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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276 views
A dictionary of string - standard physics correspondences
Motivated by the (for me very useful) remark
''Standard model generations in string theory are the Euler number of
the Calabi Yau, and it is actually reasonably doable to get 4,6,8, or 3
...
8
votes
0answers
290 views
Do intergalactic magnetic fields imply an Open Universe?
According to a recent paper on the arXiv, they do. How credible is this result? The abstract says:
The detection of magnetic fields at high redshifts, and in empty
intergalactic space, support ...
6
votes
0answers
141 views
Does local physics depend on global topology?
Motivating Example
In standard treatments of AdS/CFT (MAGOO for example), one defines $\mathrm{AdS}_{p+2}$ as a particular embedded submanifold of $\mathbb R^{2,p+1}$ which gives it topology ...
5
votes
0answers
78 views
Do semiclassical GR and charge quantisation imply magnetic monopoles?
Assuming charge quantisation and semiclassical gravity, would the absence of magnetically charged black holes lead to a violation of locality, or some other inconsistency? If so, how?
(I am not ...
5
votes
0answers
87 views
Equation of state of cosmic strings and branes
I'm sure these are basic ideas covered in string cosmology or advanced GR, but I've done very little string theory, so I hope you will forgive some elementary questions. I'm just trying to fit some ...
5
votes
0answers
91 views
Positivity of Total Gravitational Energy in GR
I read the following statement in the introduction to an article:
Over the last 30 years, one of the greatest achievements in classical
general relativity has certainly been the proof of the ...
5
votes
0answers
156 views
Penrose Conformal diagram for flat 2-dim Lorentz space-time
I have the following metric
$$ds^2 ~=~ Tdv^2 + 2dTdv,$$
defined for
$$(v,T)~\in~ S^1\times \mathbb{R},$$
e.g. $v$ is periodic.
This is the according Penrose diagram:
Question 1) Is the ...
5
votes
0answers
99 views
Maximal kinetic energy due to gravitational attraction
Two related questions:
Small object of mass $m$ is falling into the supermassive black hole of mass $M$. What is the maximal kinetic energy can be acquired by the small object, from the point of ...
5
votes
0answers
146 views
Energy balance of closed timelike curves in Gödel's universe
I recently read Palle Yourgrau's book "A World Without Time" about Gödel's contribution to the nature of time in general relativity.
Gödel published his discovery of closed timelike curves in 1949. ...
4
votes
0answers
54 views
Gravitational redshift of Hawking radiation
How can Hawking radiation with a finite (greather than zero) temperature come from the event horizon of a black hole? A redshifted thermal radiation still has Planck spectrum but with the lower ...
4
votes
0answers
89 views
Alternate geodesic completions of a Schwarzschild black hole
The Kruskal-Szekeres solution extends the exterior Schwarzschild solution maximally, so that every geodesic not contacting a curvature singularity can be extended arbitrarily far in either direction.
...
4
votes
0answers
45 views
Kerr solution for finite collapse time
The Kerr black hole solutions gives an analytic continuation that is asymptotically flat. Some people have argued that this is another universe, but others state that the analytic continuation ...
4
votes
0answers
130 views
Implications of Unruh-inertia to theories of gravity
If it turns out to be true that the galaxy rotation curves can be explained away by Unruh modes that become greater than the Hubble scale at accelerations around $10^{-10} m/s^2$ as proposed in here, ...
4
votes
0answers
57 views
gravitational convergence of light
light has a non-zero energy-stress tensor, so a flux of radiation will slightly affect curvature of spacetime
Question: assume a flux of radiation in the $z$ direction, in flat Minkowski space it ...
4
votes
0answers
25 views
What is the state-of-the-art on spacelike singularities in string theory?
What lessons do we have from string theory regarding the fate of singularities in general relativity?
What happens to black hole singularities? What happens to cosmological singularities?
Which ...
4
votes
0answers
99 views
K3 gravitational instanton
Could you please recommend a sufficiently elementary introduction to K3 gravitational instanton in general relativity and the problem of finding its explicit form?
Under 'sufficiently elementary' I ...
3
votes
0answers
71 views
Curvature and spacetime
Suppose that it is given that the Riemann curvature tensor in a special kind of spacetime of dimension $d\geq2$ can be written as $$R_{abcd}=k(x^a)(g_{ac}g_{bd}-g_{ad}g_{bc})$$ where $x^a$ is a ...
3
votes
0answers
109 views
Going through a ring of black holes
Mathematician here with a speculative physical question -- feel free to boot me if the level isn't right.
Suppose one finds, or builds, a constellation of several black holes arranged in a circle. ...
3
votes
0answers
56 views
Gravitational effects and metric spaces
Could somebody please explain something regarding the Nordstrom metric?
In particular, I am referring to the last part of question 3 on this sheet -- about the freely falling massive bodies.
My ...
3
votes
0answers
95 views
Would warp bubbles emit gravitational Cerenkov radiation in general relativity?
Inspired by the gravtiomagnetic analogy, I would expect that just as a charged tachyon would emit normal (electromagetic) Cerenkov radiation, any mass-carrying warp drive would emit gravitational ...
3
votes
0answers
79 views
Materials with different gravitomagnetic permeability?
If you start with general relativity, and assume small perturbations around a nearly flat metric, it is possible to obtain linearized equations of gravity that look a lot like Maxwell's equations, ...
3
votes
0answers
258 views
How do the Einstein's equations come out of string theory?
The classical theory of spacetime geometry that we call gravity consists of the Einstein equation, which relates the curvature of spacetime to the distribution of matter and energy in spacetime.
for ...
3
votes
0answers
69 views
are pinch-off bubbles valid solutions to general relativity?
are bubbles of spacetime pinching-off allowed solutions to general relativity? With "pinch-off bubble" i really mean a finite 3D volume of space whose 2D boundary decreases until it reaches zero and ...
3
votes
0answers
404 views
Derivation of the Gauss-Codazzi equation
I'm interested in the derivation of the Gauss equation (Gauss-Codazzi). Usually we consider the definition of the Riemann tensor on the hypersurface.
$$^{(n-1)}R_{abc}^{~~~~~~~d}~w_d=[D_a,D_b]w_c$$
...
3
votes
0answers
173 views
Asymptotic Invariants in General Relativity
I was trying to understand Witten's proof of the Positive Energy Theorem in General Relativity by reading the original argument given by Witten. I am comfortable with the overall argument, but I would ...
2
votes
0answers
66 views
Ising Hamiltonian for relativistic particles
An Ising system is described by the simple Hamiltonian:
$$H = \sum\limits_{i} c_{1i} x_{i} + \sum\limits_{i,j} c_{2ij} x_i x_j \,\,\,\,\,\,\,\,\,\,(1)$$
Here the $x_i$ are spins (+1 or -1 in units ...
2
votes
0answers
60 views
Wald problem 11.4
Consider a stationary solution with stress-energy $T_{ab}$ in the context of linearized gravity. Choose a global inertial coordinate system for the flat metric $\eta_{ab}$ so that the "time direction" ...
2
votes
0answers
66 views
Why doesn't this metric cover all of de Sitter space?
This represents a confused attempt to work through a problem in Carroll's Spacetime and Geometry. Supposedly I should be able to use the geodesic equation,
...
2
votes
0answers
48 views
Naked singularity and extendable geodesics
I'm currently trying to understand the notion of a naked singularity. After consulting books by Wald and Choquet-Bruhat, it seems that for a naked singularity one must have that the causal curves can ...
2
votes
0answers
31 views
Are there functions of the metric that are scalars under spatial diffs up to total derivatives?
Let $g_{\mu\nu}$ be a metric on a manifold with a time direction $x^0$ singled out. I'm wondering if there exists a function $F(g_{\mu\nu},\partial_\rho g_{\mu\nu},\ldots)$ that transforms under ...
2
votes
0answers
44 views
does a rotating moving body in “flat” space curve its path because of frame dragging?
I am not a physicist.
let's say we have a space with an object in it, where all other gravitational bodies are so far away that their affect on the shape of the space is negligible.
let's say the ...
2
votes
0answers
74 views
Fermi Walker vs. Fermi transport
A vector field $f^\mu$ is said to be Fermi-Walker transported along a curve $\gamma$ parametrized with $\tau$ if the following holds $$\frac{\mathrm{D}}{\mathrm{d}\tau}f^\mu = -(a^\mu v^\nu - a^\nu ...
2
votes
0answers
89 views
Falling into a black hole emitter vs observer
Let's say we are working with the Schwarzschild metric and we have an emitter of light falling into a Schwarzschild black hole.
Suppose we define the quantity $$u=t- v$$ where $$dv/dr= ...
2
votes
0answers
40 views
What is (or where can I discover) the Burke Potential?
I have very much enjoyed William L. Burke's Applied Differential Geometry. Reading around on the web it seems that he discovered something which is called the (retarded) Burke Potential, but I have ...
2
votes
0answers
67 views
Is eternal inflation Lorentz invariant?
Start without general relativity. Consider a metastable vacuum over good ol'-fashioned Minkowski space. It decays. A bubble forms and the domain wall expands. The domain wall is timelike, and ...
2
votes
0answers
129 views
Entropy of a de Sitter horizon
The cosmological event horizon found in a de Sitter universe has some interesting similarities to that of a black hole. For example, since we can find a temperature at the horizon, we are able to use ...
2
votes
0answers
123 views
Using the area element in derivation of geodesic
In the derivation of the geodesic, one starts with the integral of the line element (arclength):
$$L(C)=\int_{\tau_1}^{\tau_2}d\tau\sqrt{g_{\mu \nu}\dot{x}^{\mu} \dot{x}^{\nu}}$$
The integrand is ...
2
votes
0answers
249 views
composition of space expansion and movement as a gauge invariance
suppose i have a space-time where we have one point-like object* which we will call movement space probe or $\mathbf{M}_{A}$ for short, and it will be moving with constant velocity $V^A_{\mu}$ in ...
2
votes
0answers
301 views
Calculation of the non-Gaussity parameter for primordial cosmological perturbations by the ADM Formalism
Maldacena has used the ADM Formalism in one of his papers (http://arxiv.org/abs/astro-ph/0210603) in computing the the three point correlation function (i.e the non-Gaussianity) parameter for ...
2
votes
0answers
253 views
net displacement and path dependence
reading the paper about spacetime swimming by Wisdom
(something related to this has been previously asked here) can't help but think that there is more to this than what is on the paper.
Basically ...
2
votes
0answers
210 views
Singularities in Bianchi models in general relativity ( physical science)
what are the conditions to check point type singularity in a bianchi type model ?
bianchi type model are of Type I,II,III,IX,IV or u can say we use different Bianchi type models having some specific ...
1
vote
0answers
35 views
Null vector fields given Bondi metric
I'm trying to understand how to compute the null future-directed vector fields if I have a given (Bondi) metric
$g=-e^{2\nu}du^{2}-2e^{\nu+\lambda}dudr+r^{2}d\Omega$
with $d\Omega$-standard metric ...
1
vote
0answers
50 views
Singularities in Schwarzchild space-time
Can anyone explain when a co-ordinate and geometric singularity arise in Schwarzschild space-time with the element
$$ ...
1
vote
0answers
56 views
Lecture Notes confusion: Constructing the Einstein Equation
This question is on the construction of the Einstein Field Equation.
In my notes, it is said that
The most general form of the Ricci tensor $R_{ab}$ is $$R_{ab}=AT_{ab}+Bg_{ab}+CRg_{ab}$$
...
1
vote
0answers
54 views
Stress-energy tensor of point particle when the trajectory is a transcendental equation?
I'm working through Carroll's GR book, and Problem 7.8 is not coming together. I'm missing something idiotically simple, but I'm not sure if I can cleanly write a stress-energy tensor for a point ...
1
vote
0answers
49 views
The interior of a cylinder as an Einstein manifold
The interior of a curved cylinder is an Einstein manifold (the Ricci Curvature Tensor is proportional to the Metric $R_{\mu\nu}=kg_{\mu\nu}$) since it has a constant curvature.
However, I was unable ...
1
vote
0answers
56 views
Newman-Penrose tetrad question
I have a question/exercise relevant to students of mathematical relativity:
Let $\left \{ l^{a},n^{a},m^{a},\bar{m}^{a} \right \}$ be a Newman-Penrose tetrad, where only the direction of $l^{a}$ is ...
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vote
0answers
82 views
Weyl's axisymmetric static solution
I'm currently doing a course on general relativity, and I'm struggling with the following exercise - I would greatly appreciate the help anyone might offer. It is as follows:
Weyl's solution to the ...
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vote
0answers
46 views
When is spacetime homogenous and isotropic?
When is spacetime homogenous and isotropic?
For example, some metric $g_{\mu \nu}$ is homogeneous and isotropic. We now construct effective metric
$$n_{\mu \nu} ~\rightarrow~ g_{\mu \nu} + ...
1
vote
0answers
45 views
Naked singularity and null coordinates
I'm trying to understand the notion of a naked singularity on a more mathematical level (intuitively, it's a singularity "one can see and poke with a stick", but I'm having troubles on how to actually ...
