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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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
330 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 ...
12
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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
371 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
132 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
516 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
182 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
296 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
564 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
791 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
304 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?
4
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2answers
283 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
208 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
60 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
107 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
689 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
58 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
158 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
356 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
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5answers
10k 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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2answers
2k 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
206 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
147 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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4answers
6k 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
2k 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
301 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
170 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
148 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
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 ...
2
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1answer
348 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
740 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
220 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
1k 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
616 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
293 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 ...
-1
votes
1answer
191 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
159 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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0answers
58 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?
-1
votes
2answers
458 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 ...
0
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3answers
872 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 $q$ $$ ...
3
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2answers
800 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 ...
0
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1answer
292 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 ...
1
vote
2answers
110 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 ...
8
votes
2answers
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 ...
2
votes
5answers
17k views

Einstein gravity versus Newton's gravity

What's the basic difference between the gravity as seen by Einstein, and that by Newton?
1
vote
1answer
175 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 ...
10
votes
2answers
392 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 ...
3
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1answer
170 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
votes
1answer
464 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
135 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?