetime? So is an inertial frame ...
2
votes
2answers
399 views

Local inertial coordinates/Fermi normal coordinates

It is said that we can introduce local inertial coordinates/Fermi normal coordinates for any timelike geodesic. But why only for timelike geodesics? What about null geodesics? Perhaps it has to do ...
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5answers
600 views

How universal gravitation falls short

As a non physicist I can understand how Newtonian mechanics falls short in cases of high velocity etc. and is properly generalized by the special theory of relativity. What is not clear to me is how ...
0
votes
0answers
173 views

The interior of a cylinder as an Einstein manifold

The interior of a curved cylinder is an Einstein manifold (the Ricci Curvature Tensor is proportional to the Metric $R_{\mu\nu}=kg_{\mu\nu}$) since it has a constant curvature. Using the metric $$ ...
0
votes
1answer
50 views

Zero-zero (lower indicies) term for affine connection ($\Gamma_{00}^\lambda$), why do some terms dissapear?

More simply a tensor algebra question, but in General relativity I have the following when I calculate $\Gamma_{00}^\lambda$:- $$ \Gamma_{00}^\lambda = \frac{1}{2}g^{\nu\lambda}\left( \frac{\partial ...
6
votes
2answers
591 views

Does non-mass-energy generate a gravitational field?

At a very basic level I know that gravity isn't generated by mass but rather the stress-energy tensor and when I wave my hands a lot it seems like that implies that energy in $E^2 = (pc)^2 + (mc^2)^2$ ...
4
votes
1answer
173 views

Wald problem 11.4

Consider a stationary solution with stress-energy $T_{ab}$ in the context of linearized gravity. Choose a global inertial coordinate system for the flat metric $\eta_{ab}$ so that the "time direction" ...
8
votes
1answer
296 views

Cancelling special & general relativistic effects

We know that for a GPS we need to make a correction for both general and special relativity: general relativity predicts that clocks go slower in a higher gravitational field (the clock aboard a GPS ...
11
votes
1answer
335 views

General definition of an event horizon?

Horizons are in general observer-dependent. For example, in Minkowski space, an observer who experiences constant proper acceleration has a horizon. Black hole horizons are usually defined as ...
0
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1answer
71 views

Change of variables in an interval expression

This question is a continuation of How to calculate a scalar curvature fast? . Let's have Lorentz-Fock spacetime with an interval $$ d \hat {s}^{2} = \frac{t_{0}^{2}R^{2}}{\hat {t}^{4}}\left( d \hat ...
1
vote
3answers
213 views

Combining metric tensors/curvature tensors

I was thinking about the following scenario: Consider a particle which causes a metric $g_{\mu\nu}$ on an otherwise Minkowski spacetime (or any manifold). Now, consider another particle, somewhere in ...
2
votes
2answers
128 views

Can the effects of a person's mass upon the local gravitational field be detected and measured remotely?

As the title suggests, Can the effects of a person's mass upon the local gravitational field be detected and measured remotely? I am aware any mass produces and effects gravity but couldn't find ...
1
vote
1answer
311 views

Why four velocity under covariant differential is considered to be zero?

In Einstein's general theory of relativity the elements of four velocity $U^{\mu} (\gamma c, \gamma v)$ under covariant differential is considered to be zero, why? $$\mathcal{D} U^{\mu}=0$$ in other ...
1
vote
1answer
438 views

What is the curvature of an empty universe?

My calculations tell me an empty universe has hyperbolic curvature. Is this correct? If it is, can anyone help me understand why this is intuitively?
0
votes
1answer
49 views

If there's a light ray and it's turned to a new location by a certain angle

Imagine that there's a light ray, with source at point A, and it's directed towards point B (which is very far from point A) and it continues for a huge distance. How will an observer at point B ...
2
votes
0answers
171 views

Why doesn't this metric cover all of de Sitter space?

This represents a confused attempt to work through a problem in Carroll's Spacetime and Geometry. Supposedly I should be able to use the geodesic equation, ...
3
votes
1answer
230 views

Space time a function of itself, objects in it, or both?

Is spacetime a function of itself, objects within it, or both? I am struggling to understand just what is spacetime without objects in it (or theoretical reference points) and thus no frame of ...
22
votes
6answers
2k views

Why do we still need to think of gravity as a force?

Firstly I think shades of this question have appeared elsewhere (like here, or here). Hopefully mine is a slightly different take on it. If I'm just being thick please correct me. We always hear ...
3
votes
1answer
115 views

Energy Functional

I am a graduate student in pure mathematics, during my study on Ricci Flow I faced some functional known as energy functional. For example Einstein-Hilbert functional is called an energy functional, ...
3
votes
2answers
172 views

Theoretical need for Newtonian Gravity

I've been wondering: Are there, still, some advantages, for current research, to study Newtonian gravity? I mean, not experimentally, where Newton gravity is a very good approximation to everyday ...
1
vote
2answers
162 views

What is path of light in the accelerating elevator?

Mathematically, (by mathematically I means by equations) what is path of light in the accelerating elevator? What is the difference between an ordinary derivative and covariant derivative (which is ...
5
votes
2answers
468 views

How (or why) equivalence principle led to Einstein field equations?

If equivalence principle was origin of general relativity what was the process that this principle led Einstein to developed his theory of general relativity?
-1
votes
1answer
235 views

What is mathematical definition of a strong gravity?

Mathematical definition of a weak gravity is simple $g=\frac{GM}{r^2}$ but what is mathematical definition of a strong gravity? (blackhole-like or close to a blackhole-like object)
2
votes
3answers
146 views

Transforming an equation to the co-vector version

Ok, this question is more a result of my lack of knowledge of how to manipulate equations involving index notation rather than about physics... I have the geodesic equation with ...
2
votes
1answer
433 views

The role of the affine connection the geodesic equation

I apologise in advance that my knowledge of differential geometry and GR is very limited. In general relativity the equation of motion for a particle moving only under the influence of gravity is ...
2
votes
3answers
251 views

Why are black holes special?

A black hole is where it's mass is great enough that light can't escape at a radius above the surface of the mass? I've been told that strange things happen inside the event horizon such as ...
1
vote
0answers
80 views

When is spacetime homogenous and isotropic?

When is spacetime homogenous and isotropic? For example, some metric $g_{\mu \nu}$ is homogeneous and isotropic. We now construct effective metric $$n_{\mu \nu} ~\rightarrow~ g_{\mu \nu} + ...
1
vote
0answers
130 views

Naked singularity and null coordinates

I'm trying to understand the notion of a naked singularity on a more mathematical level (intuitively, it's a singularity "one can see and poke with a stick", but I'm having troubles on how to actually ...
2
votes
0answers
75 views

Naked singularity and extendable geodesics [duplicate]

I'm currently trying to understand the notion of a naked singularity. After consulting books by Wald and Choquet-Bruhat, it seems that for a naked singularity one must have that the causal curves can ...
0
votes
1answer
371 views

proper variation of action term

I have a term I want to vary by a field, $\phi$. $$ `S' = \frac{-1}{2}\,\sqrt{-g}\,g^{\mu\,\nu}\,\delta\left[h(\phi)\,\partial_{\mu}\phi\,\partial_{\nu}\phi \right]. $$ Is it correct to get this? ...
0
votes
3answers
759 views

What would happen to the Moon if Earth is turned into a black hole?

Assume that all of sudden the Earth is turned into a black hole. And the moon revolves around the Earth (before turning into a black hole). What would happen to the Moon after earth changes to black ...
0
votes
2answers
87 views

Changing the scalar curvature (k = 0,+1,-1) with coordinate transformations?

I would like to prove that I can (or can't) change curvature of space, k = 0,+1,-1, via general coordinate transformations, which in principle can mix space and time coordinates together.
1
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1answer
240 views

Ricci scalars for space and spacetime, local and global curvature

If Ricci scalar describes the full spacetime curvature, then what do we mean by $k=0,+1,-1$ being flat, positive and negative curved space? Is $k$ special version of a constant "3d-Ricci" scalar? ...