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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GR matter-free equations and Schwarzschild geometry

I am reading some lecture notes on General relativity (undergraduate level) and I do not understand a sequence of statements about the topics in the title. After stating that the for matter-free ...
3
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2answers
225 views

The wave equation in general relativity, special relativity, and Cartesian coordinates

The relativistic wave equation is $$\square\varphi=\rho$$ where $\varphi$ is the field, $\rho$ is the source, and $\square$ is the D'Alembert operator, defined by ...
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1answer
59 views

Where is the way on a rotating black hole to another Universe? [closed]

Where is the way on a rotating black hole to another Universe? Where and how should it be entered by to get away from here?
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4answers
238 views

What was the Law of Gravity better explained by?

In mechanics, our professor made the declaration that "all laws of physics" have been disproven. He mentioned several examples including the Law of Gravity, mentioning briefly that it is better ...
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1answer
37 views

Luminosity distance from angular diameter distance

Consider that I know the cosmological angular diameter distance at a given redshift : $$D_{A}\left(z\right)=\frac{x_{object}}{\theta_{observer}}$$ Is there a general formula to compute the ...
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1answer
73 views

Knots and singularities

Can space-time singularities be treated as mathematical knots occurring in dimensions greater than four? I just drew an analogy with knots in one-dimensional strings. When a rubber-band is looped over ...
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0answers
68 views

How to draw the Poincaré patch of ${AdS_3}$?

My main reference for this question are these notes (maximally symmetric spaces.pdf) by Kurt Hinterbichler. I'm using Global Coordinates: \begin{align} x^0&=\sec{R}\cos\tau\\ ...
3
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1answer
133 views

Metric Perturbations in General Relativity and quasi-normal modes?

I am familiar with the tools that appear in (linear) perturbation theory for general relativity, that is namely that one writes: $$g_{\mu \nu} = g^{(0)}_{\mu \nu} + \epsilon g^{(1)}_{\mu \nu} + ...
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0answers
65 views

Stationary and Static

I have some confusion about the concept of stationary and static. A metric $g$ is called stationary if there is a time like Killing vector $K$. $g$ is called static is further HSO (hyper surface ...
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3answers
82 views

Speed/direction of gravity for a moving source [duplicate]

Consider the Earth, and a bowling ball held 186,000 miles (1 light second) above it. When the ball is released, it will start to fall vertically downwards towards the Earth. Now consider the case if ...
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3answers
252 views

Which clock is the fastest inside an accelerating body?

The picture shows an accelerating spaceship with two clocks inside it. It is so far away from all other bodys that gravity is of no importance. Will the bottommost clock be slower than the topmost ...
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0answers
20 views

Angular and luminosity distance in general?

Consider a non-Friedmannian Universe in which we know the trajectories of photons, ie in which we know null geodesics $\left(\eta, x^{1}, x^{2}, x^{3}, a, z\right)$ where : $\eta$ is the conformal ...
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59 views

Dark Matter and Modified Gravity

Could someone please explain briefly or refer me to an article or manuscript that shows how f(R) modified gravity theories can be used to explain the problem of Dark Matter, particularly Galaxy ...
3
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1answer
116 views

Taylor expansion of the metric

Consider a coordinate change $$ x^a\mapsto \tilde x^a=x^a+\epsilon y^a $$ In the note I am reading, the author calculate the change of metric by $$ g_{ab}(x) = \tilde g_{ab}(\tilde x)=\tilde ...
5
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2answers
249 views

Confusion about Lie derivative on metric

According to this site, the Lie derivative of a $(0,2)$-tensor is $$ \mathcal{L}_XT_{ab}=\partial_XT_{ab}+T_{cb}\partial_aX^c+T_{ac}\partial_bX^c $$ However, according the same website, the Lie ...
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0answers
74 views

About the proof of the second Bianchi Identity

The second Bianchi Identity is $$ \nabla_{[a}R_{bc]de}=0 $$ As far as I know, the proof (say, Walfram Mathword) start by stating the representation of Riemann tensor in local inertial coordinates $$ ...
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2answers
75 views

Understanding emergent phenomena in the block universe. (Reworded question)

Each person exists as an unchanging 4D worldtube in the block universe. At each slice of the worldtube there is a present, past and future. However, there is a black box* which appears to exist in ...
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2answers
130 views

Confused about the concept of time and time dilation [duplicate]

I am having a hard time understanding what is time. If scientists define time as a multiple of caesium frequency, then time itself is dependent on motion, so what if I have a number of particles that ...
5
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1answer
172 views

Schwarzschild Metric coordinate sign change in $0\leq r \leq 2GM$

In the event horizon of the Schwarzschild-metric not only the time coordinate but also the radial space coordinate seems to change sign: ...
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1answer
1k views

Would the inside of a black hole be like a giant mirror?

As any light reflected or emitted from objects inside a black hole (if it is possible to be there) does not leave the event horizon and comes back inside, would it be like seeing yourself? What I ...
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0answers
90 views

Newtonian Physics vs Relativity - the results [closed]

Does anyone have examples of the results calculated by using Newtonian physics vs the same ones calculated using relativity, compared with real measurements obtained in those experiments? Please ...
5
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3answers
320 views

Is there any relationship between gauge field and spin connection?

For a spinor on curved spacetime, $D_\mu$ is the covariant derivative for fermionic fields is $$D_\mu = \partial_\mu - \frac{i}{4} \omega_{\mu}^{ab} \sigma_{ab}$$ where $\omega_\mu^{ab}$ are the spin ...
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0answers
52 views

The border of the System

In General Relativity, if the system accelerates, the inside of the system and the outside of the system will have different speed of time. Where is the boundary of the system? If a human ...
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3answers
2k views

Why is spacetime curved by mass but not charge?

It is written everywhere that gravity is curvature of spacetime caused by the mass of the objects or something to the same effect. This raises a question with me: why isn't spacetime curved due to ...
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2answers
306 views

Global Properties of Spacetime Manifolds

When solving the Einstein field equations, $$R_{\mu\nu}-\frac{1}{2}g_{\mu\nu}R = 8\pi GT_{\mu\nu}$$ for a particular stress-energy tensor, we obtain the metric of the spacetime manifold, ...
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1answer
54 views

Isotropy of Space

Weinberg writes in his Cosmology text "Likewise,isotropy requires the mean value of any three-tensor $t_{ij}$ at $x=0$ to be proportional to $\delta_{ij}$ and hence to $g_{ij}$, which equals ...
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1answer
64 views

de Rham Cohomology of Schwarzschild Manifold

Let $C^p(M)$ denote the group of closed $p$-forms on the manifold $M$, and $Z^p(M)$ the group of all exact $p$-forms on the manifold $M$. The de Rham cohomology is given by the quotient, ...
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1answer
202 views

proper distance and proper length

I am wondering if I mix up the notion of proper distance and proper length. I have two cuves in Schwarzschild space-time describing the flight of two photons (think of it as photons guided in by ...
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3answers
139 views

Is Space-Time a special form of energy?

I know space-time can be influenced by matter and energy, so it must be somehow mingled in with the mix of it all, but does space-time have a fundamental particle? Can we make a little bit of ...
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2answers
296 views

Space-time Topologies?

When it comes to questions of existence of bounds for PDE's and such, one must often make some assumptions regarding the topology of the space-time to use well known theorems. My question is ...
3
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1answer
43 views

Differences between strong, weak, and micro lensing distinct or subtle?

In gravitational lensing, there are three categories of lensing: strong, weak, and micro. As I understand it, strong lensing (just as the name implies) occurs when a source and a gravitational lens ...
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3answers
1k views

Rocky Planet in the center of System [duplicate]

We all know that mostly stars are at the center of planetary systems, but is it possible that instead of star there was a rocky planet in the center with stars (and other planets and moons) orbiting ...
5
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1answer
120 views

Equivalency of Gauge Conditions

How is the Lorenz gauge condition $\partial_\mu \overline{h}^{\mu \nu}=0$ equivalent to the harmonic gauge condition $\Box x^\mu=0 $?
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1answer
144 views

Trajectory of a photon around a Schwarzschild black hole?

Consider a photon coming from the infinity in a unbounded orbit to a Schwarzschild black hole (Schwarzschild radius $r_{s}$) (see this for illustration). Its impact parameter is $b$ and its distance ...
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2answers
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Is there a simple layman way to explain the incompatibilities between quantum mechanics and (general) relativity to high school students?

Is there a simple layman way that I can use to explain the incompatibilities between quantum mechanics and (general) relativity to high school students (people with not much knowledge of the intricate ...
5
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1answer
211 views

Why is $S^1\times\mathbb{R}^{n-1}$ the topology of $AdS_n$?

Anti-de Sitter $AdS_n$ may be defined by the quadric $$-(x^0)^2-(x^1)^2+\vec{x}^2=-\alpha^2\tag{1}$$ embedded in ${\mathbb{R}^{2,n-1}}$, where I write ${\vec{x}^2}$ as the squared norm ${|\vec{x}|^2}$ ...
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2answers
160 views

Violating Cosmic Censorship

Let's say we try to remove the event horizon of a Kerr black hole by throwing in matter with some large angular momentum. If it starts with GM > a, could we increase a at all? Would such a particle be ...
2
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1answer
67 views

Friedmann Equations with varying G?

If Newton's constant $G$ actually varies with cosmological time $t$ would a suitably modified form of the Einstein field equations: $$G_{\mu \nu} + \Lambda g_{\mu \nu} = \frac{8 \pi G(t)}{c^4} T_{\mu ...
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1answer
135 views

Relation between impact parameter and distance of closest approach of a light ray in Schwarzschild Geodesics

The following wikipedia articles are incompatible : Two body problem / bending of light by gravity Schwarzschild geodesics / bending of light by gravity According to both articles, the equation ...
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2answers
57 views

Show that two families of curves are orthogonal (without using orthogonal trajectories)

I'm reading through Hartle's General Relativity and came across this question: Consider the following coordinate transformation from rectangular coordinates $(x,y)$, labeling points in the plane ...
11
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1answer
273 views

Suggested reading for quantum field theory in curved spacetime

I want to learn some QFT in curved spacetime. What papers/books/reviews can you suggest to learn this area? Are there any good books or other reference material which can help in learning about QFT ...
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3answers
128 views

About the speed of light and gravity

I read (I think ) that part of relativity theory is that a strong gravitational field distorts the uniform passage of time. If this is true and a lightwave 'travelling' to Earth passes a star near ...
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1answer
142 views

Is the cosmological redshift caused by the Planck mass increasing?

The standard explanation for the cosmological redshift is that photons emitted from far away galaxies have their wavelengths lengthened as they travel through the expanding Universe. But perhaps the ...
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3answers
717 views

Is gravitational time dilation different from other forms of time dilation?

Is gravitational time dilation caused by gravity, or is it an effect of the inertial force caused by gravity? Is gravitational time dilation fundamentally different from time dilation due to ...
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5answers
149 views

Can the equivalence principle be shown to follow from special relativity?

Einstein showed in various papers that the energy content of a body was a measure of its inertial mass. If you increase the internal energy of a system while keeping the center of energy at rest, its ...
5
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1answer
148 views

$L^{1}$ energy-momentum tensors in general relativity; semi-classical gravity

I was unsure whether to pose this question in a physics or mathematics forum, but it is an interesting idea I have been thinking about for some time. In any (semi-)classical field theory it is often ...
2
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1answer
170 views

What happens when an electron jumps through the event horizon of a black hole?

If quantum teleportation is performed into a black hole (by an electron for example), what happens to that electron? Let's say a hydrogen atom is very close to a black hole and the electron jumps ...
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1answer
174 views

What are the anomalies with General Relativity?

If general relativity is the newest model of Gravity which is so far been proven. Does it still have any anomalies such as the problem of Mercury's orbit during Newtonian gravity period? If so are ...
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0answers
63 views

$M^{+}_4$ Randall-Sundrum Brane Calculation

The basic Randall-Sundrum model is given by the metric, $$\mathrm{d}s^2 = e^{-2|\sigma|}\left[ \mathrm{d}t^2 -\mathrm{d}x^2-\mathrm{d}y^2 - \mathrm{d}z^2 \right]-\mathrm{d}\sigma^2$$ where $\sigma$ ...
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1answer
101 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 ...