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.

learn more… | top users | synonyms (1)

2
votes
0answers
49 views

How does GR determine the topology of spacetime? [duplicate]

The crux of GR is the action $$ S=\int _\mathcal M d^n x \sqrt{|g|}\,R $$ Varying this and setting $\delta S=0$ gives you the Einstein field equations. However, that only determines the metric, not ...
1
vote
1answer
40 views

Eccentric binary black holes

Comparable-mass binary black hole inspirals and mergers are expected to be an important source of gravitational wave signals for current and future ground-based detectors. It is generally expected ...
0
votes
0answers
28 views

Dark Energy Density Paramater For Unlimited Expansion

Suppose that the universe is dominated by matter and dark energy. Let $\Omega_m$ and $\Omega_\Lambda$ denote the respective relative density parameters. Given $\Omega_m$, what does $\Omega_\Lambda$ ...
55
votes
8answers
5k views

Turbulent spacetime from Einstein equation?

It is well known that the fluid equations (Euler equation, Navier-Stokes, ...), being non-linear, may have highly turbulent solutions. Of course, these solutions are non-analytical. The laminar flow ...
2
votes
1answer
210 views

Riemann tensor with 2nd and last indice the same will vanish?

I calculated that Riemann tensors are antisymmetric with respect to 2nd and last indice,as the symmetry properities of $R_{\rho\nu\sigma\mu}$ goes. $$R^{\omega}_{\ \ \ ...
1
vote
1answer
79 views

Geodesic equation (free particle)

How to find a coordinate system whose geodesic equation does not have the "Christoffel symbol" term? (i.e. free particle - generalized Newton's second law.)
0
votes
0answers
17 views

Acceleration measured when hovering over a non-rotating black hole [duplicate]

I’m wondering what would be the acceleration theoretically measured (for example by an accelerometer) locally by an astronaut whose (ideally pointlike) spacecraft is hovering steadly over a non ...
1
vote
0answers
31 views

Gravity effect of a star behind the sun during a solar eclipse [closed]

We know that stars blocked by the sun during a solar eclipse may still be observable as if they are not behind the sun but rather visible to the side unblocked by the sun (because the photons are ...
0
votes
2answers
62 views

Minkowski geometry definition

The general relativity is based on Minkowski geometry definition with its special properties. The general relativity cant be approved wihout Minkowski geometry definition. Why Minkowski geometry is ...
4
votes
1answer
85 views

In what manner does momentum of a particle with mass decrease due to spatial expansion?

I've read that the momentum of particles declines due to the universe's expansion. In particular, that $p \propto \frac{1}{a}$, where $a$ is the scale factor. For light, this momentum reduction ...
0
votes
1answer
27 views

A book containing a large subset of known exact solutions to the EFEs

I am looking for a good book which contains the known exact solutions to the EFEs. A "library" of sorts. I am aware that it's not really possible to get all of them in a single book, but at least one ...
-6
votes
2answers
100 views

Traveling through time, reaching the past - POSSIBLE? [closed]

I was obsessed in studying the "faith" and I've made several great discoveries. I don't want to publish anything yet, but I have a semi-proven (proven partially) / theories / so I am curious on bones. ...
1
vote
1answer
19 views

Vacuum solutions to the EFEs

I was wondering if there are any papers in which authors have compared cosmological observations to those phenomena predicted by vacuum solutions to the EFEs? Obviously there is matter in the ...
1
vote
1answer
72 views

Are all maximally symmetric spacetimes constant curvature spacetimes?

A $d$ dimensional maximally symmetric spacetime is a spacetime with the maximum allowed number of Killing vectors. This number is $\frac{d(d+1)}{2}$. Constant curvature spacetimes are spacetimes ...
8
votes
1answer
658 views

The final parsec “problem”

Many and perhaps all galaxies seem to contain supermassive black holes of about $10^7 M_\odot$ at their centres. Determining their origins is of great astrophysical interest. In what I understand to ...
2
votes
0answers
34 views

Why is it useful to study spatially inhomogeneous spacetimes? [closed]

There are many scholars who have dedicated their efforts towards finding solutions to the Einstein Field Equations that are spatially inhomogeneous. Current cosmological observations indicate that on ...
2
votes
0answers
22 views

In causal dynamical triangulation, what equation(s) give the distribution of angles of the triangles?

I know very little about this topic, but going on what I learned in my one semester of QM, there has to be some Schrodinger-like equation they are using to get the distribution of angles of triangles ...
2
votes
0answers
65 views

Gravitational mass defect

In nuclear physics we have a mass defect by the binding energy of the nuclides. A similar effect appears in the theory of gravitation induced by the gravitational binding energy, which reduces the ...
3
votes
2answers
193 views

Is the popular explanation given for gravity in General Relativity misleading? [duplicate]

In most popular explanations of General Relativity, both in print and film/television, gravity is demonstrated using an example of a 2 dimensional plane being flat, then when putting a heavy object in ...
0
votes
1answer
35 views

Why only binary star system produce ripples in space-time (gravitational waves)?

I saw a statement being made in a video, but it didn't explain why. It originally said, "stars orbiting each other does not create gravitational waves, binary system of two massive stars or black hole ...
3
votes
1answer
165 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 ...
-3
votes
1answer
71 views

How can light follow curved spacetime?

At the speed of light, there is supposedly infinite length contraction so the entire universe is a single zero-dimensional point (or an infinitely thin 2D plane perpendicular to the direction of ...
0
votes
2answers
78 views

Are there continuous spacetime events?

What is the formal definition of an event? According to Wikipedia, "an event is a point in spacetime (that is, a specific place and time) and the physical situation or occurrence associated with it." ...
1
vote
1answer
78 views

Time independent Kerr metric

The Kerr metric expressed in terms of polar coordinates $r,\theta,\phi$, such that $x = r\sin(\theta)\cos(\phi)$, $y = r\sin(\theta)\sin(\phi)$, $z = r\cos(\theta)$. Then the Kerr metric is given as ...
0
votes
1answer
43 views

Galileo 5 and 6 satellites testing gravitational time dilation

In today's Guardian there an article titled "Satellite launch accident provides unexpected test of Einstein’s theory" - ...
3
votes
2answers
196 views

G4v Gravity Theory: Why does this get rid of Dark Energy?

Earlier this year, Carver Mead of CalTech published a paper which seems to be garnering a lot of attention: http://arxiv.org/abs/1503.04866 http://www.npl.washington.edu/AV/altvw180.html ...
1
vote
1answer
68 views

Numerical relativity in causally pathological spacetimes

To perform numerical relativity simulations one almost universally adopts the so called "3+1" approach: spacetime is divided up into spacelike slices, each representing a "moment in time". After some ...
2
votes
4answers
140 views

From the photons perspective

Probably been answered but couldn't find the answer. From the perspective of a photon: - For the photon to travel from body A to body B would take 0 secs. - The universe would be one point in ...
5
votes
1answer
205 views

Does frame dragging apply to linear motion?

Firstly I will admit I do not understand the real cause of rotational frame dragging and some of the math heavy explanations are too complicated for me. To me frame dragging looks like unsubstantiated ...
1
vote
2answers
60 views

Light and Gravity

The gravitational force does not affect the speed of light rather affects the frequency of light (hence light changes colors, red to blue and vice-versa). I know this has been verified but I have ...
3
votes
0answers
35 views

Sources for black hole geodesic orbits

I am looking for good sources that discuss both Kerr and Schwarzschild particle orbits (geodesics). Most sources write down the geodesic equations, constants of motion and the Hamiltonian, but do not ...
1
vote
1answer
117 views

Is max speed of causality (light) proven experimentally?

Is it possible to have an alternative theory which is consistent with experiments supporting GR, but which doesn't mandate a speed limit on causality? In other words, I understand there is ...
0
votes
0answers
27 views

Are only measurements registered as events?

When we measure an electron or some other system behaving quantum mechanically, we observe something. Now, this can be called as an event in relativity terms meaning if we live in 1-D spacetime, only ...
1
vote
1answer
59 views

Is there a way to write the Lorentz force in terms of one field, $L$, and one charge, $X$?

I have heard that physicists like to write electromagnetism as one force (the Lorentz force) and define it as $\vec{F_L}\left(q, \vec{v}, \vec{E}, \vec{B}\right) = q\left(\vec{E} + \vec{v} \times ...
0
votes
1answer
47 views

Show that $R_{\mu\nu}=C g_{\mu\nu}$ from the vacuum Einstein equation with a nonzero $\Lambda$ [closed]

If I begin with the vacuum field equation with a nonzero cosmological constant: $$R_{\mu\nu}-\dfrac{1}{2}g_{\mu\nu}R+g_{\mu\nu}\Lambda=0$$ How can I show that $$R_{\mu\nu}= ...
1
vote
0answers
77 views

Black hole's effect on itself with faster than the speed of light [closed]

If something were pulled into a black hole, my understanding is that you would approach the speed of light. Upon hitting the event horizon, you would be moving the speed of light. After that, you ...
5
votes
1answer
135 views

Finding diffeomorphism given vector fields [closed]

Given a vector field how do you find the associated diffeomorphisms? Say I am given a vector field in Minkowski space $$\xi = x \frac{\partial}{\partial t} + t \frac{\partial}{\partial x}.$$ How do ...
0
votes
0answers
32 views

Gibbons-Hawking Variation

I know there already exist some questions about this and some very good answers. However, I am still having trouble understanding one part of the calculation. The GHY term is given by ...
1
vote
1answer
92 views

What is the sum of the angles of a triangle on Earth orbit?

Gauss went out and measured triangles made up of mountain peaks to show that the angles sum up to 180 degree. However, general relativity leads to non-Euclidian space and I would like to get a better ...
1
vote
0answers
27 views

Non-time orientable quotient of de Sitter space

Examples of non-time orientable spacetimes are pretty scarce, but it seems the big one is quotients of de Sitter space of the form $dS^n/\pi_1$, where $\pi_1$ is some subgroup of the isometries of de ...
6
votes
4answers
353 views

What is the general relativity explanation for why objects at the center of the Earth are weightless?

The idea that as you move through the earth you get a symmetric cancelling of gravitational acceleration which approaches zero acceleration due to gravity at the center of the earth makes a lot of ...
2
votes
0answers
62 views

Two dimensional spacetime and the Gauss Bonnet theorem

Generally two dimensional spacetimes are deemed to be static, as the Gauss Bonnet theorem implies that the Einstein Hilbert action would be a constant independent of $g$. But as far as I can tell, ...
0
votes
0answers
57 views

Which property do the word Pressure refer to in General Theory of Relativity?

In this course by MIT Alan Guth while delivering the lecture stated " Both Pressure and Energy densities can produce gravitational fields. Negative pressure creates repulsive gravity and positive ...
2
votes
5answers
221 views

Is boundary well defined if variation of metric don't vanish on the boundary?

Suppose that you want to calculate the variation $\delta S$ of an action induced by some arbitrary variation $\delta g_{\mu \nu}$ of the spacetime metric : \begin{equation} S = \int_{\Omega} ...
3
votes
1answer
158 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} ...
1
vote
2answers
77 views

If curved paths imply that the vehicle is accelerated, how come do we assume that light gets curved whilst its speed is constant?

I don't understand how we can accept these two sentences at the same time: Light speed is constant, therefore experiences no acceleration. On the presence of a gravitation field, light path is ...
13
votes
5answers
581 views

What are some ways to justify the Einstein field equations?

Since they are a postulate of general relativity, it is not really possible to "derive" the Einstein field equations $$R_{ab} + \left(\Lambda - \frac{1}{2}R\right)g_{ab} = -8\pi T_{ab}$$ in any very ...
2
votes
0answers
69 views

Can a Set of “Maxwell's Equations” for Newtonian Gravitation be Derived from Newton's Force + Special Relativity?

When I learned about electromagnetism in my first year of undergraduate school, Maxwell's equations were derived roughly in the following way (see also here or in [1]): Gauss's law for a static ...
3
votes
5answers
125 views

Local inertial frame

In general relativity we introduce local inertial frames to be such frames where the laws of special relativity holds. Let $\xi^{\alpha}$ the coordinates in the local inertial frame, so we get ...
0
votes
2answers
49 views

Form of Spin Four-vector

The spin angular momentum of a gyro is represented, in special and general relativity, by a spin four-vector $S^{\mu}$. In the rest frame of the gyro, the spin four-vector takes the form ...