A theory that describes how matter produces and responds to 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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Why does weak equivalence principle say gravity is equivalent to acceleration?

I am told that the weak equivalent principle, that $m_i=m_g$ (inertial and gravitational masses are equivalent) is equivalent to the statement that in a small system you can't tell whether you are in ...
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1answer
49 views

Can a spacetime solution in GR have no Killing vector fields?

Sometimes Killing vector fields in a given spacetime are described as giving information about a symmetry of that particular spacetime solution. If I look at the requirement of a Killing vector field ...
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1answer
266 views

Geodesic equation from Euler - Lagrange

There are several ways to derive the geodesic equation. One of which is the variational method which I seemed to understand it because it was written in great details. Then it was mentioned that the ...
2
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1answer
503 views

Minimal vs. Non-minimal coupling

What is the difference between Minimal vs. Non-minimal coupling in General Relativity? A brief introduction to Minimal Coupling in General Relativity could be useful too.
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1answer
500 views

Surface gravity of Kerr black hole

I'm going through Kerr metric, and following the 'Relativist's toolkit' derivation of the surface gravity, I've come to a part that I don't understand. Firstly, the metric is given by ...
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1answer
536 views

How will the Twin Paradox become, for Time Dilation, if no acceleration was ever involved?

I think one catch in Twin Paradox was about the big acceleration that can turn back the traveling twin from light speed outward bound, to become light speed inward bound. What if there is strictly no ...
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0answers
43 views

Time functions in general relativity

In my general relativity notes a function $f$ is called time function, if $\nabla f$ is time-like past-pointing. Say that we are in Schwarzschild spacetime and I want to check if $f=t$ is a time ...
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3answers
54 views

Gravitational time dilation, does time of the observer at a lower gravitational potential looked slowed down in the frame of the higher one

This question is mainly inspired after watching the movie known as Interstellar We knew that for time dilation caused by relativistic motion between A and B. A will measure B's clocks slowing down, ...
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255 views

“Redshifting” of forces in stationary spacetime

Here's the problem statement: Let $(M,g_{ab})$ be a stationary spacetime with timelike killing field $\xi ^{a}$. Let $V^{2} = -\xi _{a}\xi ^{a}$ ($V$ is called the redshift factor). (a) Show that the ...
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1answer
53 views

Why do we need frame-fields to describe fermions in SUGRA?

I'm learning about the frame formalism and read that to couple fermions to gravity you need to go to the frame-formalism. As a motivation to learn more about frame-fields would someone sketch me why ...
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5answers
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Is the total energy of the universe constant?

If total energy is conserved just transformed and never newly created, is there a sum of all energies that is constant? Why is it probably not that easy?
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3answers
126 views

Time slowed by gravity

If time moves more slowly on Earth (due to our proximity to a gravitational body) than for someone orbiting Earth in a spaceship, yet the opposite occurs in the frequently cited "twin paradox" of the ...
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1answer
78 views

Questioning Einstein's view on gravity [duplicate]

Oke, so my mind is blown by Einsteins view on gravity, at least as far as I understand the basics and principles he based his views on. One of the first things that struck me was that most of his ...
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213 views
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Is quantum gravity, ignoring geometry, the theory of a fictitious force?

This question is motivated by this question and this one, but I will try to write it in such a way that it is not duplicate. In short, I don't understand the motivation for a "quantum theory of ...
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3answers
88 views

Is gravitational Chern-Simons action “topological” or not?

Here are the 2+1D gravitational Chern-Simons action of the connection $\Gamma$ or spin-connection: $$ S=\int\Gamma\wedge\mathrm{d}\Gamma + \frac{2}{3}\Gamma\wedge\Gamma\wedge\Gamma \tag{a} $$ $$ ...
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3answers
229 views

Is energy conserved in general relativity? Does $\nabla_aT^{ab}=0$ represent the conservation of energy and momentum?

For example, the radiation dominated cosmology, the energy density of radiation is propotional to $a^{-4}$ and the volume is propotional to $a^3$, where $a$ is the scale factor. So the total energy ...
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3answers
841 views

What is the most compelling evidence of General Relativity in the presence of matter and energy?

The most oft-cited triumphs of GR are things such as the shifting perihelion of Mercury, gravitational redshift experiments, and gravitational lensing. But, as far as I know, these are only ...
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1answer
61 views

Can Einstein's 'Theory of General Relativity' exist in Harmony with 'Quantum Mechanics'? [on hold]

From the Book 'In Search of Schrodinger's Cat': Coordinates in space-time represent position; causality depends on knowing precisely where things are going, essentially on knowing their momentum. ...
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5answers
2k views

Newton's Bucket

Newton's Bucket This thought experiment is originally due to Sir Isaac Newton. We have a sphere of water floating freely in an opaque box in intergalactic space, held together by surface tension and ...
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2answers
141 views

Akin to gauge field, why GR's lagrangian is not $R_{abcd}R^{abcd}$? What's the mathematical or physical meaning of $R_{abcd}R^{abcd}$?

For gauge field theory, the Lagrangian of the gauge field is $$\mathcal{L}=-\frac{1}{4}\mathrm{tr}(\mathcal{F}_{\mu\nu}\mathcal{F}^{\mu\nu})=-\frac{1}{8}F_{a\ \mu\nu}F^{a \ \mu\nu}$$ The field ...
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1answer
129 views

Why should we believe in clock hypothesis?

It is often assumed in special relativity that the rate of a clock in a non inertial frame does not depend on the proper acceleration of the observer. The point is, Rindler's observer shows us that ...
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22 views

Ricci tensor of schwarzschild metric [closed]

In schwarzschild metric: $$ds^2 = e^{v}dt^2 - e^{u}dr^2 - r^2(d\theta^2 +sin^2\theta d\phi^2)$$ where $v$ and $u$ are functions of r only when we calculate the Ricci tensor $R_{\mu\nu}$ the non ...
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1answer
206 views

Why do galaxies “disappear?”

So, this bit of information confused me lately. Before, I figured galaxies were no longer visible by us because their luminosity decreased in an inverse square manner. However, while watching a movie ...
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1answer
68 views

Conformal Killing fields on Schwarzschild

I am trying to understand which are the conformal Killing Fields on the Schwarzschild spacetime. I say that $X$ is a conformal Killing field on $S$ ($S$ is Schwarzschild) if there exists a function ...
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1answer
130 views

What would happen if a negative mass crossed the event horizon of a black hole?

If negative mass really existed and somehow a very fast traveling negative mass object reached near the black hole's event horizon. What would happen when it crosses the event horizon? According to ...
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4answers
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Can general relativity be completely described as a field in a flat space?

Can general relativity be completely described as a field in a flat space? Can it be done already now or requires advances in quantum gravity?
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63 views

A proof for Newtonian origin of residual perihelion advances in solar system

In an Amazon book it is given a very simple formula $$\delta = \frac{k}{T^{5/3}}$$ conforming to which the so-called residual advance of perihelion $\delta$ of each inner planet in solar system ...
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0answers
49 views

Is it possible to assign a physical radius to a black hole?

The Schwarzschild metric is given by: $$c^2d\tau^2 = \left(1-\frac{r_s}{r}\right)c^2 dt^2-\left(1-\frac{r_s}{r}\right)^{-1}dr^2 - r^2 \left(d\theta^2 + \sin^2 \theta \, d\varphi^2\right).$$ The ...
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1answer
119 views

Do Gravitational Waves Actually Repel Spacetime?

I read something explaining that g-waves actually repel space-time. It described the following. Mass bends space-time creating gravity. An object like the sun, if it suddenly disappeared the ...
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2answers
84 views

How does covariant derivative act on Christoffel Symbols?

the question is how the covariant derivative acts on the following? $\nabla_\nu(\Gamma^\alpha_{\mu\lambda}R^{\beta\lambda})=?$ and ...
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1answer
53 views

How are these types of time dilation related?

How are these two phenomena related (if at all): 1. Gravitation slowing down time 2. High speed slowing down time
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1answer
140 views

Pressure and Density Using a General Lagrangian

Given a lagrangian of a form: \begin{equation}\mathcal{L}=f(\phi,\partial_{\mu}\phi\partial^{\mu}\phi)\end{equation} where $f$ is a function, I need to derive pressure and density in a FLRW universe ...
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1answer
116 views

Thought experiment: Tethered galaxies - to the extreme

If two rocks were tied together with a tight, absurdly long, non-elastic rope, and placed on planets at either end of Earth's observable universe - or beyond - What would happen? Is the structural ...
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1answer
42 views

Does inflation predict a closed universe?

I read somewhere that both a closed and a finite flat universe would have zero total energy in General Relativity (On the Zero-Energy Universe). But the best evidence shows that the universe is flat ...
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1answer
58 views

Effect of cosmological constant on time

The cosmological constant is introduced in Einstein equations in the form : $G_{\mu\nu} = T_{\mu\nu} + \Lambda g_{\mu\nu}$, as I understand it, shouldn't the term $\Lambda g_{\mu\nu}$ have effects on ...
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1answer
73 views

How close can an observer approach the black hole in an unpowered flyby without falling into it?

In classical mechanics by choosing the right trajectory you can approach a planet arbitrarily closely, if there is no atmosphere or anything to slow you down, you can approach the surface then fly ...
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219 views

Is the Graveyard Really so Serious?

Calculations in relation to black holes are solely in consideration of spacetime curvature and its effects. They are in total alienation with respect to the action of inertial agents[external ...
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1answer
143 views

GR exercise: falling particles on earth's surface

I'm having some trouble with Exercise 5.1 in Shapiro's BH,WD&NS book, which goes as follows: Consider two particles of mass $m$ at distance $r$ and $r+h$, such that $h\ll r$, on the same ...
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0answers
50 views

Discontinuous momentum in relativity

I'm thinking about a fantastical scenario where the velocity of all macroscopic objects in the universe is instantaneously set to 0. In a Newtonian reference frame, this is relatively easy to ...
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3answers
2k views

Why does pressure act as a source for the gravitational field?

I'm asking for a qualitative explanation if there is one. My own answer doesn't work. I would have guessed it's because when a gas has pressure the kinetic energy adds to the rest mass of a given ...
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3answers
311 views

Entire Universe's Momentum

I was thinking about the definition of the conservation of momentum, which says that momentum is conserved unless outside forces are acting on the system, and I was wondering that if the system is the ...
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1answer
31 views

Are quantum-entangled particles affected by relativistic speeds? [duplicate]

In my answer to a recent question on World Building, I suggested that quantum-entangled particles would be a good way for ships traveling at relativistic speeds to communicate. My understanding is ...
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0answers
47 views

Difference between Gravitational and Matter Scalar Fields

In the context of Scalar-Tensor theories of gravity (for example in Brans-Dicke) what is the difference between gravitational and matter scalar Fields? My doubt comes from "The scalar-tensor Theory ...
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1answer
48 views

Length contraction, front middle or back

I still don't have a solid understanding of Length contraction. Imagine we have a ruler of length $L$ that starts at rest upon a ground with markings on it, then accelerates until nearly the speed of ...
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0answers
30 views

Does a body curve spacetime at higher velocities? [duplicate]

Suppose we have two objects where the distance over time decreases. Now, as I understand it, general relativity says that we can observe the Universe from the perspective of both objects an get a ...
7
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1answer
540 views

What is the maximum time dilation factor when orbiting a rotating black hole?

Suppose one spaceship is stably orbiting a rotating black hole and another is far away from the black hole. What is the maximum time dilation factor between the two ships? Can it be made arbitrarily ...
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6answers
36k views

How exactly does time slow down near a black hole?

How exactly does time slow down near a black hole? I have heard this as a possible way of time traveling, and I do understand that it is due in some way to the massive gravity around a black hole, but ...
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1answer
69 views

From affine space to a manifold?

One of the several definitions of an affine space goes like this. Let $M$ be an arbitrary set whose elements are called points, let $\mathcal{V}$ be a vector space of dimension $n$, and let ...
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2answers
714 views

Can colliding gravitational waves create a black hole?

Whether gravitational waves are real or just a coordinate freedom was argued in the early days of GR. Eventually the conclusion was that they were real. And if they are 'real' then I'm curious if... ...
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1answer
109 views

Time dilation - Earth & Jupiter [duplicate]

I have this doubt after watching Interstellar movie :) Lets assume I am in Jupiter. (I know it is a gas planet, full of hydrogen and helium, has extreme pressure etc. Lets please ignore those facts ...