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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1answer
498 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?
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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
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0answers
196 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
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1answer
251 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 ...
23
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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
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1answer
120 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
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2answers
173 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 ...
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2answers
175 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 ...
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2answers
547 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?
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1answer
255 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)
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3answers
149 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
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1answer
483 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
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3answers
302 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
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0answers
83 views

When is spacetime homogenous and isotropic? [duplicate]

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} + ...
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0answers
137 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
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0answers
76 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
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1answer
415 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? ...
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3answers
865 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 ...
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2answers
93 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.
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1answer
261 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? ...
2
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2answers
111 views

Interval and proper time

Is the definition of $$d s^2=-d \tau^2$$ assuming that $c=1$, so that we always have $$\left({ds\over d\tau}\right)^2=-1$$? Is there a reason for this definition? Don't we get an imaginary ${ds\over ...
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2answers
307 views

Can dark matter be relativistic dust?

As far as I know the mass of an observed object increases as it approaches the speed of light. Is it possible that the excess mass called "dark matter" is due to relativistic dust? Surely, stars ...
2
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1answer
573 views

Cartan equations versus Einstein equations in classical gravity

Are Cartan structural equations equivalent to Einstein's equations $$G_{\mu\nu}=T_{\mu\nu}$$ and why (in the case of torsionless geometries, of course)? Does it also apply with a non-null ...
5
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1answer
166 views

Why don't orbits expand with the Universe?

Consider two bodies orbiting each other. As the Universe expands would the distance between them increase? Most people say that a gravitationally bound system will not expand with the Universe. They ...
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0answers
56 views

Ex 0.2.1 in Sachs and Wu's textbook

In the next attachements are: 1. Exercise 0.2.5 which I want help with. Proposition 0.2.1 and its proof. Now, basically a few things are changed in the theorem, I don't think I can use here the ...
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2answers
349 views

Coordinate and conformal transformations of the FRW metric

I'm considering a metric of the following form (signature $(+,-,-,-)$): $$ds^2 = (F(r,t)-G(r,t))dt^2 - (F(r,t)+G(r,t))dr^2 - r^2(d\Omega)^2$$ where $F(r,t)$ and $G(r,t)$ are arbitrary scalar ...
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1answer
1k views

Why is Einstein gravity not renormalizable at two loops or more?

(I found this related Phys.SE post: Why is GR renormalizable to one loop?) I want to know explicitly how it comes that Einstein-Hilbert action in 3+1 dimensions is not renormalizable at two loops or ...
2
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1answer
840 views

Ricci identity/Riemann curvature tensor and covectors

Can somebody please explain to me how the following statement is true? The Riemann curvature tensor $R^c_{dab}$ is given by the Ricci identity $$(\nabla_a\nabla_b-\nabla_b\nabla_a)V^c\equiv ...
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3answers
3k views

Understanding Einstein's field equation

Einstein's field equation: $$G_{\mu\nu} = \frac{8\pi G}{c^4}T_{\mu\nu} - g_{\mu\nu}\Lambda$$ I'm trying to understand each of the terms in this equation intuitively, but I'm struggling. Basically, ...
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3answers
342 views

What truly is mass, and is there a direct way to measure it?

We know a mass of an object of one kilogram as an object that weighs W = mg = 9.8 N and we reference it to that, (when it should as a fundamental parameter describe weight not the opposite). But if we ...
25
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1answer
620 views

Overcharging a black hole

Hubeny's 1998 paper got a lot of people interested in determining whether cosmic censorship can be violated by dropping too much charge onto a black hole. It suggested that you might be able to get a ...
3
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1answer
126 views

How can the derivative of this trace be constrained?

I am studying for my exam on relativity and I am going through some problems sets including ones where I was not very successful in so I want to know how to do this problem. (Convergence of ...
3
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4answers
717 views

Time inside a Black hole

If time stops inside a black hole, due to gravitational time dilation, how can it's life end after a very long time? If time doesn't pass inside a black hole, then an event to occur inside a black ...
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1answer
273 views

Space time curvature real or theoretical (mathematical)?

Assuming one were in a capsule of some kind, with no window or instruments, and you swung into the gravitational field of a massive object (planet). Assuming no atmosphere to provide friction, could ...
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2answers
2k views

What is the definition of a timelike and spacelike singularity?

What is the definition of a timelike and spacelike singularity? Trying to find, but haven't yet, what the definitions are.
6
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1answer
333 views

Why is $R^2$ gravity not unitary?

I have often heard that $R^2$ gravity (as studied by Stelle) is renormalisable but not unitary. My question is: what is it that causes the theory to suffer from problems with unitarity? My naive ...
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0answers
110 views

What is the physical meaning of charges at light-like infinity in asymptotically flat space-times?

In the case of charges defined at space-like infinity, I can understand the physical meaning of them because they can be related to measurements made by a physical observer (that is an observer whose ...
0
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2answers
453 views

Einstein's theory tells us that gravity is a curve in space and time but how does that causes attraction in mass? [duplicate]

The sun is incredibly massive object and it causes the space around it to bend. This causes the planets to pulled to the sun or the planets move in an elliptical path around the sun. But I don't ...
2
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1answer
177 views

Privileged coordinate system (or lack thereof) in general relativity

What does the following statement mean and why is it true? The Weak Equivalence Principle (WEP) implies that in general curved space-time there is no privileged coordinate system. I have looked ...
3
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4answers
285 views

About gravity through space time curvature

Is it possible to produce virtual gravity? I mean gravity without the help of mass by curving spacetime with other effects like fast rotating objects?
2
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2answers
477 views

Different approaches to calculating the Christoffel symbols

I would be very grateful to whoever can debug the following calculations... We have the metric for static spacetime: $$ds^2 = -\exp(2U(\vec x))dt^2+h_{ij}(\vec x) d x^i d x^j$$ I want to find the ...
8
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4answers
592 views

How do you tell if a metric is curved?

I was reading up on the Kerr metric (from Sean Carroll's book) and something that he said confused me. To start with, the Kerr metric is pretty messy, but importantly, it contains two constants - ...
4
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3answers
270 views

Runge-Lenz vector and Keplerian Orbits

Is the loss of closed Keplerian orbits in relativistic mechanics directly tied to the absence of the Runge-Lenz vector?
0
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0answers
63 views

Switching from an accelerated frame of reference to a locally inertial reference system

Using the equivalence principle, show that the interval for an accelerated observer ($\textbf{g}$ uniform and constant) has the form $$ ds^2|_{\text{first order in ...
4
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2answers
243 views

Difference between slanted indices on a tensor

In my class, there is no distinction made between, $$ C_{ab}{}^{b} $$ and $$ C^{b}{}_{ab}. $$ All I know, and read about so far, is the distinction of covariant and contravariant, form/vector, etc. ...
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0answers
184 views

Dust generated static space-time implications on fluid 4-velocity

Imagine we have a perfect fluid with zero pressure (dust), which generates a solution to Einstein's equations. Show that the metric can be static only if the fluid four-velocity is parallel to the ...
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1answer
59 views

Help me to understand this conversion (4-vectors)

$u^{\mu}$ - 4-velocity $b^{\mu}$ - 4-vector of magnetic field $ u_{\mu}u^{\mu}=-1, \qquad u_{\mu}b^{\mu}=0 $ $$ ...
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1answer
103 views

Can the fuzzball conjecture be applied to microscopically explain the entropy of a region beyond the gravitational observer horizon?

In this article discussing this and related papers, it is explained among other things, how the neighborhood of an observer's worldline can be approximated by a region of Minkowsky spacetime. If I ...
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0answers
511 views

covarient derivative of electromagnetic field tensor

I'm trying to prove the energy momentum tensor in curved spacetime for Electromagnetic field is Divergence-less directly(Without using general lie derivative method which can prove any energy momentum ...
2
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0answers
55 views

Are there functions of the metric that are scalars under spatial diffs up to total derivatives?

Let $g_{\mu\nu}$ be a metric on a manifold with a time direction $x^0$ singled out. I'm wondering if there exists a function $F(g_{\mu\nu},\partial_\rho g_{\mu\nu},\ldots)$ that transforms under ...