# 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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### Calculation of co-moving coordinate separation for a moving object in a time-varying spacetime metric

My calculus has 30+ years of rust on it and I am stuck on the integration of the interval in General Relativity... I wish to calculate the spatial coordinate at time t of an object moving with ...
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### If the Einstein Field Equations are so hard to solve, how did Einstein know they were correct in the first place?

Consider a formula like $y = mx + b$. For instance, $y = 2x + 3$. It is simple to check that $(1,5)$ is a solution, as is $(2,7)$, as is $(3,9)$, etc. So it's easy to see that $y =2x + 3$ is a useful ...
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### Can curvature waves in f(R) theories explain gravitational lensing in cluster collisions?

The Einstein-Hilbert action leading to Einstein's equations is $$S\sim\int R \sqrt{-g}\, {\rm d}^4 x$$ There is a class of modifications of Einstein's relativity called $f(R)$ theories of gravity ...
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### Why does General Relativity predict more light deflection than Netwonian Physics?

If one looks at the limit as light's mass approaches zero, Newtonian Physics predicts a deflection of light (this can be seen by the fact that all objects are accelerate the same due to gravity.) ...
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### Geodesic equation proof confusing me

I was looking through this proof and have no idea where the $u$ comes from. Any help is appreciated. This is from here; I want to know how they got from eqn 5 to eqn 6.
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### Should gravitational waves be discovered already? [closed]

Gravitational waves are not discovered directly (yet). But does this have any consequences? Should we suspect out theories are wrong or not yet? I found some data about gravitational waves suspected ...
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### Why does moving near light speed keep you young? [duplicate]

As was shown in the movie Interstellar, when you go close to a black hole or move near the speed of light in space, then your clock runs slower than a clock on Earth. In the movie, Matthew ...
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### What is an “Einstein transformation” in general relativity?

When introducing the vielbein formalism in general relativity, I came across the use of an infinitesimal general transformation, or Einstein transformation. The latter term seems not to be covered on ...
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### Is it in general true that $\nabla_\mu T^{\mu\nu}=0$ implies the matter equations of motion?

I know of several cases where the covariant conservation of the energy momentum tensor $\nabla_\mu T^{\mu\nu}=0$ can be used to derive the equations of motion of the matter fields. Is this in general ...
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### What besides the metric do you need to set up the EFEs and the geodesic equation?

One of my professors wrote on the board (1) Mass tells spacetime how to curve $\to$ Metric/Einstein Field Equations (2) Spacetime tells mass how to move $\to$ Geodesic equation Suppose I am given ...
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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 ...
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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 ...
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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 $\gamma$...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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### 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,...
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### 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 ...
Why the curvature parameter can be interpreted as the difference between the average potential energy and the average kinetic energy of a region of space? Curvature parameter:\Omega_{k}\equiv\Omega-...