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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Why can't we see things swallowed by black holes?

Apologies in advance, I'm a layman with only a school-level education in physics. If an object approaching the event horizon of a black hole has its light cone progressively bent towards the black ...
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64 views

Compatibility conditions of spinors and Riemannian Metrics

I came across an interesting article by Montesinos (J. Geom. Phys. 2 (1985), no. 2, 145–153.). In it, he finds that spin structures (as lifts of $SO(4)$) are not compatible with all Riemannian metrics ...
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18 views

Is it possible to express “free”-ness of a time-like world line without referring to “tangent space” (but only directly to causal relations )?

I don't know much about tangent spaces, or tangent vectors, "as such"; nor about affine parametrization (which seems to be closely related to the notion of tangent vectors, as far as I understand for ...
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87 views

Trapped Surfaces. Any good articles?

I'm currently writing a dissertation on trapped surfaces as minimal surfaces. I have exhausted all of the resources I have, and the internet is pretty limited (in that it is fairly repetitive on just ...
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91 views

Geodesics in a point mass universe

This question may reflect my (lack of) knowledge about general relativity, please ask for any clarifications or note any corrections in the comments and I'll try to address them. The Schwarzschild ...
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63 views

Problem with relativity of acceleration

In this answer http://physics.stackexchange.com/a/92833/36977 John said that acceleration is not relative in the general theory of relativity. But this is a problem: as we all know, accelerating ...
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54 views

How strong is the spacetime curvature at distance $d$ for a nonmoving point mass?

Consider a point mass $A$ with mass $m$ in empty space. The point mass $A$ does not have a velocity and does not rotate. Since gravity is symmetric for nonmoving objects, the spacetime curvature ...
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510 views

How to find the Stress-Energy tensor?

I am a bit at loss about how to proceed to find the stress-energy tensor given some distribution of matter. The Wikipedia page gives some examples, and some (inequivalent) definitions for it: Using ...
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53 views

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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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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99 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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182 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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3answers
201 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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655 views

Can colliding gravitational waves create a black hole?

Whether gravitational waves are real or just a coordinate freedom was argued in the early days of GR. Eventually the conclusion was that they were real. And if they are 'real' then I'm curious if... ...
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131 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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313 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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129 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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94 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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47 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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101 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
163 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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1answer
100 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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112 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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1answer
92 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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395 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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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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76 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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maximum rotational speed

I am wondering if there is a limit to rotational speed of an object just like there is one for translation speed ? what are the implications of general relativity for rotating objects ?
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322 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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66 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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1answer
165 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} = ...
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245 views

In the static spacetime, the extrinsic curvature of hypersurface $t=constant$ is zero

How can I prove that in the static spacetime, the extrinsic curvature of hypersurface $t=constant$ is zero? My efforts all are failed. Any hint would be greatly appreciated.
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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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45 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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272 views

Deriving Gauss-Bonnet Gravity (Or just higher order corrections)

I have been working for some time now on deriving the equations of motion (EOM) for the Gauss-Bonnet Gravity, which is given by the action: $$\int d^D x \sqrt{|g|} ...
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145 views

Are there any good references on the “gravitational” curvature of spacetime of a moving mass being distorted due to special relativity?

In this Wikipedia paragraph suggesting an explanation for the phenomenon of inertia, it claims: Another physicist, Vern Smalley, has derived the Lorentz transformation for mass by assuming that ...
7
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186 views

Book on optics in curved space-time

As evidenced from my earlier questions on vision and curved space, I am struggling a little bit with visual perception in curved space-time. I would like a book recommendation on optics and vision in ...
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2answers
106 views

Are orbits reversible in general relativity?

It seems if I reverse velocities then things begin orbiting backwards, at least in classical mechanics. From here: Every orbit and trajectory outside atmospheres is in principle reversible, i.e., ...
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6k views

Newtonian gravity vs. general relativity: exactly how wrong is Newton?

Is there a simple function I can use to describe the difference between simple Newtonian dynamics and the actual observed motion? Or maybe some ratios for common examples of, say, the motion of stars ...
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 ?
4
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109 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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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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109 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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2answers
280 views

Local inertial coordinates

It is said that we can introduce local inertial coordinates for any timelike geodesic. But why only for timelike geodesics? What about null geodesics? Perhaps it has to do with invertibility or ...
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215 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 ...
3
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1answer
244 views

What does “all future lies within the event horizon” mean?

I was trying to find an answer as to why light does not escape black holes and I stumbled upon this Phys.SE question. In the answer it said that: "Since all future lies within the event horizon, ...
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1answer
127 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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71 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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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 $z$ ...