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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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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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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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
104 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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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 ...
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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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153 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 ...
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1answer
321 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
6k 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? ...
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1k 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 ...
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2answers
200 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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139 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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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
245 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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169 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.
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1answer
126 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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2k 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 ...
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1answer
324 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 ...
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3answers
620 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 ...
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1answer
186 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 ...
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1answer
892 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 ...
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1answer
484 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 ...
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1answer
250 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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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 ...
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1answer
143 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} ...
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56 views

Curved space to flat space calculation

When changing the curved space co-ordinate into a flat space co-ordinate if a cone. I got the result transformation that i cannot get a transformation at the vertex(apex) why?
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2answers
381 views

General Relativity & Kepler's law [duplicate]

According to Kepler's law of planetary motion, the earth revolves around the sun in an elliptical path with sun at one of its focus. However, according to general theory of relativity, the earth ...
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3answers
800 views

Advanced Heaviside-Feynman formula implies electromagnetic inertia?

The Heaviside-Feynman formula (see Feynman Lectures vol I Ch.28, vol II Ch. 21) gives the electric and magnetic fields measured at an observation point $P$ due to an arbitrarily moving charge $q$ $$ ...
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2answers
629 views

Future light cones inside black hole

In Caroll's Spacetime and Geometry, page 227, he says that from the Schwarzschild metric, you can see than from inside a black hole future events all lead to the singularity. He says you can see this ...
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1answer
256 views

Time Dilation in relation to Acceleration

What I am looking for is a layman's explanation on the equations required to work out Time Dilation at high speeds including acceleration and deceleration of velocity. Or I would greatly appreciate it ...
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2answers
101 views

What does it mean that an inspiral is 'adiabatic'?

Binary systems emit gravitational radiation. This causes the system to lose energy, which results in a shrinking of the semi-major axis. I have read on countless occasions that this 'inspiral' is ...
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2k views

Dirac equation in curved space-time

I have seen the Dirac equation in curved space-time written as $$[i\bar{\gamma}^{\mu}\frac{\partial}{\partial x^{\mu}}-i\bar{\gamma}^{\mu}\Gamma_{\mu}-m]\psi=0 $$ This ...
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5answers
12k views

Einstein gravity versus Newton's gravity

What's the basic difference between the gravity as seen by Einstein, and that by Newton?
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1answer
159 views

Where to read about Minkowski space [duplicate]

When I learned Special Relativity, it was taught in terms of basic linear algebra, without any mention of the Minkowski space, proper time as integration on the metric, etc. However, when I am trying ...
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2answers
337 views

“Redshifting” of forces in stationary spacetime

Here's the problem statement: Let $(M,g_{ab})$ be a stationary spacetime with timelike killing field $\xi ^{a}$. Let $V^{2} = -\xi _{a}\xi ^{a}$ ($V$ is called the redshift factor). (a) Show that the ...
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1answer
162 views

How can photons exert gravity if they are wave-like?

As a reference, see this question: Does a photon exert a gravitational pull? It turns out the answer is "Yes" -- but this does not seem consistent with light being wave-like. I am imagining a ...
2
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1answer
367 views

Deriving the conservation of mass in a perfect fluid

I have a problem on a homework assignment. I will write the question and then what I have so far. I just want some guidance on what I am doing wrong (or right). Any help would be greatly appreciated: ...
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2answers
133 views

Are electrons moving? If so relative to whom? and why is there no magnetic field?

electrons on earth moving with us, due to rotation of earth, revolution of earth, sun and our galaxy right? Then, why is there no magnetic field around a piece of copper wire?
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180 views

Gravitational distortion of an object's diameter, at a distance,

Does the curvature of space-time cause objects to look smaller than they really are? What is the relationship between the optical distortion and the mass of the objects?
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71 views

does a rotating moving body in “flat” space curve its path because of frame dragging?

I am not a physicist. let's say we have a space with an object in it, where all other gravitational bodies are so far away that their affect on the shape of the space is negligible. let's say the ...
3
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1answer
705 views

Fermi Walker vs. Fermi transport

A vector field $f^\mu$ is said to be Fermi-Walker transported along a curve $\gamma$ parametrized with $\tau$ if the following holds $$\frac{\mathrm{D}}{\mathrm{d}\tau}f^\mu = -(a^\mu v^\nu - a^\nu ...
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1answer
539 views

Can negative energy explain black holes?

I think black holes are peculiar and I want to know if there is a relation to negative energy. Does negative energy have positive mass and therefore can explain the nature of black holes? IS there any ...
2
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1answer
126 views

General Relativity Paradox - Different local times of two frames a constant distance apart

Suppose there is a habitable star with a significantly large mass, and thus a huge gravitation field. It has a clock on it that ticks each local second. And it also has a mirror. This is Star A. ...
3
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1answer
181 views

Going through a ring of black holes

Mathematician here with a speculative physical question -- feel free to boot me if the level isn't right. Suppose one finds, or builds, a constellation of several black holes arranged in a circle. ...
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64 views

Trying to speak correctly of spacetime intervals and how to compare them

Is it correct to speak of "magnitude of a spacetime interval"? For instance, considering a pair of (distinct) events, $A$ and $B$, which are lightlike separated, is it correct to say that "the ...
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2answers
743 views

The uncertainty principle and black holes

What are the consequences of applying the uncertainty principle to black holes? Does the uncertainty principle need to be modified in the context of a black hole and if so what are the implications ...
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3answers
3k views

Did Hilbert publish general relativity field equation before Einstein?

Did Hilbert publish general relativity field equation before Einstein?
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1answer
570 views

Calculating Riemann Tensor Using Tetrad Formalism

I was trying to calculate the Riemann Tensor for a spherically symmetric metric: $ds^2=e^{2a(r)}dt^2-[e^{2b(r)}dr^2+r^2d\Omega^2]$ I chose the to use the tetrad basis: $u^t=e^{a(r)}dt;\, ...