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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14
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2k views

What is the exact gravitational force between two masses including relativistic effects?

I was wondering if there is a closed-form formula for the force between two masses $m_1$ and $m_2$ if relativistic effects are included. My understanding is that the classic formula $G \frac{m_1 ...
0
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1answer
94 views

How to find a metric of a general observer?

Yes, that's it. How to find a particular metric of an observer in general relativity? Let's say we have a static metric: ...
1
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3answers
100 views

In general relativity, how do we think of Newton's third law for gravity?

In GR everything become geometric, gravity becomes curvature in spacetime. How do we think of Newton's third law in the context of GR? What corresponds to action and what to reaction?
3
votes
3answers
230 views

Books on cosmology

I am a 14 year old who is independently studying physics. I finished the book: Spacetime and Geometry: An Introduction to General Relativity by Sean Carroll. I am specifically interested in cosmology, ...
10
votes
6answers
291 views
+50

Extended object passing near an event horizon

Suppose a physically realistic object of nontrivial size (such as a star) free-falls past a black hole. The center-of-mass trajectory for the object is hyperbolic and (therefore) completely outside ...
11
votes
2answers
837 views

The Role of Active and Passive Diffeomorphism Invariance in GR

I'd like some clarification regarding the roles of active and passive diffeomorphism invariance in GR between these possibly conflicting sources. 1) Wald writes, after explaining that passive ...
7
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2answers
274 views

Gravitational waves as information carriers

Is it possible to utilize gravitational waves as a delivery system for information between two observers straddling the event horizon of a black hole? And why ?
1
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2answers
136 views

Locally flat coordinate and Locally inertial frame

I am having some doubts on myself regarding the above concepts in General Relativity. First, I want to point out how I understand them so far. A male observer follows a timelike worldline ($\gamma$) ...
20
votes
2answers
1k views

Layman's explanation and understanding of Einstein's field equations

Most of us have heard of Einstein's amazing equations which describe the universe around us, yet only some of us understand what the equations are actually saying. What are these equations ...
13
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4answers
4k views

Is there a maximum possible acceleration?

I'm thinking equivalence principle, possibilities of unbounded space-time curvature, quantum gravity ...
1
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0answers
59 views

Christoffel Symbol for Vaidya metric [on hold]

Can any one help me in getting nonvanishing Christoffel symbols for the metric $$ ds^2 = −f(u, r)du^2 - 2du\,dr + r^2d\theta^2 + r^2(\sin\theta)^2d\phi^2, $$ where $$f(u, r) = (1 −2m(u))/r.$$ This ...
2
votes
1answer
244 views

How come that an Infinite universe will collapse under gravity?

In this PSE post the issue is about the stability of an infinite universe under Newtonian gravity. Here I'will drop the Newtonian constraint because we know of the finite speed of interactions and I ...
2
votes
4answers
75 views

Any tips on evaluating Riemann tensor?

I am calculating the Riemann tensor for the Schwarzschild solution. I've calculated all 9 non-vanishing Christoffel symbols already. Now I need to evaluate the Riemann tensor and I find no easy way to ...
2
votes
1answer
27 views

Mass Distribution Inside Sphere with Relativity

(Shell Theorem) If a mass is spherically symmetrically distributed within a spherical region, an observer measuring the gravitational pull from that spherical region would not know how the mass is ...
7
votes
1answer
215 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 ...
7
votes
1answer
471 views

Was Einsteins work with relativity necessary for successful space travel?

So I know that Einstein and general relativity had huge impacts on the way we view the world, but how crucial were these scientific advancements to the success of our space programs? Would Newtonian ...
3
votes
1answer
34 views

Is there an algorithm for N body simulations in General Relativity [duplicate]

I am new to general relativity but have a background in computer science. Why is it so hard to do n-body simulations in GR? For example, there could be a program which takes the properties (mass, ...
0
votes
2answers
46 views

A couple of questions on the ADM formalism in general relativity

I've been reading up on the ADM formalism in general relativity and have been stuck on a couple of concepts. The first is to do with the foliation of spacetime into space-like hypersurfaces. I ...
0
votes
0answers
27 views

Derivative of time with respect to proper time

When wants to solve the Schwarzschild-Two-Body-Problem with the Runge-Kutta-Method, the second derivative of the time $t$ with respect to the proper time of the moving particle $\tau$ is needed. How ...
0
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0answers
16 views

Diversion of large Earth impactors

I ask"Can a beam of particles at relativistically high speeds be directed 'across the bow'of an object moving toward the Earth in order to use gravity to gradually divert it from its path?"I am ...
1
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1answer
108 views

Age of the universe [on hold]

Does the fact that the edge of our observable Universe contains information from the beginning of the Universe give us an ability to determine its age? The edge of our observable universe surely has ...
1
vote
2answers
130 views

Why does the second Weyl scalar describe electromagnetic radiation?

I've been reading about the null tetrad, the Weyl tensor, and the Newman-Penrose identities, and so I found out about the Weyl scalars. While the zeroth, first, third, and fourth scalars describe ...
0
votes
1answer
30 views

Determinant of the curved space scalar wave operator

I am reading a paper titled 'Analogue Gravity' (http://www.livingreviews.org/lrr-2011-3 or http://arxiv.org/abs/gr-qc/0505065) In the paper (page 15/159) they say this: $$\det(\sqrt{-g} g^{\mu \nu}) ...
0
votes
1answer
81 views

Relationship between mass and the radius of curvature of space and time

What is the relationship between mass and the radius of curvature of space and time created due to the presence of the mass? please give the mathematical relation if there is any?
6
votes
2answers
232 views

Doesn't the Schwarzschild metric combined with Hawking radiation imply that nothing ever gets past the event horizon of a black hole?

According to the General Theory of Relativity, the coordinate time distance per spacetime distance traveled by a particle freely falling into a black hole gets closer and closer to $0$ as the particle ...
0
votes
2answers
151 views

If you shine a light away from the center of a Schwarzchild black hole, will it stay still?

$$ A $$ Light is travelling away from the absolute center of the Schwarzchild black hole (i.e. none of that spinning/stretching field) at $\ C $, and so shouldn't $\ \Delta C$ need to be greater than ...
4
votes
1answer
257 views

What kind of object is the Landau--Lifshitz pseudotensor?

I understand that it's called a pseudotensor because it's not a tensor. Wikipedia says most pseudotensors are sections of jet bundles, which are perfectly valid objects in GR. ...
0
votes
0answers
34 views

Finding inverse tensor operator

For example I have such tensor operator: $$ O^{\mu \nu \alpha \beta} = (a^2+m^2)(\eta^{\mu\nu} \eta^{\alpha\beta} + \eta^{\mu\alpha} \eta^{\nu\beta}) + a^\mu a^\nu \eta^{\alpha\beta} + a^\mu ...
-5
votes
3answers
72 views

Need of Fourth Time dimension [on hold]

What is the need of 4th dimension in GR. Can we solve the problem without assuming 4th dimension. If we specify in three dimensional grid values of relative time in all the elements of grid, can we ...
0
votes
0answers
20 views

References on the 3 body problem

Does anyone know good references for the general 3 body problem? I'm looking for both analytical and numerical approaches.
2
votes
0answers
46 views

GR. Gauge fixing in 2-sphere [closed]

I am working in GR with a tensor field ($A^\mu$) and a complex scalar ($\Psi=M e^{i\Theta}$). My geometry is $S^2$. I have my Lagrangian and my 2nd order equations. They are invariant under $\Theta ...
1
vote
1answer
109 views

Why a timelike geodesic maximizes path length?

I'm studying some GR and my book says that in Pseudo-Riemannian manifolds geodesics may even maximize the path locally. That's what happen to the timelike geodesics, for example. My first question: Is ...
3
votes
2answers
2k views

Can anyone please explain Hawking-Penrose Singularity Theorems and geodesic incompleteness?

Can anyone please explain Hawking-Penrose Singularity Theorems and geodesic incompleteness? In easy to understand plain English please.
0
votes
0answers
25 views

Gravitoelectromagnetism or graviton thory to derive equivelent formulas to relativity theory [closed]

Is it possible to change the definitions of an event happening (which currently in relativistic theory is defined by the moment you see* something - the time light took to travel to you) such that ...
0
votes
0answers
41 views

value of $n$ in modified gravity model

In the modified gravitational model $ f(R)=R+\lambda{R_{0}}\left(\left(1+\frac{R^{2}}{R_{0}^{2}}\right)^{-n}-1\right) $ Are there any restrictions on the value on $n$. Also is this model valid for ...
1
vote
2answers
550 views

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 ...
2
votes
0answers
26 views

Maximum Power transmitted using General Relativity waves - cf Schwinger limit

In Electromagnetism, QED says that the linearity of Maxwell's equations comes to an end when field strengths approach the Schwinger limit. Its about 10^18 V/m. What is the corresponding formula for ...
1
vote
0answers
65 views

Lagrangian, geodesics and relativity [closed]

My background is in maths, but I have been studying some basic physics with occasional input from a friend who is studying for a physics PhD. Due to my background, I am keen to visualize things ...
-15
votes
2answers
152 views

When will physics understand it is the 'dark mass' not the 'dark matter'? [closed]

There is new thinking occurring in physics where 'dark matter' is considered to be incorrect. The new thinking is that mass fills 'empty' space. The mass which fill's 'empty' space is being referred ...
0
votes
1answer
49 views

General Relativity - Four Velocity Derivative Question

I am trying to get my head around a small point used in a book I am reading about General Relativity. The book states that because $u_au^a = c^2$ it follows that $u_a \nabla_b u^a = 0 $ The first ...
-2
votes
0answers
28 views

Is Twin Paradox solved in Special Relativity or General Relativity? [duplicate]

I'm getting pretty frustrated about finding the true solution to the Twin Paradox. If I open 10 relativity books, they all tell that they have the correct solution and the other books are wrong. So I ...
21
votes
1answer
959 views

Is general relativity holonomic?

Is it meaningful to ask whether general relativity is holonomic or nonholonomic, and if so, which is it? If not, then does the question become meaningful if, rather than the full dynamics of the ...
0
votes
1answer
47 views

How can we define a frame of reference in general relativity?

I have started reading general relativity. (A First Course in General Relativity, Bernard Schutz). I am finding very hard to understand a frame of reference. When I was reading special relativity ...
1
vote
1answer
133 views

Thermal radiation in the Unruh Effect

The following formula has been given in 't Hooft's black holes notes ($|\Omega \rangle$ is the vacuum state of Minkowski space, O is a operator): $$\langle \Omega| O|\Omega \rangle = \sum_{n \ge 0} ...
17
votes
3answers
3k views

Nature of gravity: gravitons, curvature of space-time or both?

General relativity tells us that what we perceive as gravity is curvature of space-time. On the other hand (as I understand it) gravity can be understood as a force between objects which are ...
36
votes
5answers
7k views

Shine a beam of light horizontally, drop a stone from same height - would both hit the ground at the same time?

If a beam of light was shone horizontally, and simultaneously a stone was dropped from the same height, would they both hit the ground a the same time? Of course on Earth they would not, but let's ...
13
votes
1answer
403 views

Why are anti-de Sitter spaces so interesting when we believe the universe is expansionary?

Perhaps this is a naive question, but in my recent (admittedly limited) readings about AdS spaces, I keep wondering why they seem to be such a hotbed for theoretical research (AdS/CFT correspondence, ...
3
votes
1answer
41 views

Do two bodies spinning about the same axis in the opposite direction repel each other?

I recently read about the GEM equations, which look very much like the Maxwell's equations. Does this mean the behavior of mass is like the the behavior of the electric charge? So for example if you ...
0
votes
2answers
137 views

Does the universe have a different age to different observers?

Although I understand that the universe is approximately 12 billion light years wide, and that may mean that it took the light photons 12 billion years at 186,000 miles per second to reach the ...
0
votes
1answer
60 views

Spinor notation in general relativity

I have a somewhat broad/big question, and I know that there are many references for it available out there. However, so far I couldn't find anything that I can really understand, that's why here is my ...