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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192 views

Why is the mass of a Kerr black hole proportional to its angular momentum?

I'm a third year mathematics undergrad, and have just started the module General Relativity and spacetime geometry, I also have a keen interest in black holes. However I would like to know why and ...
4
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4answers
189 views

Distance in General relativity

I read a few lines about general relativity and one of the first equations is the one defining the eigentime of a time - like curve. But observers should also be able to measure length, right? So is ...
5
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1answer
196 views

The cosmological constant as a Lagrange multiplier?

The cosmological constant $\Lambda$ can be introduced into the gravitational action like this : \begin{equation} S = \frac{1}{2 \kappa} \int_{\Omega} (R - 2 \Lambda) \sqrt{-g} \; d^4 x + \text{matter ...
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1answer
73 views

Signification of “finite but unbounded universe”?

I recently read Einstein's book about relativity and he says that his theory predicts the shape of the universe. It would be finite but unbounded. But how is this possible? What's the difference ...
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4answers
3k views

Are neutrinos affected by gravity?

Layman here, but EE and BS physics. I know that light is affected by gravity. But are neutrinos? During the collapse of a star into a neutron star, as the electrons join protons to form neutrons ...
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0answers
40 views

Beyond gravitational waves- what now? [duplicate]

Now that the existence of gravitational waves has been established, what is the position regarding the incompatibility of general relativity and quantum mechanics in the creation of matter? Has this ...
8
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1answer
143 views

Acceleration of particle “held in place” at $x = 1$ [closed]

The metric components in a two-dimensional spacetime are given in terms of the coordinates $(t, x)$ by$$ds^2 = -\cosh x\,dt^2 + dx^2.$$Consider a particle that is "held in position" at $x = 1$. What ...
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1answer
23 views

Deriving Electromagnetism energy-stress tensor in GR [closed]

Please find the mistake in the following calculations. We have $L=-F^{\mu\nu}F_{\mu\nu}$, and try to derive the energy-stress tensor using $\delta(-g)^{1/2}=\frac{1}{2}(-g)^{1/2}g^{\mu\nu}\delta ...
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1answer
357 views

Higher-Dimensional Metrics in (Hyper)-Spherical Coordinates

I want to compute the components of the Riemann curvature tensor (for a case similar to the Schwarzschild solution) in 4 + 1 dimensions, but I want to use a higher-dimensional analogue of spherical ...
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0answers
35 views

Does energy produce a gravitational force [duplicate]

$E=mc^2$. From this, I would assume that any form of energy (not just rest-mass energy, but kinetic energy as well) would produce a gravitational force. Am I being too naive in my application of ...
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0answers
45 views

Gauge invariance in gravitational field

I have read that the linearized equation for the metric fluctuations $h_{\mu\nu}$, namely: $$ \partial^2h^{\mu\nu}-\partial_{\alpha}(\partial^{\mu}h^{\nu\alpha}+\partial^{\nu}h^{\mu\alpha}) ...
3
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1answer
167 views

Local translations in curved spacetime

A global Poincare transformation on a scalar field induces $$\delta(a, \lambda)\phi(x) = [a^{\mu}+\lambda^{\mu\nu}x_{\nu}]\partial_{\mu}\phi(x). \tag{11.46}$$ In curved spacetime we replace $a^{\mu} ...
5
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1answer
211 views

An argument that massive particles don't redshift?

I start with the spatially flat FRW metric in conformal co-ordinates: $$ds^2=a^2(\eta)(d\eta^2-dx^2-dy^2-dz^2)$$ This metric has the following non-zero Christoffel symbols: \begin{eqnarray} ...
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0answers
36 views

GR - curve (in)completeness & (in)extendibility

Seeking clarification of the distinction between completeness of geodesics/extendibility of curves in GR spacetimes? (Confirm: not the geodesic completeness of a spacetime but the completeness of an ...
0
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1answer
55 views

Information from inside a black hole

Now I'm hardly a physicist, but I am pretty interested in it. I was thinking about black holes and the movie Interstellar, and if you've seen it, then one of the central points about it is that they ...
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0answers
61 views

Relation between second covariant derivative of Killing vector and Riemann tensor [closed]

I need to prove that $$D_\mu D_\nu \xi^\alpha = - R^\alpha_{\mu\nu\beta} \xi^\beta$$ where D is covariant derivative and R is Riemann tensor. $\xi$ is a Killing vector. I have proved that $$D_\mu ...
10
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2answers
197 views

Can you have black holes in your black holes?

Inspired by Are we inside a black hole?, can you have a black hole such that other black holes are in them? In particular, the event horizon of the larger black hole should completely enclose the ...
4
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1answer
84 views

LIGO event - energies involved?

So, we have two Black Holes merging shortly after LIGO turns on after the upgrade. Some questions: a) How lucky was it to see this event? What are the expected rate of occurrence? b) Was this event ...
6
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1answer
115 views

Two “Robertson-Walker observers,” velocity of baseball as seen by second observer right before it's caught?

The spacetime metric of a spatially flat ($k = 0$) radiation dominated FLRW universe is given by$$ds^2 = -dT^2 + T[dx^2 + dy^2 + dz^2].$$Consider two "Robertson-Walker observers," i.e., observers with ...
0
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0answers
35 views

Help needed to understand Kerr coordinate transformation

The (uncharged) Kerr metric for a black hole of mass $M$ and angular momentum $Ma$ takes the form $$ds^{2} = \Sigma\Big(\frac{dr^{2}}{\Delta} + d\theta^{2}\Big) + (r^{2} + a^{2})\text{sin}^{2}\theta ...
8
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1answer
4k views

Do residents of the Hudson Bay area have more time?

Apparently there is a gravity anomaly in the Hudson Bay Area in Canada: gravity is "missing" or it is slightly less than it is in the rest of the world. Does that mean that things in the Hudson Bay ...
1
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1answer
58 views

Rotational relativity? Is there an universal frame of reference for rotation?

So, there is obviously no such thing as an universal frame of reference for velocity. According to the relativity theory, there is no difference between two observers moving with respect to each ...
4
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2answers
611 views

Introduction to relativity books [duplicate]

Possible Duplicate: Getting started general relativity I am an engineer who loves to read science fiction books especially when there's more science than fiction but usually I see that I ...
1
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2answers
105 views

Where do I begin in order to study relativity? [duplicate]

I am in high school now and I want to get the basic idea of what relativity. Can anyone suggest me a book or website for it? I am also curious about the mathematics behind it. Is it possible for me to ...
0
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1answer
159 views

Time dilation triplet paradox

Here is the twin paradox with a twist. Scenario 1: An observer (A) leaves from the equator of the earth and travels with an acceleration of $9.8\,\mathrm{m/s^2}$ in a north direction ( i.e. in the ...
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2answers
53 views

Bending of Light in General Relativity using Perturbation

It is standard textbook calculation (e.g. Schutz's First Course in General Relativity page 294) that we can find a total angular change in light deflection due to gravity to be ...
3
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1answer
86 views

The dimension of the energy-momentum tensor and the Einstein-Hilbert action

I have been thinking recently what will happen if one uses the energy momentum tensor of the Dirac field as a source in the Einstein Field equations. It is well known that in this case $$ ...
1
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1answer
39 views

Solving systems of equations using Levi-Civita and index notation?

I'm doing some self-studying out of Hughston and Tod's Introduction to General Relativity and I stumbled upon a few problems asking me to solve systems of equations using Levi-Civita and index ...
6
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2answers
103 views

Scanning the universe - edit: expanding or shrinking

I know that this may sound as a very basic question, but how come that we can detect CMB radiation, light or gravitational waves from the big-bang era? Shouldn't this radiation has overtaken us a ...
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0answers
17 views

Simple Question About Repulsive Potential Field Time Dilation

A space-time with a point mass gravitational potential given by $\Phi(r)$ has a metric described by, $$ds^2=-\left(1+\cfrac{2 \cdot \Phi(r)}{c^2} \right) \cdot c^2 \cdot dt^2+\left(1-\cfrac{2 \cdot ...
2
votes
1answer
64 views

Does Alcubierre drive allow time travel? [closed]

In Alcubierre drive, one can travel apparently faster than the speed of light by "compressing" space in front in the direction of travel. So let's say we have a stationary observer at point A, and an ...
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2answers
287 views

what is relation between time and space in general relativity?

there is a relation between time and space in special theory of relativity: $$t^2c^2-L^2=\tau^2.c^2$$ what is relation between time and space in general relativity?
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2answers
59 views

Power of blueshifted light falling on observer in circular orbit around Schwarzschild black hole

This answer explains that the time dilation for an observer in a circular orbit around a Schwarzschild black hole, relative to a distant observer at rest relative to the black hole, is given by the ...
3
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3answers
158 views

Large gravitational waves

The recently detected gravitational wave at LIGO were extremely small - requiring a $1 billion interferometer to even detect its presence as it passes Earth. The gravitational constant G is small: ...
5
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2answers
58 views

Wald's General Relativity, section 6.3 Page 144

I cannot understand how he reaches the conclusion in equation 6.3.36 and 6.3.37; even the terminology is somewhat confusing. This is a problem of bending of light under gravitational field. This is ...
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2answers
75 views

How can geometrized units have more than one constant equal to 1?

I can understand how you could manipulate units to make a certain constant equal to $1$, like $c$ or $G$, et cetera. But how can you make it so two constants (in this case $c$ and $G$) are equal to ...
37
votes
4answers
6k views

Are black holes very dense matter or empty?

The popular description of black holes, especially outside the academia, is that they are highly dense objects; so dense that even light (as particle or as waves) cannot escape it once it falls inside ...
3
votes
1answer
163 views

What is the problem with quantizing GR in the Effective Field Theory approach?

In the modern view due to Wilson, the cut-off $\Lambda$ is an intrinsic property of a theory and renormalization just means that the theory is invariant under scale transformations below $\Lambda$. ...
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4answers
292 views

Why didn't LIGO wait for a second observation of a gravitational wave? Are not reproducible results fundamental to science? [closed]

Wikipedia states, "Reproducibility is one of the main principles of the scientific method." So why did LIGO ignore a main principle of the scientific method? My whole life I have been taught that ...
3
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2answers
88 views

Gravity and spacetime bending [duplicate]

Something that puzzles me if gravity is just bending of space time near a mass then what is gravitational force? If say two massive bodies were perfectly at rest relative to each other they would ...
0
votes
2answers
79 views

Are gravitational force and gravitational time dilation proportional?

Particles in gravitational fields are subject to gravitational time dilation. The closer a particle is near a gravitational source, the slower is running its clock. I would like to know more about the ...
1
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0answers
31 views

Einstein-Infeld-Hoffman-Lagrangian for a Test-Particle as Limit of Schwarzschild-Geodesic

Consider a test particle of mass $m$ which is in orbit around a spherical-symmetric body with mass $M$. It therefore has a position as described by the coordinates $r,\phi$, and its motion can be ...
3
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7answers
857 views

Is there a universal rest frame of reference?

I am still struggling with C being a constant and what that implies. So can an experiment be done to find the resting state for the universe? Take a device with an observer and a light source and two ...
1
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1answer
46 views

Coordinate form of divergence of anti-symmetric tensor field [closed]

just a quick question on something that might save me a little bit of time and effort. In a general curved metric, the divergence of a vector field, $A^\mu$, can be written as: $ \nabla_\mu A^\mu = ...
2
votes
2answers
191 views

What is the metric tensor for?

I am wondering how to use the metric tensor, in practice? I read the book and done the exercises in A student's guide to vectors and tensors by Dan Fleisch. The concept of a tensor and their ...
0
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1answer
50 views

Classical Limit of Schwarzschild Metric

The orbit of a test particle orbiting a black hole can be described by the Lagrangian $$\mathcal{L} = -\frac{1}{2}\left(-\left(1-\frac{2 G m}{c^2 r}\right) \dot{t}^2 + \left(1-\frac{2 G m}{c^2 ...
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0answers
34 views

What is a zero temperature horizon?

While reading the paper "Disorder horizons: Holography of randomly disordered fixed points" by Hartnoll and Santos, I came across this: We are interested in solutions with a zero temperature ...
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0answers
25 views

Why don't big bang photons conserve mass and energy? [duplicate]

A photon from the big bang has lost most of its momentum and energy. What does it push against? Does it break the 'laws' of conservation of energy and momentum? Is there any possibility that momentum ...
4
votes
1answer
105 views

Do gravitational waves travelling through a medium produce sound?

Say Alice decided to orbit dangerously close to a couple of black holes circling each other. She is in a heavily enclosed astronaut suit, as is Bob, who is floating much further away. Assuming Alice ...
6
votes
2answers
181 views

Implementing Category Theory in General Relativity

I was thinking if it may be possible to implement category theory in general relativity. I don't mean writing simply in terms of categories, but actual fundamental ideas (i.e. physics of the theory ...