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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124 views

Are conformal, Killing and homothetic vector fields the same in pseudo-riemannian manifolds?

I work in the Lorentzian manifolds, more generally in pseudo Riemannian manifolds and applications to general relativity. I know the definitions of conformal, Killing and homothetic vector fields in ...
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29 views

concept of density in gravitational lensing

I may just be being very dense (no pun intended) but i'm reading up on gravitational lensing and it seems to require a notion of density (e.g. see here) I'm working on a question involving light ...
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1answer
117 views

Do we still need Newtonian G in General Relativity?

I believe we can use Newtonian Physics to make incredibly good predictions about the movement of celestial bodies as long as they are not too fast/massive and there are only two of them (well, we can ...
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106 views

Would time dilation be too great for the early universe to expand?

I read that one second after the big bang the universe was composed of photons electrons and neutrinos. Wouldn't the density of energy/matter have caused such extreme time dilation that the universe ...
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0answers
69 views

Homeomorphism between the space of all Ashtekar connections and spacetime?

Excerpt from an essay of mine: Let $\Psi(\varsigma)$ be the wavefunction in the loop representation, where $\varsigma:[0,1]\to\mathcal{M}$, where $\mathcal{M}$ is spacetime. Then, let ...
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210 views

Superspace as the Hilbert Space for Quantum Gravity

Let $\mathcal{A}$ be the Ashtekar connection. Since $^{(3)}g_{AB}=i\frac{\delta}{\delta\mathcal{A}^{AB}}$ (see R. Penrose, 2004: Road to Reality. Vintage Books, 1136 pp.), the Ashtekar connection, in ...
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69 views

Timelike Loop Spaces as Projective Null Twistor Spaces

Let $\mathcal{M}$ be a spacetime, and let $\Omega\mathcal{M}$ denote the loop space of the spacetime. My idea is that the set of all closed timelike curves of $\mathcal{M}$ forms the projective null ...
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64 views

One particle near two Schwarzschild black holes

I have a particle near two Schwarzschild black holes. Let the black holes remain at rest so that only the particle is moving for the observer. We are in a plane. I calculate the distance travelled by ...
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1answer
143 views

Why in some cases $0\alpha$ component of stress-energy tensor don't form 4-vector?

In electrodynamics there is Poynting vector and energy density, which refer to $0\alpha $ components of stress-energy tensor, don't create 4-vector. Analogous situation with mass density and mass ...
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58 views

How 4-vector nature of the value is connected with it's conservation law?

In electrodynamics Poynting vector and energy flux of field don't create 4-vector. Also they aren't conserved independently from substance (conservation law includes summand connected with current ...
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1answer
208 views

Variation of modified Einstein Hilbert Action

In general relativity one can derive the Einstein Field Equations by the principle of least action through variations with respect to the inverse of the metric tensor. In some modified theories of ...
2
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1answer
63 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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159 views

Can the Cosmological Constant explain an accelerated expansion?

From what I've learned so far, it appears that all models that attempt to explain the expansion of the universe are either based on Lambda-CDM or quintessence. The former support a big bang with ...
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1answer
137 views

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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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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87 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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60 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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140 views

What is the equation for the scale factor of the universe, a(t), for the best fit of data to the $\Lambda CDM$ Model of Cosmology?

Ideally I like a single formula or multiple formulas for different time ranges that would cover the time from the end of inflation through 100+ billion years after the big bang using the $\Lambda ...
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1answer
51 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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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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2answers
184 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
268 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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88 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
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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66 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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225 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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175 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
206 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
286 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, ...
3
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1answer
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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569 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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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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3answers
199 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
175 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
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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1answer
147 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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99 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
96 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
93 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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110 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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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 ...
3
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4answers
380 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
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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1answer
90 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
308 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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61 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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134 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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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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44 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 ...