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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Stringy corrections to Friedmann equation

Does anyone know a reference or a paper which discusses string theory correction to Friedmann equations?
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2answers
190 views

Does relativistic mass exhibit gravitiational effects?

Groundhog Day Update, 2014 The simple and dumb way to ask my main question is this: If something like a neutron start goes sailing by at very close to the speed of light, say fast enough to double ...
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2answers
280 views

What is the geometrical interpretation of Ricci tensor?

In differential geometry and general relativity space is said to be flat if the Riemann tensor $R=0$. If the Ricci tensor on manifold $M$ is zero, it doesn't mean that the manifold itself is flat. So ...
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92 views

Some questions about spacetime topology, causality structures and other GR businesses

1) What are the exact conditions required for the canonical transformation? Most papers just assume away with global hyperbolicity, but is there a more general condition for it? "Quantum gravity in ...
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1answer
100 views

Is the center of mass in general relativity equal to the center of mass in newtonian gravity?

Consider 2 point masses $A,B$ a distance $d$ away from eachother without velocity or rotation spin. Is the center of mass in general relativity equal to the center of mass in newtonian gravity ? In ...
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68 views

The time dilation in an oscillating elevator

Suppose you are in an elevator which oscillates vertically with a frequency $\nu$. How will we find the time dilation in this oscillating reference frame ? If the lift is accelerating upward or ...
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2answers
246 views

Would the horizon of a black hole be different for a tachyon than for subluminal matter or photons?

One of the most useful black hole analogies I've seen imagines that space is "flowing" like a river into a black hole, and the point at which it flows in faster than c is the horizon. This analogy ...
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1answer
193 views

Equation for Hubble Value as a function of time

I am trying to write the equation for the situation where the Hubble parameter $H$ would be changing over time. In other words, it would represent an accelerated expansion of the Universe. That is, ...
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1answer
221 views

Why has a gravitational wave spin 2? (Group theoretically?)

How can I see, using group theoretic arguments, that a the quantum of a gravitational wave has spin 2? How can one show that it is described by a 5 dimensional representation of $SO(3)$? I know the ...
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1answer
372 views

Can a macroscopic body have wavelength as that of electron? [duplicate]

Einstein has suggested that light can behave as a wave as well as like a particle i.e, it has dual character. In 1924, de-Broglie suggested that just as light exhibits wave and particle properties, ...
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1answer
132 views

Schwarzschild geodesics

I've found on Wikipedia that energy $E$ and angular momentum $L$ of a particle are conserved quantities in Schwarzschild metric. It's written: $$L=mr^2 \frac {d\phi} {d\tau},$$ ...
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599 views

Is it possible to explain general relativity without tensors?

I do not know much about tensors. So I wonder: Is it possible to explain general relativity without tensors? I have some understanding of special relativity. I also have some understanding about ...
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48 views

General relativity && quantum mechanics “incompatibillity” [duplicate]

Now this may be utterly weird layman-physics-question, but anyways... I have read recently following: "The fundamental universe laws are everywhere the same. It's just that the manifestation (!) of ...
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3answers
205 views

What makes matter travel along geodesics?

The relativistic explanation of gravity is geometric, the motion of a body in a field of space-time distortion can be described as being at rest and travelling along a geodesic of that field, but why ...
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2answers
180 views

Lorentzian and Einstein Manifold

I am studying for my Bachelor thesis (in Mathematics). I and my advisor agreed on the Penrose-Hawking singularity theorems. My question is: 1) Which mathematical background should I focus on ...
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1answer
131 views

Where is a closed form also exact?

I'm not very familiar with exterior derivatives. I've some trouble following argument (which is a part of a proof that if the Riemann tensor vanishes, $R^{\,\rho}_{\;\,\sigma \mu \nu}=0$, iff there ...
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1answer
177 views

Foucault pendulum explanation, rotating earth or rotating universe?

If we start from the assumption that all frames of reference are valid for describing motion, how can a foucault pendulum either prove or disprove that the earth rotates or is stationary? Couldn't ...
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102 views

One more time about Nordstrom theory

Wikipedia says that Nordstrom theory with equations of motion of the test particle $$\tag{1} \frac{d (\varphi u_{\alpha})}{d \tau} = \partial_{\alpha} \varphi $$ and field equation $$\tag{2} \varphi ...
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1answer
101 views

How is it possible for you to be at the centre of the universe wherever you are? [duplicate]

I saw on Richard Hammond Builds A Universe on BBC2 a few days ago that you are always at the center of the universe wherever you are. Surely this is illogical, because you could never get to the edge ...
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1answer
100 views

Physical interpretation of $Q^i = \partial _\nu T^{i \nu}$

I'm trouble with exercise 1.8 of Carroll's Space-Time and Geometry: If $\partial_\nu T^{\mu \nu} = Q^\mu$, what physically does the spatial vector $Q^i$ represent? Use the dust energy momentum ...
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113 views

Why can apparent horizon be computed based on its local geometry?

Why can apparent horizon be computed based on its local geometry? In the paper titled Black Holes, Geometric Flows, and the Penrose Inequality in General Relativity by Hubert L. Bray, has been ...
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0answers
70 views

gravitational field as a spin 2 particle using gauge invariance [closed]

can someone help me prove that a gravitational field corresponds to a spin 2 particle using gauge invariance. i know about the tensor formulation of GTR and the gauge invariance in electrodynamics ...
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4answers
419 views

General relativity in terms of differential forms

Is there a formulation of general relativity in terms of differential forms instead of tensors with indexs and subindexs? If yes, where can I find it and what are the advantages of each method? If ...
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1answer
77 views

Will a space traveller slow down due to space expansion?

Photons of relic radiation loose their energy as they propagate through space. Will a space traveler loose their peculiar velocity as he travels through vast distances? Will he stop somewhere or still ...
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1answer
95 views

Physical meaning of the Rindler hyperbola vertex and the Rindler lines

Two questions regarding the Rindler diagram: 1) Does the vertex of a given hyperbola in the diagram have physical meaning? I know it is the inverse of the constant proper acceleration ($\alpha$) ...
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1answer
336 views

Step by step algorithm to solve Einstein's equations

I cannot completely understand what is a regular method to solve Einstein's equations in GR when there are no handy hints like spherical symmetry or time-independence. E.g. how can one derive ...
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74 views

What is the physical meaning of the Eddington - Finkelstein metric?

I want to see a some physical process (experimental) that could explain the many transformations of coordinates into this mathematical procedure. (really two transformations, but i think that is a ...
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3answers
145 views

Really nothing special when falling into a black hole?

It has been said time and again, that an observer who falls into a black hole will not notice anything special. Is this really true? There is of course the problem with the tidal forces, but I ...
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2answers
95 views

What does this summation mean in relativity?

Equation 1.2 of 't Hooft's Introduction to General Relativity gives the Lorentz transformations: $$ (x^\mu)' = \sum\limits_{\nu = 1}^4 {L^\mu}_\nu x^\nu $$ Is this the sum of four square matrices ...
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0answers
47 views

What is the “momentum” referred to in the energy-momentum tensor

What is the "momentum" referred to in the energy momentum tensor from GR? Is it $m\dot{x}$ or is it the canonical momentum $\frac{d}{dt} \left(\frac{\partial L}{\partial \dot{x}}\right)$ Also, I ...
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1answer
171 views

Pauli-Fierz “massive” equation and linearized gravity

It it known that the massive spin-2 irreducible representation of the Poincare group is the traceless symmetrical transverse 4-tensor $h_{\mu \nu}$ with rank 2: $$ (\partial^{2} + m^{2})h_{\mu \nu} = ...
3
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1answer
91 views

Warped AdS geometry

I am having difficulty of finding more basic information on warped geometries. All the standard textbooks are not covering it. In the wiki article it's only said that warped geometry is the one which ...
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53 views

General relativity and global aspects [duplicate]

The theory of general relativity tells me something about the global structure of space-time, eg simply connected ?
5
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1answer
80 views

how affine connection follows from Two derivative operator

IN wald's GR book in chapter 3 This is stated behind the definition of affine connection : First He showed that if we have two derivative operator $\nabla_a , \tilde\nabla_a$ (both of which ...
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1answer
110 views

Extent of coordinate freedom to set metric components along a spacetime path

If we describe spacetime with a Lorentzian manifold, it is always possible to choose a coordinate system such that at any particular point $x^\alpha$, the components of the metric are: $$ ...
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1answer
113 views

Field action of linearized gravity associated with spin-2 particle in Thorne book

In MTW book there is one exercise in which there was proposed to discuss linearized tensor gravity, which is represented as $$ g_{\mu \nu} = \eta_{\mu \nu} + h_{\mu \nu}, \quad \eta_{\mu \nu} = ...
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1answer
72 views

Energy difference in General Relativity

Why exactly are absolute energies important in General Relativity, unlike for example EM where only energy differences matter?
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1answer
129 views

Curved spacetime point particle Lagrangian density

This is probably trivially related to the question: Action for a point particle in a curved spacetime , but am a bit unsure how to write it as a Lagrangian density. In curved spacetime the action is ...
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223 views

The geodesic line on Poincare half plane

I was calculating the geodesic lines on Poincare half plane but I found I somehow missed a parameter. It would be really helpful if someone could help me find out where my mistake is. My calculation ...
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3answers
153 views

Can General Relativity Metric Tensor be independent of a particular co-ordinate index in a local area?

For example in a particular local area, can the metric tensor be totally independent of $z$ co-ordinate in $(t,x,y,z)$ co-ordinate system? This way the distance function will not contain $z$ ...
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1answer
125 views

How to prove that zero Weyl tensor predicts no deflection of light?

There is Nordstrom theory, which can be given as $$ C_{\mu \nu \alpha \beta} = 0. $$ The solution of Einstein equations for this case is conformally flat metric: $$ g^{\mu \nu} = e^{\epsilon \varphi ...
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2answers
167 views

I need help understanding a step in the derivation of the Schwarzschild solution

I am looking at Wikipedia's article on deriving the Schwarzschild solution. In the section "Simplifying the components", it says, On the hypersurfaces of constant $t$ and constant $r$, it is ...
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4answers
265 views

The universe is expanding but why the galaxies have no motion?

It is said that the universe is expanding and the galaxies are moving apart. I understand that the space between every two galaxies is increasing. Doesn't this seem to imply that the galaxies will ...
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2answers
182 views

Metric Expansion Of Space

I just do not understand this concept of metric expansion of space. Shouldn't the galaxies move away from each other. How can the space between them expand if the galaxies are not moving away from ...
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0answers
53 views

Will accelerating a massive particle generates a blackhole? [duplicate]

I have a naive question about blackhole. If I accelerate a massive particle very close to the speed of light, the particle will have large energy-momentum tensor. Will it become a blackhole?
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71 views

4 of Einstein equations without 2nd order time derivative

This question is related to my previous one and it was a homework problem and was due two weeks ago. Problem:prove that four of Einsteins' equations $$ G_{0\nu} = 8\pi T_{0\nu} $$ have to 2nd order ...
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3answers
143 views

Gravity on the International Space Station - General Relativity perspective

My question is an extension to this one: Gravity on the International Space Station. If all the outside views of the ISS was sealed, then the crew inside would not be able to tell whether they were ...
4
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0answers
130 views

Calculating Forces via Feynman diagrams?

How would one go about calculating forces that test objects feel using Feynman diagram methods? For example, say we have a massive object in GR so that the metric takes on the standard ...
3
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2answers
378 views

How do gravitons and curved space time work together? [duplicate]

I've heard two different descriptions of gravity, and I'm wondering how they work together. The first is Gravitons: "The three other known forces of nature are mediated by elementary particles: ...
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43 views

Allowed transformations in General Relativity [duplicate]

So in Special Relativity we have: $$ \Lambda \eta \Lambda^T=\eta $$ Is there an analagous formula for the metric in General Relativity?