A theory that describes how matter produces and responds to 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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2
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2answers
105 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 ...
5
votes
2answers
264 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
votes
1answer
507 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
votes
1answer
152 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 ...
1
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0answers
55 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 ...
1
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2answers
327 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 ...
9
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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
votes
1answer
652 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 ...
7
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3answers
2k 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, ...
2
votes
3answers
310 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 ...
24
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1answer
581 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
124 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
votes
4answers
537 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 ...
1
vote
1answer
217 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 ...
10
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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
291 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 ...
0
votes
0answers
89 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
votes
2answers
403 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
votes
1answer
167 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 ...
2
votes
4answers
269 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
417 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
votes
4answers
465 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
votes
2answers
218 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
60 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
votes
2answers
224 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
151 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 ...
0
votes
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 $ $$ ...
1
vote
1answer
97 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 ...
0
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0answers
432 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
votes
0answers
53 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 ...
6
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0answers
142 views

Do semiclassical GR and charge quantisation imply magnetic monopoles?

Assuming charge quantisation and semiclassical gravity, would the absence of magnetically charged black holes lead to a violation of locality, or some other inconsistency? If so, how? (I am not ...
2
votes
1answer
294 views

Contracting the Riemann tensor issues, p540 hobson

I am stuck trying to work through something on p540 in Hobson (General Relativity: An Introduction for Physicists), one is supposed to use the variation of the full Riemann tensor and then contract it ...
4
votes
5answers
4k views

Does everything with mass or energy have a gravitational pull?

As small as it may be, does every 'thing' have a gravitational pull? That is, something with mass or energy. No matter how obsolete or negligible it may be, is it there? If so, how is it calculated? ...
1
vote
2answers
985 views

If the universe is 3D, how is space-time like a “fabric”? [duplicate]

I have been taught that space-time should be viewed as a fabric and that objects with a large gravitational influence indent that fabric. My question is, if the singularity of a black-hole punctures ...
1
vote
2answers
195 views

How to find a curvature of the space-time by having $g^{\alpha \beta}$ in the following case without cumbersome calculations?

The metric tensor for Fock-Lorentz space-time, $$ \mathbf r_{||}{'} = \frac{\gamma (u)(\mathbf r_{||} - \mathbf u t)}{\lambda \gamma (u) (\mathbf u \cdot \mathbf r) + \lambda c^{2} (1 - \gamma (u))t + ...
1
vote
0answers
135 views

Use of Principle of Equivalence

Let $x^\mu$ be the coordinates of a reference frame, $K$, where all bodies feel the same constant and uniform acceleration $\textbf{a}=\textbf{g}=-\nabla\varphi$; let $\xi^\mu$ be the coordinates of a ...
18
votes
3answers
3k views

Does gravity slow the speed that light travels?

Does gravity slow the speed that light travels? Can we actual measure the time it takes light from the sun to reach us? Is that light delayed as it climbs out of the sun's gravity well?
2
votes
1answer
814 views

Difference between proper and comoving frames

I'm reading this book "Introduction to Quantum Fields in Classical Backgrounds" by Mukhanov & Winitzki, and there in the chapter 8 "The Unruh Effect" they introduce 3 reference frames. Laboratory ...
1
vote
1answer
215 views

Pound-Rebka-Snider experiment in the inertial frame

In Schutz's book (page 120), Schutz first derives the gravitational redshift in the PRS experiment in a previous paragraph. $\frac{\nu^{\prime}}{\nu}=\frac{m}{m+mgh+O(v^4)}=1-gh+O(v^4)$. Here ...
10
votes
1answer
163 views

Have general relativistic effects of the sun's rotation been measured?

I was wondering if general relativistic effects of the sun's rotation have also been measured, like gravity probes A and B measured GR effects from the earth.
0
votes
1answer
97 views

Is weak lensing the statistical effect of microlensing?

I am looking into the effects of gravitational lensing of gravitational waves. I know that gravitons travel along null geodesics, just as photons, and so they will suffer the same deflection angle by ...
0
votes
2answers
979 views

Spacetime around a Black Hole

If we consider the sun, then space-time is curve around it. My question is that what is the kind of curvature of space and time around the black hole. Is that space and time more curved around the ...
2
votes
1answer
304 views

Cosmological constant

I have always wondered about how cosmological constant is characterized. So since it is still a hypothesis you often read the “cosmological constant measured to be ….”. Shouldn't the statement read ...
3
votes
3answers
494 views

What does it mean that a wavevector is null?

I have derived geometric optics for gravitational waves and I am trying to interpret one of the results. I have \begin{equation} k_{\rho}k^{\rho}=0 \end{equation} for the wavevector. For the case ...
0
votes
1answer
161 views

Can you enter a timelike hypersurface?

As I understand it, a timelike hypersurface is one that has only spacelike normal vectors. But does this not imply that a the geodesic of a particle crossing it must be spacelike at that point? But ...
3
votes
1answer
746 views

Change of coordinates from an arbitrary frame to a locally inertial frame in General Relativity

If I have the following metric: $$ds^2=(1-2\phi)c^2 dt^2 - (1-2 \phi)(dx^2+dy^2+dz^2)$$ $\phi$ being the gravitational potential with $|\phi| << 1$ everywhere. How do I find a coordinate ...
4
votes
1answer
379 views

Diving into a charged (Reissner-Nordstrom) Black hole

Apparently there are two event horizons in this type of black hole, where the second one is known as the Cauchy horizon. According to Carroll, if you go into the first one, you will fall until you ...
2
votes
1answer
227 views

Motion of mercury [duplicate]

I studied that mercury motion around the sun slightly displace by a certain value in each year. But, this is not predicted by kepler until general theory of relativity. What does general theory does ...
-2
votes
1answer
181 views

Does Dark Matter have more space-time or particle characteristics?

Dark Matter appears to have more in common with phenomena related to spatial geometry then a particle. I thought in General Relativity, space can be curved without the presence of matter so ...
2
votes
1answer
136 views

Non-diagonal elements when switching metric signature?

Considering a metric tensor with the signature $(-,+,+,+)$: $g_{\mu\nu}= \begin{pmatrix} -c^2 & g_{01} & g_{02} & g_{03}\\ g_{10} & a^2 & g_{12} & g_{13}\\ g_{20} & g_{21} ...