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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Spherically Symmetric Metric in Nordstrom gravity

Nordstrom's theory of gravity postulates that the metric is of the form $g_{\mu \nu} = \phi ^2 (x) \eta_{\mu \nu}.$ The field equations, in vacuum are of the form $R=0$, where $R$ is the Ricci ...
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50 views

Perfect fluid and EM tensor in rest frame

I see that we use perfect fluid which is characterized by a energy density and isotropic pressure for general forms of matter. When guessing the values of energy momentum tensor indices we can use ...
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1answer
88 views

Is it possible to tell which way a Universe is spinning?

Imagine a Universe spinning on the x-axis. So there is a centripetal directed away from the x-axis. According to General Relativity this is entirely equivalent to a non-spinning Universe with a ...
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1answer
67 views

How to obtain the four-velocity of a fluid from the metric?

Let's say I'm working with a metric tensor for some spacetime with components $g_{\alpha \beta}$ relative to some coordinates $(\tau, x, y, z)$. Is there a general way of obtaining the four-velocity ...
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2answers
99 views

Mountains and their local effects on Earth's gravity

I was once a truck driver and can feel the inertia and kinetic energy on heavy loads while traveling. While climbing mountains in the Rockies I noticed gravity was different on the side of the ...
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1answer
72 views

Looking for a reference for $\gamma_a e^{a}_{\mu} D^\mu \gamma_b e^{b}_{\nu} D^\nu =D^\mu D_\mu - \tfrac{1}{4}R$

I am having trouble finding references for the following identities: Dirac Operator: $$ \gamma_a e^{a}_{\mu} D^\mu \gamma_b e^{b}_{\nu} D^\nu =D^\mu D_\mu - \tfrac{1}{4}R \tag{1} $$ QED Operator: $$ ...
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3answers
136 views

What happens 'inside' the event horizon of a black hole, in particular to photon speed

This is a follow-up question to two answers given here and here, where the speed in different coordinate systems is discussed when approaching the Schwarzschild radius. To cite, derived directly from ...
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32 views

Definition of vacuum and occupation number in expanding Universe

Suppose for simplicity we have theory of free quantum scalar field in expanding Universe (metric plays the role of background field) $g_{\mu \nu} = \text{diag}(1, -a^2,-a^2,-a^2)$, where $a(t) \sim ...
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47 views

Leading order approximation of Proper Radial Distance in General Relativity

Context: I'm currently going through this article (http://arxiv.org/pdf/0704.2667v1.pdf). In the 3rd page last paragraph the variable corresponding to the proper distance $y = ...
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60 views

Would quantum fluctuations cause problems for scalar-field inflation?

Wheeler once said that spacetime would be highly curved at very small scales because of the uncertainty principle for energy-momentum. In which case the spacetime becomes very bumpy and not smooth ...
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1answer
58 views

Time dilation at the Innermost Stable Circular Orbit

According to general relativity the time dilation is given by following formular: $d \tau = \sqrt{g_{\mu \nu} \dot{x^{\mu}} \dot{x^{\nu}}}$ If I'm interestet in the time dilation at the ISCO I set ...
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1answer
134 views

Gravity: Why Do things fall to Earth? [duplicate]

If gravity is in reality spacetime geometry why when I drop an object on the surface of the Earth does it fall to the ground? Does spacetime push it?
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1answer
84 views

Exact meaning of radial coordinate of the Schwarzschild metric

In this answer as well as on Wikipedia the radial coordinate of the Schwarzschild metric is described as follows: ...the r co-ordinate is the value you get by dividing the circumference of the ...
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1answer
120 views

Is there something similar to Gauss's Law For Gravity in General Relativity?

In Newtonian Physics there is an equation that for the Gravitational Flux of an object known as Gauss's Law For Gravity. Gauss's Law for Gravity describes the number of Gravitational Field Lines ...
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2answers
92 views

Age of universe?

Well relativity teaches us that time interval between two events is a frame dependent quantity, then how can we say that our universe is 13.8 billion years old? Should it not depend on who is asking ...
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I don't see that general relativity is really needed for GPS to work correctly [duplicate]

From what I understand, GPS localization is based on the difference in the reception time from the time of emission of a signal from different GPS satellites whose positions are known. For this we ...
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3answers
249 views

Confusion about the concept of cosmological horizon

This question was inspired by this one By definition we cannot see any event happening beyond the cosmological horizon. Let us assume that the expansion rate of the universe is such that the radius ...
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5answers
1k views

How does “curved space” explain gravitational attraction? [duplicate]

They say that gravity is technically not a real force and that it's caused by objects traveling a straight path through curved space, and that space becomes curved by mass, giving the illusion of a ...
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2answers
109 views

Should dark matter play an important role in designing a quantum theory of gravity?

Since dark matter "accounts" for most of the matter of the universe, and its effect are inferred from the gravitational effects, should it play an important role in designing an unified theory between ...
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26 views

String spreading?

What is 'string spreading' (in the context of string theory)? Does it have implications for the observability of post-classical effective field theory of gravity terms near macroscopic black hole ...
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4answers
269 views

Relation of General Relativity to Dark Matter and Dark Energy

I was reading an elementary book on dark matter (in fact, a historical perspective) and there were mentioned how the scientific community react to the idea of dark matter proposed as a solution to ...
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1answer
61 views

What does Kaluza-Klein theory say about the attraction/repulsion of opposite/same charges?

Since Kaluza-Klein theory is made out of general relativity - a gravitational theory in 4 dimensions which is only attractive, then how does it takes into account the attraction/repulsion of ...
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4answers
162 views

Which tensor describes curvature in 4D spacetime?

I heard these two statements which don't work together (in my mind): In 4D spacetime the curvature is encoded within the Riemann tensor. He holds all the information about curvature in spacetime. ...
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4answers
251 views

Why is “dark matter” theory accepted? Why wasn't general relativity rejected?

Dark matter was made up to account for unexplained effects such as gravitational lensing, the speed of expansion of the universe, or the rate of rotation of certain galaxies. However, as Feynman ...
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1answer
172 views

Null geodesic equations

If one is constrained to the $xt$ plane, one can define the intersection with that plane of the null hypersurfaces originating at some point $P$ as $$ g_{tt} \frac{d P^t}{d \lambda}\frac{d P^t}{d ...
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34 views

Can gravity affect light speed? [duplicate]

Can gravity affect light speed, for example slow it down ?
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49 views

Questions arising from the presentation of “Schild's ladder” in “Gravitation” (Misner, Thorne, Wheeler)

MTW, p. 248, presents a description of "Schild's ladder" construction which I quote here extensively enough for referencing some subsequent questions. A. Transport any sufficiently short stretch ...
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38 views

How is speed of light constant if it bends? [duplicate]

Gravitational lensing causes light to be bent.If light changes direction how can it be travelling with constant speed?Where am I wrong.Thanks for any help.
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1answer
111 views

Spacetime curvature effect on chemistry

Do current chemistry / astrophysics / stellar chemistry calculations include the effects of the curvature of spacetime on chemical reactions? For example, the heat transfer from a point closer to the ...
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1answer
58 views

Notation: tetrad indices

I am trying to understand the meaning of upper and lower indices as used in the Newman-Penrose formalism. The tetrad is $\lbrace l^{a},n^{a},m^{a},\overline{m}^{a}\rbrace$, where the upper index ...
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0answers
214 views

Stephen Wolfram claims to deduce the field equations from cellular automata, has anyone seen the actual mathematics?

In his new blog post Stephen Wolfram claims that he can derive general relativity from cellular automata. OK, so one can derive Special Relativity from simple models based on networks. What about ...
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47 views

Bending of light in a gravitational field & the principle of equivalence

I have a few conceptual issues following a standard thought experiment to argue why light bends in a gravitational field and I'm hoping I can clear them up here. Consider an observer in a lift in ...
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45 views

What would happen, gravitationally, to ships passing by each other at high speeds vs high accelerations?

Consider this scenario: Two identical space ships, the SS Observer and the SS Accelerator. In scenario A, the SS Accelerator is accelerated up to near C, stops accelerating, then flies past the SS ...
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51 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 ...
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63 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 ...
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32 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 $\Omega_\Lambda$ ...
59
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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
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1answer
214 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}_{\ \ \ ...
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1answer
96 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.)
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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 ...
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2answers
71 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 ...
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1answer
91 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 ...
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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 ...
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1answer
121 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. ...
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1answer
23 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 ...
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1answer
103 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 ...
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1answer
779 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 ...
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35 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 ...
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27 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 ...
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92 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 ...