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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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
110 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
301 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
560 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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159 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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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
348 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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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
814 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
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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
338 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 ...
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608 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 ...
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1answer
125 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 ...
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4answers
686 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
265 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.
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1answer
325 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
108 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 ...
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2answers
449 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 ...
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1answer
174 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 ...
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4answers
281 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?
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2answers
474 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 ...
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4answers
575 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 - ...
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3answers
268 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?
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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 ...
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2answers
239 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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182 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
102 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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504 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 ...
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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 ...
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0answers
151 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
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1answer
316 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 ...
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5answers
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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? ...
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2answers
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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 ...
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2answers
198 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 + ...
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0answers
138 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 ...
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3answers
4k 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?
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1answer
1k 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 ...
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1answer
242 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 ...
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1answer
167 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
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1answer
121 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 ...
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2answers
1k 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
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1answer
320 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
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3answers
598 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
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1answer
179 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
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1answer
872 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
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1answer
464 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
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1answer
246 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 ...
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1answer
186 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 ...