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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Stress-Energy Tensor Integral Identity [closed]

I'm attempting to work a problem in Schutz's A First Course in General Relativity, and I'm running into something curious with tensor indices. The problem states: Use the Identity ...
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1answer
85 views

White Hole Formation [duplicate]

How does a white hole form in nature if it were to exist? No knowledge of general relativity or advanced mathematics but doing a researching a physics project and need a basic explanation.
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2answers
239 views

What am I missing in this thought experiment about a black hole?

I've got a problem setting up a general relativity (GR) thought experiment. Thanks for your help! I'm the observer, in a lab that is falling through the event horizon of a black hole, observing a ...
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1answer
59 views

Definition of “nonlinear” in the context of perturbation of gravity

What exactly is the definition of a nonlinear perturbation when applied to a background spacetime metric? I have seen so called "linear perturbations" which look like $$ds^2 = -(1+2\Phi)dt^2 ...
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3answers
770 views

Are quantum mechanics and general relativity predictions of string theory, or were they built into the theory from the start?

Are quantum mechanics and general relativity predictions of string theory, or were they built into the theory from the start? If the former, why aren't tests of GR and QM considered simultaneous tests ...
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1answer
140 views

Spin connection and covariant derivative

How to prove explicitly (i.e., to don't postulate it) that by including Lorentz indices $a$ the covariant derivative $D_{\mu}$ looks like $$ D_{\mu}A^{\nu a} = \partial_{\mu}A^{\nu a} + ...
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1answer
86 views

Hawking radiation (black hole evaporation) [duplicate]

I understand that one of the simplified ways of looking at Hawking radiation is a pair of virtual particles close to the event horizon (but outside of it). The particle with negative energy falls into ...
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1answer
109 views

Question on Einstein's derivation of the equation of the geodesic line?

While reading one of the original paper on general relativity written by Albert Einstein, titled the foundations of general relativity, I came across the following passage in pages 167-168, or pages ...
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81 views

What does this Hodge dual symbol $\star_3$ mean?

We know that in this $$\star {f(...)}$$ the $\star$ represents the Hodge dual. But in this: $\star_3 f(...)$ what does specifically the $\star_3$ symbol mean?
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84 views

How much of General relativity follows from the invariance of $c$ and an escape velocity?

Just supposing Einstein hadn't come up with his idea of the equivalence principle, leaving him blind for a while. Would he still have been able to come up with General Relativity just using the ...
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1answer
47 views

Schwarzschild Solution Convention

In looking at the components of the Schwarzschild Metric, one finds $ g_{00} = (1 - \frac{r_s}{r})c^2 $. Wikipedia states that $r$ is measured as the circumference, divided by $2π$, of a sphere ...
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67 views

Can a free falling observer localize the event horizon by calculations?

I'm think that in general relativity we can always pass the one curve in one coordinate system for another coordinate system. My intuition say that the free falling observer locate the event horizon ...
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Can a metric in General Relativity, Supergravity, String Theory, etc., be asymmetric?

Why is it that all problems I encountered until now have metrics that when represented in a matrix form turn out to be symmetric? Aren't there asymmetric matrices representing some metrics?
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56 views

Duality and 1 forms

If a Killing vector is equal to: $$X= -\frac{1}{\sqrt{2}}\partial _t + \frac{\alpha}{\sqrt{2}}\partial_1.$$ But as far as I know is that the dual of a vector is a 1-form, so can I represent that ...
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3answers
605 views

Is it correct to say that falling object are standing still?

As I was browsing youtube I came across the BBC video "Brian Cox visits the world's biggest vacuum chamber - Human Universe: Episode 4 Preview - BBC Two" He drops a bowling ball and a feather in a ...
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3answers
129 views

If a Killing vector field is timelike, can it be set to $\partial/\partial t$?

If one has a Killing vector that turned out to be a timelike Killing vector field because of negative norm. Can we set this Killing vector field equal to $\partial/\partial t$?
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5answers
165 views

Is $ds^2$ just a number or is it actually a quantity squared?

I originally thought $ds^2$ was the square of some number we call the spacetime interval. I thought this because Taylor and Wheeler treat it like the square of a quantity in their book Spacetime ...
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1answer
45 views

Are the gravitational redshift and blueshift factors inverses of each other? [closed]

at a point in gravitational field assuming swcharzschild metric and the exact analysis. The other point in context is infinity. It would be helpful if you can provide citation/source of the ...
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1answer
149 views

Question about universe expansion

In general relativity, we cannot determine the global structure of the universe (since it is not flat), therefore all measurements and observations are only meaningful locally. In particular, we can ...
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1answer
47 views

Can someone clarify how many metrics exist that satisfy the EFEs?

As I currently understand it, there are two ways to work with the Einstein Field Equations: (1) exact solutions and (2) approximations that work under certain conditions. I also understand that ...
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3answers
192 views

Uniqueness or multiplicity of ADM masses for spacetime manifolds with more than one “end”?

The question is: What is the mathematical and/or physical basis for saying that a (static) spacetime manifold with more than one asymptotically flat region at infinity ("end") has a distinct ...
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1answer
143 views

What is the covariant basis around a Schwarzschild black hole? [closed]

First of all, I'm not interested in time for this question. So lets consider a 3-manifold whose metric is the spatial part of the Schwarzschild metric, so it has the event horizon and the singularity ...
3
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2answers
133 views

How does one calculate the full perihelion shift of Mercury, including perturbations from other planets?

I'm talking about the full calculation, including perturbations from other planets. I've seen the general relativistic correction done a half dozen times before, but I can't say that I've seen the ...
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3answers
418 views

Why do the Einstein field equations (EFE) involve the Ricci curvature tensor instead of Riemann curvature tensor?

I am just starting to learn general relativity. I don't understand why we use the Ricci curvature tensor. I thought the Riemann curvature tensor contains "more information" about the curvature. Why is ...
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0answers
68 views

How does Space-Time Cloak work?

Well, scientists have achieved Spacetime cloaking to make events fully disappear. Currently, it works only for a trillionth of a second, but here's real-world scenario from linked page: In theory, ...
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54 views

Relativity and Galaxy Rotation Speed

If time travels slower nearer gravity wells, why can't the galaxy rotation speeds being faster on the outer edges than the inner areas be explained by relativity? What necessitates dark matter?
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369 views

Stress-energy tensor for a fermionic Lagrangian in curved spacetime - which one appears in the EFE?

So, suppose I have an action of the type: $$ S =\int \text{d}^4 x\sqrt{-g}( \frac{i}{2} (\bar{\psi} \gamma_\mu \nabla^\mu\psi - \nabla^\mu\bar{\psi} \gamma_\mu \psi) +\alpha \bar{\psi} \gamma_\mu ...
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65 views

Can we embed 2+1 space-time of GR in a 3 Dimensional Euclidean space?

Wikipedia says that inflation is the exponential expansion of space in the early universe.I'm trying to have a physical picture of this.Given that I can't visualize 3+1 pseudoriemannian manifolds,I'm ...
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0answers
59 views

Local Acceleration of an observer near a black hole

In the first page of this link https://www.math.ku.edu/~lerner/GR/Schwarzschild.pdf they calculate the magnitude of acceleration felt by an observer at $r$ from the black hole: ...
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1answer
53 views

Post-Newtonian approximation for binary gravitating system

I have been studying gravitation waves radiated by a binary source. I have linearised Einstein's field equation and approximated the source to a Quadrupole moment to get the power radiated by the ...
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0answers
89 views

What's the best GR book for recreational study? [closed]

I currently have four books. Hartle Schutz Cheng Carroll (lecture notes) Which one is best for me to read easily? (especially, for foreigners) Or Do you guys can give good recommendations that ...
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0answers
59 views

Norm of Killing vector field

Let us suppose we have a Killing vector field with $X^a = 1/2$ and $X^b = 1/3$ and $g_{ab}=1$ where the other $c$ and $d$ components are zero. Now we want to find its norm: The formula for finding ...
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Why isn't the center of the galaxy “younger” than the outer parts?

I understand that time is relative for all but as I understand it, time flows at a slower rate for objects that are either moving faster or objects that are near larger masses than for those that are ...
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1answer
74 views

Geodesic deviation

In S. Carroll Lecture Notes on General Relativity, chapter 6, pages 152-153 we have equation (6.62) $$\tag{6.62} \frac{\partial^2}{\partial t^2} S^\mu=\frac{1}{2} S^\sigma \frac{\partial^2}{\partial ...
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3answers
216 views

Coordinates for FLRW metric

In GR, coordinate are just a tool for us to describe the physics, they should be equivalent. However, in standard form of FLRW metric, it can be inferred that the universe is expanding, but we can do ...
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1answer
121 views

How to find a metric of a general observer?

Yes, that's it. How to find a particular metric of an observer in general relativity? Let's say we have a static metric: ...
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1answer
49 views

Is this cosmological scenario possible?

Is it possible that the universe is infinitely large and contains an infinite amount of mass that is distributed in such a way that gravitational force is never infinite? If so, is it possible that ...
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1answer
89 views

Naturalness of tensor fields in general relativity?

In the third chapter of the book The Large Scale Structure of Space-Time, the authors say regarding the matter fields in general relativity: These fields will obey equations which can be expressed ...
2
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1answer
48 views

Does the payload of an Alcubierre drive have to be on board during the preparation phase?

I was thinking about the practical aspect of using an Alcubierre drive, assuming one existed. I'm no expert, but my understanding is that, since the destination has to be in the forward light-cone of ...
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1answer
37 views

isotropy of 3-space and spacetime metric

The most general spacetime metric is given by $$ds^2=g_{\mu\nu}dx^\mu dx^\nu=c^2dt^2+g_{0i}dtdx^i-g_{ij}dx^i dx^j$$ Why does the second term said to violate isotropy of 3-space? It is true that, ...
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3answers
316 views

How strong must gravity be to stretch time?

I'm not sure if this is true or not but I heard that gravity has the ability to stretch time, and I was wandering if this is true. If so, how intense/powerful does the gravitational force have to be ...
2
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1answer
256 views

At what rate does light 'bend' around the surface of the earth?

Since the g force of earth is 9.8 m/s*2 does that mean light 'drops' at that rate as it travels past earth? Or is general relativity a lot more complex than that?
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2answers
88 views

Does the escape velocity of a black hole exceed $c$ *before* a singularity is created?

As an offshoot of the question Can we have a black hole without a singularity? I'm curious if the point of no return at which the massive object is condemned to become a singularity happens before its ...
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1answer
113 views

Why does $\frac{d\tau}{d\sigma} = L$?

I am given a (3+1)-dimensional spacetime that has the line element \begin{equation} ds^2 = -\left(1-\frac{2M}{r}\right)dt^2 + \left(1-\frac{2M}{r}\right)^{-1} dr^2 + r^2 d\phi^2 \end{equation} ...
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2answers
204 views

Locally flat coordinate and Locally inertial frame

I am having some doubts on myself regarding the above concepts in General Relativity. First, I want to point out how I understand them so far. A male observer follows a timelike worldline ($\gamma$) ...
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0answers
88 views

Gravitational time dilation in changing curved space time

Imagine a portion of spacetime which is changing its spacetime curvature because of an object with great mass travelling nearby. For instance, before it was flatter, and after the object passes it ...
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1answer
111 views

Acceleration of stationary observers in their own reference frame?

In the beginning of this link: https://www.math.ku.edu/~lerner/GR/Schwarzschild.pdf they calculate the acceleration of a stationary observer. As I understand, this accleration is seen by an ...
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1answer
336 views

What is the largest disparity of gravitational time dilation from earth's that life can survive?

In certain theoretical scenario's a human can be in a gravitational field where he would age half as fast as on earth's surface. However, for light to travel half as fast in one direction, we are ...
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1answer
73 views

What is an “equation of motion” as used in context of geodesic equation?

I am studying general relativity and using the book Gravity by James Hartle. On page 170, he provides the following table: I don't understand what he means by "equation of motion" nor do I ...
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0answers
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Do GR and SR have to be considered together to determine time dilation? [duplicate]

In another related question: How to connect Einstein's Special Relativity(SR) with General Relativity(GR)? , John Rennie stated that SR is a subset (or rather can be derived from) GR, but not vice ...