# Tagged Questions

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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### How do we expect distance measurements to compare inside and outside the event horizon of a black hole?

I've read that as one approaches the event horizon of a black hole, time is dilated relative to time measured farther away from the event horizon (clocks tick slower near the event horizon). I've ...
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### Is a metric tensor field the same thing as $ds² = -dt² + dx²+ dy² + dz²$?

I am having trouble understanding the nature of the metric tensor field on spacetime manifolds. In particular, a Riemannian manifold $(M,g)$ is defined as a real smooth manifold $M$ equipped with an ...
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### Tensors as multilinear maps

Sean Carrol's in his book on GR introduces tensors as a multilinear map of a set of dual vectors and vectors onto R. I usually think of tensors as a multidimensional array of numbers with fixed ...
1answer
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### Where is the mass energy of potential energy (such as for the universe?)

As you know, energy has mass via $E=mc^2$. If I understand right, mass must be inside of a particle, and can not just be "free floating." Gravitational potential energy (or what ever its equivalent ...
1answer
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### Geodesic equation from the proper time integral

This is something that has been bothering me for a little while. The usual procedure that I've seen is to write the proper time as the line integral $$\tau=\int_\gamma d\tau$$ along some curve $\gamma$...
2answers
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### Are time and gravity affected when at rest compared to free fall?

A falling object moves along a geodesic path ('straight path') in spacetime. When it comes to rest it now follows a 'curved path' through spacetime. Is the passage of time and force of gravity ...
1answer
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### Curved paths through spacetime when standing still?

I have heard that falling objects fall at the same rate irrespective of their mass. They are 'following straight line paths through curved spacetime'. Does this mean that objects that accelerate in ...
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### Einstein's equation: good, intuitive introduction anywhere? [duplicate]

Baez - like most others - gives (IMHO) a quite unsatisfactory introduction to Einstein's equation. They all start with the equivalence principle or similarly unintuitive reasoning, relating it to ...
1answer
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### General relativity: is curvature of spacetime really required or just a convenient representation?

I'm not really far into the general theory of relativity but already have an important question: are there formulations that can do without spacetime curvature and describe the general theory of ...
1answer
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### Gravitational wave solutions to the Einstein field equations

It is well known that general relativity predicts gravitational waves, but I would like to know how. What solution(s) to the Einstein field equations yield something which can be interpreted as a wave(...
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### Expanding universe as predicted by the Einstein Field Equation

Without the cosmological constant, the Einstein field equation predicts the universe is expanding. Why is that? It is counter-intuitive because generally gravity should pull things closer and shrink ...
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### Books on cosmology

I am a 14 year old who is independently studying physics. I finished the book: Spacetime and Geometry: An Introduction to General Relativity by Sean Carroll. I am specifically interested in cosmology, ...
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### How to demonstrate frame dragging through the Kerr metric?

I derived the Kerr metric, but in a form which doesn't seem to relate to frame dragging. I have been trying this for some time, so how do we relate the Kerr metric to frame dragging?
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### Schwarzschild Solution

I'm able to derive the Schwarzschild solution under the assumptions that the metric is (1) static (2) spherically symmetric and that the space is the vacuum. However, I have read that the ...
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### How much additional light does Earth receive from the Sun due to Earth's gravitational field?

I was reading about how gravity affects light, and that got me wondering how much additional light is collected by the Sun due to the Earth's gravitational field. Is it a significant amount of light (...
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### Difference between the metric tensor in general relativity and the metric tensor in mathematics?

Is the metric tensor in general relativity the same as the metric tensor in maths, or is there a difference?
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### Why is the cosmological constant a scalar?

Maybe my understanding is just off, but the cosmological constant is just a scalar, right? What are it's units? Why a scalar? - was a tensor 'cosmological constant' ever considered or is it just not ...
1answer
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### Galactic Rotation Speeds - Ehrenfest Paradox, Gravitational time dilation, Dark Matter - all of the above?

The observed paths and speeds of objects, part of some distant galaxy, do not match up with speed vs distance curves it seems - the observed speeds are not falling off in fact they're trending as ...
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### Does relativistic glider violate principle of equivalence?

The relativistic glider proposed can slow down the fall of an object in gravitational field. Will this violate the principle of equivalence which says that one cannot distinguish between free falling ...
1answer
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### How did Einstein arrive at the right hand side of his general relativity tensor equation?

It seems Einstein postulated the right hand side of his field equations… I see in books that tell the story of how he arrived at what to put on the right hand side of his tensor equations, the physics ...
2answers
870 views

### Curvature of spacetime as a real thing?

I get the curvature tensor in General Relativity, it is “just” math. Does space-time REALLY curves as a tangible thing, or is Einstein proposing a mathematical abstraction? More naively, please allow,...
3answers
196 views

### What is the evidence of interpreting $g_{\mu\nu}$ as the metric of space-time?

I think if we don't mention the meaning of $g_{\mu\nu}$ as the metric of space-time, we can still construct the equation of motion and Einstein field equation in a way such that $g_{\mu\nu}$ is just a ...
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### Is space stretched with no limits by a black hole?

Some depictions of black holes show space being warped into a singularity, with no end, e.g. as pictured below. Moreover, in Cosmos, Neil Tyson speculates with the possibility that Black Holes contain ...
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134 views

### Is the surface of a heavy sphere bigger than $4 \pi r^2$ due to general relativity?

I am unfortunately not familiar with the mathematics behind general relativity. However, on a heavy planet (say a sphere) gravity will bend space-time in a way that an object initially in rest, will ...
3answers
2k views

### Event Horizon of Supermassive Black Holes

I'm going to ask/explain this as best I can; I'm sure I have some fundamentals wrong here. Spaghettification is a phenomenon which occurs only in stellar-mass black holes owing to the immense gravity ...
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### Is gravity a force? [duplicate]

If gravity just emerges from the curvature of spacetime, is it actually a force? Why is it one of the 4 fundamental forces of nature?
1answer
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### Time coordinate inside black hole horizon [duplicate]

I am new to physics and was trying to learn more especially about general relativity. The Schwarzschild metric, changes the sign of the time and radial parts of the metric once we cross the event ...
5answers
873 views

### Does coordinate time have physical meaning?

I have always been a little confused by the meaning of the "$t$" which appears in spacetime intervals or metrics in general relativity. I concluded that $t$ was just a mathematical thing which allow ...
1answer
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### Null Coordinates

I have a very basic question: what are the advantages of writing a metric in the null coordinates? Which extra insight do they provide? I've looked in Caroll's "Spacetime and Geometry" and Wald's "...
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### How does a rotating object cause frame dragging?

Frame dragging is a consequence of general relativity. But I don't really understand it. Of course I can find metaphors like the "honey metaphor" where stirring a honey can move the specks even if ...