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Questions tagged [general-relativity]

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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General Relativity and cosmology [duplicate]

What is the physical meaning of Ricci scalar is a covariantly constant?
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1answer
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Relative motion involving acceleration

Recently I came across the following thought experiment : Take a string and whirl it in a horizontal circle. Imagine that an ant is sitting on the string . From our point of view , the ant is in ...
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2answers
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In the Schwarzschild Metric does $\sin^2\theta{\Delta}\phi^2={\Delta}\phi^2\sin^2\theta$?

In the Schwarzschild Metric as the spacetime interval between two points in spacetime approaches $0$ for any ratio between the length of time and space the spacetime interval between the points in ...
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What happens to the time evolution equations in canonical quantum gravity?

Many expositions on canonical quantum gravity start from a 3+1 type formalism, where spacetime is foliated along the time dimension. The Einstein equations then decompose into constraint equations on ...
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Difference between coordinate systame and frame of reference in relativity

I have taken a relativity course, and am not quite clear as to whether the notion of a frame of referene is independent of the coordinate system. At the moment, I think that any frame of reference (of ...
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Converting from trace reversed to standard metric perturbation

In linearised gravity, when dealing with gravitational waves it is common to consider just the spatial part of the trace-reversed metric perturbation $\bar{h}_{ij}$. I know that in general the trace-...
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1answer
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Energy-momentum for gravity [duplicate]

My question is as follows: Why is it problematic to define energy-momentum tensor for the gravitational field? P.S. It is well-known that in GR we get the energy-momentum tensor of "matter" by ...
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2answers
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How can time go in different directions in the Universe?

This is not a duplicate, I am not asking about any kind of time dilation caused by a BH. My question is about the direction of time (and if it is possible to have different directions for time, other ...
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Do photons bend spacetime or not?

I have read this question: Electromagnetic gravity where Safesphere says in a comment: Actually, photons themselves don't bend spacetime. Intuitively, this is because photons can't emit ...
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Mathematical software for calculating Christoffel symbols, curvature, etc [duplicate]

I'm looking for a Mathematical software that can do the following: I put in a metric (some kind of a two-dimensional matrix), and the software calculates Christoffel symbols, Ricci curvatures, ...
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Does 'separability' mean that a physical law can function differently in separate parts of this Universe? [on hold]

Einstein referred to "separability"; what did he mean? What's the latest conclusions on separability?
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2answers
65 views

What is meant by globally hyperbolic spacetime? [duplicate]

Can somebody explain what is meant by globally hyperbolic spacetime? What other kinds can there be?
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1answer
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Accelerated frame vs gravity frame

Can accelerated frame change curvature of space as gravity does? Can there accelerated frame be pure inertial frame?
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Does Fuzzy time interpretation is able to solve the problem of Quantum mechanics unification and General Relativity? [on hold]

Does Fuzzy time interpretation (more exactly fuzzy time-space interpretation) is able to solve the problem of Quantum mechanics unification and General Relativity? Fuzzy time-space is an ...
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1answer
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Sean Carroll GR - Ex.3.6 (b) & (c) [on hold]

I'm working in the newtonian limit of GR with the metric $$ ds^2 = -(1+2\Phi)dt^2 + (1-2\Phi)dr^2 +r^2d\theta^2+r^2sin^2\theta\;d\phi^2 $$ where $$\Phi = -\frac{GM}{r}.$$ We are first asked to ...
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2answers
102 views

Can mass be ejected from a black hole within the Schwarzschild radius?

This goes far beyond my limited knowledge regarding the physics of black holes, but my colleague told me this today: I doubt that if I stand on the surface of a black hole - inside the ...
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1answer
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Stability of Schwarzschild and Reissner-Nordstrom spacetimes

I am interested to know what is the best we can say about stability of Schwarzschild and Reissner-Nordstrom black holes. I found some who study the behavior of perturbations that satisfy the ...
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2answers
51 views

Geodesics from variational principle with respect to coordinate?

I know you can find geodesic equations with respect to proper time $\tau $ using the variational principle, i.e. using Euler-Lagrange equations $$ \frac{\partial}{\partial x^{\mu}}L-\frac{d}{d\tau}\...
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How Does LIGO’s Splitter Mirror Cause Two Different Frequencies When a GW is Present?

When a gravitational wave is present in LIGO, how does the splitter mirror work to send out a different frequency than the laser frequency on the arm perpendicular to the laser direction? What are ...
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1answer
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Tangent space of pseudo-Euclidean manifold

My textbook says (without any justification that I can see) that "since Minkowski spacetime is pseudo-Euclidean, the tangent space $T_P$ at any point $P$ coincides with the manifold itself". My ...
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2answers
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How do Graviton-based theories of gravity explain the expansion of the universe?

In General Relativity, the expansion of the universe is modeled using the Friedmann–Lemaître–Robertson–Walker metric, and the expansion itself is a metric expansion by which the scale of space itself ...
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1answer
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What is the true cause of time dilation? Velocity, momentum or energy?

When learning about relativity, it is said that velocity (an object or a particle traveling close to the speed of light) results in time moving slower for the object moving. However, there is also ...
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Is the location of everything relative? [duplicate]

I have heard that everything in our physical reality is relative. But I wonder: Does the universe have an edge? In an expanding sphere, there would be an edge is it like that? If the above is true ...
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1answer
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Line Element Transformation

This is just something that I've made up to see if I understand the method. If I have the line element: $$ds^2 = dr^2 + r^2\,d\phi^2$$ and I want to carry out a transformation with $r = \dfrac{...
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1answer
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Electromagnetic gravity [on hold]

Lets assume for the purpose of this question that there is matter formed by elementary particles which do not have any charge.How strong an electromagnetic field must be to attract this kind of ...
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2answers
88 views

Information content in black holes

Bekenstein-Hawking formula for entropy of a black hole tells us that information content in a black hole is proportional to its area which is in fact proportional to the mass^2 of the black hole. The ...
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0answers
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Should stellar black holes contain a singularity? (in GR) [duplicate]

Consider a star, for simplicity a non rotating one. The corresponding spacetime will be similar to a Schwartzschild one (if the star is static and spherically symmetric). Outside the star we will ...
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2answers
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Can a black hole event horizon form before the singularity for an outside observer?

This is not a duplicate, my question is not about whether BHs have or don't have a singularity, but my question is whether, because of time dilation, no matter has reached the center and formed a ...
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Varying the Dirac action with differential forms

The Dirac action in a curved spacetime can be written in terms of the veilbein $\{ e^a \}$ and spin connection $\{ \omega^{ab} \}$ differential forms. Let the spinor field $\psi$ be interpreted as a ...
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1answer
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Dropping a rope in a black hole [duplicate]

If there is a spaceship hovering above a black hole so that it can get away, what would happen if the spaceship connected a rope to itself and dropped the rope in? Could you pull the rope out?
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1answer
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Einstein Tensor doesn't vanish [on hold]

Hello my question is how is it possible that the Einstein tensor doesn't vanish in the Schwarzschild metric. For example $G_{11}= \frac{1}{2} g_{11} g^{22} g^{33} \partial_2 \partial_2g_{33}$ is one ...
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0answers
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Curvature created by an object near Earth via energy-stress tensor

From Misner... who uses the convention of (-, +, +, +) for the metric $g^{\mu\nu}$, with the electromagnetic stress energy tensor being(pg.141): $$T^{\mu \nu} = \frac{1}{\mu_0}(F^{\mu \alpha}F^{\nu}{...
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3answers
198 views

Separating the topics of general and special relativity

So, I have managed to confuse myself beyond the point of repair. I am not a physics student, so my physical knowledge is limited. Anyway, there are a few topics of relativity, which I can not seem to ...
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Why do we visualize space time as trampoline surface? [duplicate]

It's a silly question probably. But the thing is that what is the fascinating about fabric surface. I am so sorry for this silly question in advance. I read a lot articles regarding my question. But ...
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Gravitational $N$-body mergers?

Beyond binary systems and its mergers, have numerical relativity groups computed an approximation to $N$-body GW signals/waveforms or is that a hard unsolved task?
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2answers
85 views

Metric tensor: Why relate it to Cartesian/Minkowski coordinates?

Why does the metric tensor always relate to cartesian coordinates? Let's take the simple case for the metric tensor in 3D-space without a time dimension, $g_{ij}= \begin{bmatrix} 1 & 0 &...
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0answers
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Writing the curvature tensor in terms of spin connection

I am trying to know what are the missing steps in deriving the following expression for the Riemann curvature tensor in terms of the spin connection $\omega$ and the triad $e_\mu^j$. Where the ...
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1answer
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How can I calculate time difference of things moving at different speeds?

Satellites orbiting earth are faster than it, and hence from our perspective they age slower, or, for us time moves faster. Is there a way to calculate this difference? Even though earth is fast, ...
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1answer
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Proving that test particles in GR, follow spacetime geodesics

My question is pretty much in the title. According to this paper, this is not exactly proven rigorously yet. What I dont understand is what exactly is not proven. If I'm not too wrong, a test particle ...
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1answer
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Does the density of an object play a role for it's gravitational effects?

My thought experiment: We repalce our sun with an object of identical mass, rotation, shape, etc. but not the same density, i.e. the object would have a radius of 100km. The "replacement-time" would ...
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1answer
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Whats the quickest way to compute the Ricci tensor?

I have been going through exam papers and often they ask us to calculate ricci tensor components and affine connections from a given metric. They seem to take far too long for the time you are ...
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1answer
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When GR is not valid passing the event horizon?

A test body crosses the event horizon of a black hole. When can we say that GR breaks down? Only at the singularity? At any point CLOSE enough to the singularity? How much close? In summary, do we ...
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3answers
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Rigorous procedure of gluing together two spacetimes

There seems to exist a procedure of "gluing two spacetimes together". In particular I've seem this mentioned in the context of gravitational collapse. The examples I've seem where that of gluing ...
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0answers
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g force & general relativity effect at tips of propellor blade [duplicate]

If an aircraft propeller with engine running felt a force of 100g at the tips of the blades,but only 1g at the hub,& the engine ran for an average of 6 hours per day for 10 years,how much younger ...
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Static charge in an accelerated frame

In special relativity the metric of an accelerated frame is $$ds^2= (1-2 a_j x^j)dt^2 + 2 \Omega_{m j}x^j dx^m dt + \eta_{ml}dx^m dx^j$$ where the sums over latin indices go from 1 to 3. Let's suppose ...
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0answers
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Radial infall in Schwarzschild

In Straumann's book on general relativity, one finds the following solution to the question of geodesic radial infall into the black hole: $$d\tau=(\frac{2m}{r}-\frac{2m}{R})^{-\frac{1}{2}}dr$$ To ...
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1answer
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Coordinate transformation of basis vectors

The question Let $e_a$ be the coordinate basis vectors in a manifold described by coordinate system $x^a$. The vector displacement between two nearby points is given by \begin{equation} ds=dx^ae_a=dx'...
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1answer
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Why is light affected by time dilations in space-time curvatures

My previous question on this site gave me an answer to what affects light - space warping or time warping. The answer is- both. But what now doesn't make sense to me is why light is affected by time ...
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Proper time of an object crossing event horizon in Kruskal coordinates

So I am reading a paper on a certain black hole paradox. The specifics actually don't matter, but if you want context (p16): black hole thought experiment. An object falls into a black hole. The ...
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1answer
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How slow can time get near a black hole?

The closer I get to a black hole, does time slow down proportionally? Does time stop near the event horizon?