Linked Questions

22 votes
5 answers
5k views

What does a frame of reference mean in terms of manifolds?

Because of my mathematical background, I've been finding it hard to relate the physics-talk I've been reading, with mathematical objects. In (say special) relativity, we have a Lorentzian manifold, $...
Wesley's user avatar
  • 847
5 votes
3 answers
1k views

Global Frame of Reference in General Relativity

People have been saying that a global frame of reference does not exist in General Relativity. However, from Wikipedia: In Schwarzschild coordinates ${\displaystyle (t,r,\theta ,\phi )}$ the ...
user avatar
5 votes
3 answers
4k views

Reference frames versus coordinate systems

I have the following distinction clear in my mind: Reference frame → state of motion of the observer Coordinate system → set of numbers used to map the space points within a reference frame So for ...
Federico Toso's user avatar
0 votes
3 answers
269 views

Does general relativity reduce to special relativity for free falling objects?

The following was stated in a general relativity lecture series: "Full space is needed in GR. Minkowski space is sufficient for SR. However, Minkowski space is sufficient to compute properties of free ...
Stepan's user avatar
  • 209
7 votes
2 answers
712 views

Slingshot around a black hole, dipping into event horizon

Suppose we have an object swinging by a black hole. My understanding is that if it remains outside the black hole, it just swings by and doesn't lose any energy (except maybe gravitational waves?). ...
Peter's user avatar
  • 183
2 votes
4 answers
5k views

Inertial frames of reference

I'm struggling with the notion of an inertial frame of reference. I suspect my difficulty lies with the difference between Newtonian and relativistic inertial frames, but I can't see it. I've read ...
Peter4075's user avatar
  • 3,029
3 votes
1 answer
625 views

Riemann normal coordinates and inertial frames in general relativity

The weak equivalence principle states that for infinitesimal patches of space and time, the laws of nature are identical to that of special relativity. This is mathematically reflected in the ...
Chandrahas's user avatar
  • 1,737
3 votes
3 answers
506 views

What exactly does the observer's coordinate system mean in special relativity?

This seems like a very basic question but I'm having a hard time understanding it, more precisely hard time visualizing it. Let say there is an observer, and we wish to somewhat formalize his ...
user575201's user avatar
6 votes
2 answers
366 views

Conflicting definitions of reference frames in general relativity

I'm having trouble understanding what constitutes a reference frame in general relativity as there seem to be several contradictory definitions. It is my understanding that, in special relativity, ...
xzd209's user avatar
  • 2,157
4 votes
1 answer
871 views

How a reference frame relates to observers and charts?

Recently I've been watching the General Relativity lectures from the "International Winter School on Gravity and Light" by Frederic Schuller. In those lectures he made the following two definitions: ...
Gold's user avatar
  • 35.9k
0 votes
2 answers
641 views

If I throw a ball at a black hole, will the ball exceed the speed of light when it reaches the event horizon? [duplicate]

The escape velocity of a black hole at the event horizon is the speed of light, this means an object that is dropped from the top of the black hole's gravitational well will reach the speed of light (...
Hierarchist's user avatar
0 votes
1 answer
981 views

Coordinate transformations in general relativity

Let's assume a non-rotating point mass with mass $M$. A non-massive object travels with constant velocity $\mathbf{v}_t$, with respect to the point mass, in the vicinity of the point mass. A non-...
Stark's user avatar
  • 9
2 votes
1 answer
347 views

What is this black hole merger orbital speed?

If space craft nears a black hole we see it getting slower and slower to the point it would appear to stop moving due to red shift. Then how fast are these black holes moving?
Muze's user avatar
  • 1
4 votes
1 answer
655 views

How does the Equivalence Principle imply that derivatives of the metric vanish in a freely falling frame?

Why do the first derivatives of $g_{\mu\nu}$ vanish in a freely falling coordinate system? I would like to start from the Equivalence Principle that for any point in spacetime there exists a locally ...
Alex's user avatar
  • 866
0 votes
1 answer
505 views

Time-dependent and space-dependent metric: possible combinations

I know that flat spacetime can be described using a constant spacetime metric. This is the metric of inertial observers who use Cartesian space coordinates. But consider the case where the metric is ...
Federico Toso's user avatar

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