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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Position / velocity / acceleration vs time graphs when falling towards a black hole

In Newtonian physics, as far as I understand it, for a small object falling towards a massive object, the graphs of position, speed and acceleration vs time look like this: (If the massive object ...
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1answer
51 views

Can molecules/atoms/any subatomic particle cause space time curvature?

Space-time curvature is caused by huge objects in space like black holes, merging black holes, or planets. This curvature is what causes gravity. Can molecules cause at least a really tiny curve ?
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136 views

View of the sky from inside a black hole

Consider an observer located at radius $r_o$ from a Schwarzschild black hole of radius $r_s$. The observer may be inside the event horizon ($r_o < r_s$). Suppose the observer receives a light ray ...
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38 views

Confusion with conclusion to positive mass theorem

I am trying to understand the positive mass theorem as it is presented in the survey paper by Corvino and Pollack http://arxiv.org/abs/1102.5050 I am fundamentally confused by the structure of their ...
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18 views

What is the difference between $\theta^{0}_{n}$ and $\theta_n$ in Strong gravitational lensing?

I am currently studying the strong gravitational lensing effects by general relativity. However, when studying these effects I came across several paper (especially these two papers, Paper One and ...
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46 views

Is critical mass of fissile material the same in gravitational fields with different force?

Let's take plutonium-239 for example. $10\, Kg$ (sphere $9.9\, cm$) need for a nuclear reaction. Are we talking about these numbers in Earth environment with $\approx 9.8\, m/s^2$ gravitational ...
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49 views

Lorentz surfaces, conformal metrics and eigenvalues

From what I understand of Lorentz surfaces (spacetimes of dimension 2), it seems that, according to Kulkarni's theorem, two reasonable enough Lorentz surfaces (I am only interested in surfaces with ...
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1answer
36 views

Interpretation of the operation $v^\alpha \nabla _\alpha v^\mu$

In general relativity, we can write the geodesic equation as a contraction $v^\alpha \nabla _\alpha v^\mu = f(\lambda)v^\mu$ along a path defined by coordinates $x^\mu(\lambda)$, and where $v^\mu = \...
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252 views

Geometric formulation of the equivalence principle

Let $(M,g)$ be a $4$-dimensional Lorentzian manifold. It is well know that given $(U,\psi=(x^1,\ldots,x^4))$ local chart around some $p\in M$, it is posible to find a change of coordinates given by $(...
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30 views

How do I use the value I get from the gravitational time dilation formula to calculate dilated time?

I am trying to calculate gravitational time dilation with the following formula: $\exp\left(\dfrac{1}{c^2}\cdot-\dfrac{GM}{h}\right)$, where $-\dfrac{GM}{h}$ is the integral of the g function, and $\...
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2answers
90 views

How Smooth is an Event Horizon?

For a non-rotating Black Hole, the event horizon can be described by the Schwarzschild metric as a sphere. Assuming external observer, away from the Black Hole and also assuming that there is no ...
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47 views

What is the difference between intrinsic and extrinsic curvature? [migrated]

In general relativity, energy bends spacetime. However, this doesn't mean that a fifth dimension for spacetime to "bend into" exists." That is, spacetime isn't embedded in a higher dimensional space, ...
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49 views

Maximum Angular Momentum for an orbit in GR

[The reference for this question is the book Gravitation by Misner,Thorne, & Wheeler.] The trajectories of massive particles around a spherically symmetric body is governed by the effective ...
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1answer
50 views

Confirmation of a concept under General Relativity and Frames of Reference

I would like to preface this by saying that this isn't necessarily meant to be a full question, though it may become that, but it rather a confirmation of my understanding of a concept. Newton would ...
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5answers
2k views

Does curved spacetime change the volume of the space?

Mass (which can here be considered equivalent to energy) curves spacetime, so a body with mass makes the spacetime around it curved. But we live in 3 spatial dimensions, so this curving could only be ...
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0answers
31 views

What is the minimum math level required to comprehend general relativity? [duplicate]

I am currently working on a B.S. In chemistry and only need to go up to Calculus II, though I like to dabble in physics. What other math classes could I take to gain greater understanding of higher ...
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0answers
28 views

How To Arrive At Ground State Metric of Kaluza-Klein Theory

The ground state metric, after an extra dimension of space is compactified (to a circle) in Einsteinian gravity, is the metric which corresponds to the R_4 × S_1 geometry of the separated dimensions. ...
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56 views

Kerr Metric and Asymptotically Static Frame

Suppose we are given a Kerr spacetime (e.g. containing a single uncharged rotating black hole). How does one know that the coordinates chosen is rotating or non-rotating as seen from infinity? And how ...
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1answer
55 views

How do gravitational waves transfer momentum?

In Electromagnetism I understand it in terms of the Lorentz force: the E-component of the field causes the charge to respond infinitesimally with a $\vec{v}$ in the E-direction such that the $\vec{v}\...
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0answers
103 views

Intuition behind deriving the FRW metric

I am studying the FRW metric and am looking at a motivation for it here. The motivation seems to use four spatial dimensions. Why do we need the fourth spatial dimension in this? This doesn't seem ...
2
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1answer
69 views

Is the age of the Universe relative to where you are within it? [duplicate]

The accepted age of the Universe is 13 billion years give or take. If you were a super space being and hypothetically had spent a large portion of this time sitting next to a black hole then your ...
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3answers
603 views

General relativity vs graviton discovery

Will the discovery of the graviton lead to the redundancy of general relativity even though it has been so well established. If not, will it mean that gravity will have two separate theories that ...
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2answers
83 views

Projection of a tensor

Consider the following tensor (abstract index notation, e.g. Wald's) $B_{ab}$ and timelike vector field $X^{a}$ such that $X^aX_a=-1$ and \begin{equation} B_{ab}=\nabla_bX_a \end{equation} Then one ...
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93 views

(1+1)-General Relativity

Goodevening everyone, my question is: What is the interest of studying the (1+1)dimension General Relativity? Can you explain please? Thank's in advance!
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2answers
88 views

General relativity applications other than gravity

Do the Einstein field equations successfully predict/describe physical processes other than gravitational ones?
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30 views

Can orbiting a black hole 99.99% speed of light make other object with relatively fast clock travel faster than light, relative to me?

If i orbit a black hole, 99.9% speed of light, time for me is moving slowly, relative to me, planet earth is aging fast, and i have traveled 10 years into the future(relatively) in 1 second, suppose ...
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26 views

How small can a sample size be of space to detect space-time curvature?

What is the minimal sample size of space necessary to detect space-time curvature?
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1answer
95 views

Metric with Harmonic Coefficient and Stress-Energy Tensor in General Relativity

I have two question: Is there any possible implies or interest to use in general relativity a metric whose coefficients are harmonic functions? What is the meaning (physical) if the stress-energy ...
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41 views

Lagrangian density

I really wonder : Why do we take Lagrangian density as zero for the Stokes theorem in Minkowski-space at infinity? Is there a proof of this situation?
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2answers
147 views

What does string theory predict for the singularity inside a black hole?

The usual explanation for what's going on inside a black hole goes something like "General Relativity predicts a singularity with infinite curvature, but when matters gets so tightly compressed we ...
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1answer
62 views

Black hole gravity at bottom (deepest end) [closed]

If black holes are hole in space and time then at bottom or below bottom there is no more gravity of black hole. As any hole has an end (Deepest end). Is this true ? ******** EDIT *********** http:/...
3
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1answer
85 views

Exotic differentiable structures in physics

When reading a bit on exotic spheres and exotic $\mathbb{R}^4$'s, I came across some papers of Carl H. Brans and Torsten Asselmeyer-Maluga: "Exotic differentiable structures and general relativity" (...
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3answers
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Will a giant ball of protons form a black hole?

Suppose you have enough energy and resources to put together (in a momentarily static configuration in which they are all at rest at the same time) as many protons as you want to form a "proton star". ...
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3answers
145 views

What is “a general covariant formulation of newtonian mechanics”?

I am a little confused: I read that there are general covariant formulations of Newtonian mechanics (e.g. here). I always thought: 1) A theory is covariant with respect to a group of transformations ...
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53 views

Does gravitational radiation have a formalism similar to Wheeler-Feynman electrodynamics?

Binary systems radiate energy away in gravitational waves as the orbits of the two masses spiral in towards each other. My understanding of gravity is that we think of it as a mediator of particle-...
2
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1answer
51 views

Age of universe from Hubble's constant

Assume the Robertson-Walker metric: $$g = -d\tau^2 + a^2(\tau)\gamma$$ where $\gamma$ is the flat, spherical or hyperbolic spatial metric and $a$ is the scale factor. Wald seems to calculate the age ...
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33 views

How to find tetrads corresponding to a given metric?

In General Relativity, sometimes doing calculations with a set of orthonormal tetrads $h^{a}_{\mu}$ where $h^{a}_{\mu}$$h^{b}_{\nu}$$\eta_{ab}=g_{\mu\nu}$ for some metric $g_{\mu\nu}$ is easier ...
2
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1answer
128 views

What is the relation between the metric tensor and the graviton?

In Zee's quantum theory in a nutshell, at the end of chapter I.10, he states that the graviton is of course the particle associated with the field $g_{\mu\nu}$. My understanding of quantum ...
2
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1answer
43 views

Mathematically deriving Hubble's constant

Assuming homogeneity and isotropy, the spacetime metric is of the form $g = -d\tau^2 + a^2(\tau)\gamma$ where $a$ is the scale factor and $\gamma$ is the spatial metric corresponding to a flat, ...
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0answers
104 views

Deriving the field equations for a dark energy / modified gravity effective field theory

Question I'm trying to derive the modified gravity EFT field equations and, from their 00 component, this Friedmann equation: \begin{equation} H^{2}+H\frac{\dot{\Omega}}{\Omega}=\frac{\kappa \rho_{m}+...
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1answer
88 views

How is Riemann tensor related to the curvature in the coordinates?

I came across statements such as "the acceleration observed in a weak gravitational field is mainly due to curvature in the time coordinate. " I want to know how we can explicitly find the curvature ...
4
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0answers
51 views

Is the Weitzenböck connection the only connection with Torsion but without Curvature?

In teleparallel gravity, the (local) connection coefficients of the Weitzenböck connection are given by $$ \Pi^{\beta}{}_{\mu\nu}= h^{\beta}_{i} \partial_{\nu}h^{i}_{\mu} - \Gamma^{\beta}{}_{\mu\nu}...
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52 views

Second derivative of the stress-energy tensor

Which physical meaning can have if the second derivative of stress-energy tensor is zero? In General Relativity or elsewhere.
4
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1answer
176 views

Derivation of Christoffel Symbols

So I am reading a book on relativity & differential geometry and in the text, they gave the Christoffel symbols in terms of the metric and its derivatives, but I wanted to derive it myself. ...
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1answer
53 views

Speed of light when accelerating

I'm studying special relativity and saw the 2 postulates of Einstein. The most remarkable one for me is the universal speed of light. Einstein postulated that the speed of light in vacuum is the same ...
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1answer
53 views

The form of the metric after a dimension is compactified

Upon the compactifiation of one spatial dimension, it is said (as though an axiom) that the 5 dimensional spacetime metric separates into a 4 dimensional metric, a vector, and a scalar, (4D gravity, ...
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2answers
2k views

What is black hole spin?

First of, congrats to the people at LIGO. In this article, the BBC notes that the latest LIGO results show that a new black hole was formed with a spin of $0.2$ (dimensionless number). What exactly ...
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1answer
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Why does Ligo's second detection of gravitational waves and a black hole merger look absolutely nothing like the first? [closed]

Why does Ligo's reported second detection of gravitational waves and a black hole merger look absolutely nothing like the first detection announced in Februaray? Here is the data from the first LIGO ...
3
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1answer
95 views

The most general way to write flat space metric [closed]

What is the most general way to write flat space (in d=4 in particular), but still preserving some isometries? In particular I'm interested in the case with 2 isometries, basically by using explicitly ...
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31 views

Behavior of an object in a region of uniform spacetime curvature

Let's say there is some spherical region of space. In this region, there is a large curvature of spacetime. This curvature is completely uniform throughout the region. I decide to stick some object ...