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.
6
votes
2answers
171 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
votes
1answer
100 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
33 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
106 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
106 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 ...
1
vote
3answers
135 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
votes
2answers
105 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 ...
4
votes
3answers
138 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 - ...
3
votes
2answers
75 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
votes
0answers
40 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
$$
ds^2|_{\text{first order in ...
3
votes
2answers
107 views
Difference between slanted indices on a tensor
In my class, there is no distinction made between,
$$
C_{ab}{}^{b}
$$
and
$$
C^{b}{}_{ab}.
$$
All I know, and read about so far, is the distinction of covariant and contravariant, form/vector, etc. ...
1
vote
0answers
43 views
Dust generated static space-time implications on fluid 4-velocity
Imagine we have a perfect fluid with zero pressure (dust), which generates a solution to Einstein's equations. Show that the metric can be static only if the fluid four-velocity is parallel to the ...
0
votes
1answer
52 views
Help me to understand this conversion (4-vectors)
$u^{\mu}$ - 4-velocity
$b^{\mu}$ - 4-vector of magnetic field
$
u_{\mu}u^{\mu}=-1, \qquad u_{\mu}b^{\mu}=0
$
$$
...
1
vote
1answer
69 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
votes
0answers
85 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
31 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 ...
5
votes
0answers
78 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
4answers
123 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? ...
0
votes
2answers
123 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
136 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
99 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 ...
17
votes
3answers
802 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
67 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
56 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
118 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
34 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
0answers
157 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
175 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 ...
2
votes
3answers
109 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
0answers
97 views
General Relativity exact analytical solutions
I'm interesting in exact analytical solutions of Einstein field equation with or without lambda term:
$$
R_{\mu \nu} - {1 \over 2}g_{\mu \nu}\,R + g_{\mu \nu} \Lambda = {8 \pi G \over c^4} T_{\mu ...
0
votes
1answer
52 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
130 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 ...
2
votes
1answer
86 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
74 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
147 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
40 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} ...
0
votes
0answers
37 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?
0
votes
2answers
139 views
General Relativity & Kepler's law
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
votes
2answers
131 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 $q$
$$ ...
2
votes
2answers
106 views
Future light cones inside black hole
In Caroll's Spacetime and Geometry, page 227, he says that from the Schwarzschild metric, you can see than from inside a black hole future events all lead to the singularity. He says you can see this ...
0
votes
1answer
52 views
Time Dilation in relation to Acceleration
What I am looking for is a layman's explanation on the equations required to work out Time Dilation at high speeds including acceleration and deceleration of velocity. Or I would greatly appreciate it ...
1
vote
2answers
65 views
What does it mean that an inspiral is 'adiabatic'?
Binary systems emit gravitational radiation. This causes the system to lose energy, which results in a shrinking of the semi-major axis. I have read on countless occasions that this 'inspiral' is ...
6
votes
2answers
262 views
Dirac equation in curved space-time
I have seen the Dirac equation in curved space-time written as $$[i\bar{\gamma}^{\mu}\frac{\partial}{\partial x^{\mu}}-i\bar{\gamma}^{\mu}\Gamma_{\mu}-m]\psi=0 $$
This ...
2
votes
5answers
238 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
76 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 ...
0
votes
0answers
48 views
Embedding diagram visualization
Does anyone know about a good visual explanation of embedding diagrams online?
There are some videos related to the topic on YouTube but I haven't found any that actually explains the meaning of ...
1
vote
0answers
30 views
In which direction does space “bend”? [duplicate]
Gravitation is often depicted as a ball on a cloth that curves a hole into space. But in what direction does this hole form? Into the direction the object is moving?
4
votes
1answer
87 views
“Redshifting” of forces in stationary space - times
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
votes
1answer
84 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 ...
1
vote
1answer
116 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:
...
