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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Trouble with calculating Christoffel symbols of FLRW metric using Lagrangian method

The FLRW metric which I am using is $$ds^2 = dt^2 - \frac{a(t)^2}{c^2} \left( dx^2 + dy^2 + dz^2 \right)$$ where $a(t)$ is the so-called 'scale factor'. I did not want to calculate the Christoffel ...
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138 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 ...
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149 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 $$R_{ab}=AT_{ab}+Bg_{ab}+CRg_{ab}$$ ...
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265 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 ...
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58 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 ...
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153 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= ...
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141 views

Showing that the Ricci scalar equals a product of commutators

I have to compute the square of the Dirac operator, $D=\gamma^a e^\mu_a D_\mu$ , in curved space time ($D_\mu\Psi=\partial_\mu \Psi + A_\mu ^{ab}\Sigma_{ab}$ is the covariant derivative of the spinor ...
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134 views

Does quantum Zeno effect play role in astrophysics?

For example, do two galaxies situated in proximity reduce the atom decay rate in each other? What happens with decay quanta escaped to infinity? Does the radius of apparent horizon effect the ...
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83 views

transition between extremal and nonextremal black hole states

Extremal black holes are at zero temperature, hence they do not radiate. my question is twofold: 1) is extremality of micro black holes a stable property? electric charge is quickly emitted from ...
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78 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 ...
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63 views

Any examples of negative ADM energy solutions with WEC but not DEC satisfied?

Any examples of negative ADM energy solutions with weak energy condition (WEC) but not dominant energy condition (DEC) satisfied? Witten's proof of the positive energy theorem requires the dominant ...
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121 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 ...
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88 views

quadripolar moment in curved space

So, i'm going over the Thorne's derivation of the quadrupolar radiation term, and they write the core term as: $$ \frac{3 r_i r_j - 2 r^2 \delta_{ij}}{4 r^5} $$ But if i try to obtain this term by ...
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308 views

How is the poincare conjecture(and perelman proof) helpful in studying the properties of the universe?

Can someone tell me how the poincare's famous conjecture or its proof by perelmen can be helpful in deciding some properties like the shape of the universe?
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279 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 ...
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376 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 ...
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315 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 ...
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226 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 ...
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23 views

Coordinate time difference between emiting and detecting a photon in bent spacetime

Consider an arbitrary non-trivial metric $g_{ij}$ - like the Schwarzschild metric. Now, consider two observers $A$ and $B$, staying at fixed radii $R_A$ and $R_B$, respectively, with $R_A > R_B$. ...
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26 views

Linearized Einstein equation on a general background metric

All of my texts only give the Linearized Einstein equation on the Minkowski background so I thought I'd try and figure it out by hand today. Using the standard perturbation $h_{\mu\nu}$ and denoting ...
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28 views

Going to the Einstein frame in f(R) theories

First of all thank you for your time! I have a question that I can't solve. In every review that I read, I find that when you want to go to the Einstein frame in a $f(R)$ theory what you have to do ...
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11 views

Lapse Function and Shift Vector in Minkowski and de Sitter

I'd like to find the lapse function and shift vector in 1+1 Minkowski as well as 1+1 de Sitter (flat foliation) for a region foliated this way: The $y$-axis represents time while the x-axis ...
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43 views

Showing classical spin tensor is time independent for free particle

Reading through Weinberg's gravitation book, the following definition is given for the spin tensor (Pauli-Lubanski psuedovector): $$ S_\alpha = \frac{1}{2}\epsilon_{\alpha\beta\gamma\delta} ...
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32 views

Doubts about Chern-Simons state as a solution of the Hamiltonian constraint in quantum gravity

I've been doing some work with both Baez's Knots, gauge fields and gravity (1) and Gambini, Pullin's Loops, knots, gauge Theories and quantum gravity (2), lately. I have basically two problems: I ...
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35 views

Interpreting meaning of coordinates given a metric

I was working problem 3.6 in Carroll's GR textbook and was given the following metric, which is a good approximation to the metric outside the surface of the Earth. $ds^2=-(1+2 \Phi(r))dt^2 + ...
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31 views

Geodesic tangent vector in a Riemannian 4-space

I am doing a question in Lewis Ryder's introduction to General relativity. I am very close to the answer but not quite there. The question is: A Riemannian 4-space has metric $$ds^2 = ...
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26 views

what is the metric of N-sheeted $AdS_3$?

Suppose the AdS$_3$ metric is given by $$ ds^2 =d\rho^2+cosh^2\rho d\psi^2 +sinh^2 \rho d\phi^2 $$ what is the n-sheeted space of it? Can the n-sheeted BTZ be constructed from it by identifications ...
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26 views

Inequivalent matter actions with the same stress-energy tensor in general relativity

In general relativity, suppose as usual that we have the following action for the matter fields \begin{equation} S_{\mathrm{matter}} = \int_M d^4 x \sqrt{-g} L_{\mathrm{matter}} , \end{equation} ...
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30 views

Orbital period and velocity around a Kerr black hole relative to fixed stars

I've been trying to make progress on some of the smaller pieces of this question about the environment around a Kerr black hole. In order to calculate the effects of special relativistic Doppler shift ...
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24 views

How is time evolution done in numerical GR?

Suppose we're simulating what happens when a fairly massive object falls into a black hole. Say the object starts far away, so that the initial condition is that the metric is the Schwarzschild metric ...
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74 views

Euler-Lagrange equations in General Relativity

When obtaining the Euler Lagrange equations for a scalar field with higher order derivatives in curved space is it the same to use $$ -\partial_\nu\partial_\mu\frac{\partial \sqrt{-g} ...
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24 views

Why '1+log slicing condition' and 'Gamma Driver Shift Condition' were successful in black hole simulations?

The 1+log slicing and Gamma driver shift conditions are I want to know if there is a specific reason why these conditions were used most for Black Hole simulations in Numerical Relativty. And how ...
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42 views

Can Bose-Einstein Condensates reflect gravitational waves?

This is a question based on the paper by Raymond Chiao in 2002 where it is stated: One of the conceptual tensions between quantum mechanics (QM) and general relativity (GR) arises from the clash ...
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47 views

Gauge invariance in gravitational field

I have read that the linearized equation for the metric fluctuations $h_{\mu\nu}$, namely: $$ \partial^2h^{\mu\nu}-\partial_{\alpha}(\partial^{\mu}h^{\nu\alpha}+\partial^{\nu}h^{\mu\alpha}) ...
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33 views

Einstein-Infeld-Hoffman-Lagrangian for a Test-Particle as Limit of Schwarzschild-Geodesic

Consider a test particle of mass $m$ which is in orbit around a spherical-symmetric body with mass $M$. It therefore has a position as described by the coordinates $r,\phi$, and its motion can be ...
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57 views

Why are symmetrical structures highly stable?

What makes symmetrical structures(geometry) highly stable? It is perfect to say that the forces acting on a symmetrical structure is balanced and hence stable. But why is it so? To be more specific, ...
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48 views

Using geodesic deviation for freely falling particles when gravitational waves comes through

Suppose we have a gravitational wave which gives us the following metric $$ds^2=-dt^2+(1+h_+\cos(\omega(t-z)))dx^2+(1-h_+\cos(\omega(t-z)))dy^2+dz^2$$ I want to calculate the time it takes for a ...
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62 views

Complex tetrad vs. Real metric

I asked this question almost a month ago on mathoverflow (http://mathoverflow.net/q/228138/) but received no response. I thought I could have better luck here: I have a question on the relationship ...
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68 views

Are there any conditions under which the Christoffel symbols can be treated as a damping term in a harmonic oscillator?

(Mathjax did not seem to be working as I composed this question. Hopefully it will kick into action once I post.) Note I am a novice at tensor notation. I am working with the following Lagrangian ...
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89 views

On the nature of forces in general relativity

*** EDIT: I understand that it's not wise to fixate on Schroedinger words, however their meaning still remains obscure to me. Besides this my question on the possibility to abandon the concept of ...
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65 views

Einstein's relativity of simultaneity train/embankment thought experiment

Einstein's thought experiment I'm referring to is this one: http://www.bartleby.com/173/9.html briefly: train/embankment experiment is where lightning strikes at either ends of the running train ...
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42 views

Can nonconserved energy in GR be thought of as going into gravitational field energy?

One of the most striking features of GR is that energy is not conserved. Carroll's GR text has an interesting statement about this: Clearly, in an expanding universe... the background is changing ...
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34 views

Can a micro black hole hover above a regular black hole?

So let's say you have a black hole $A$, that is small enough for its gravity to be very small, but has strong hawking radiation, and larger black hole, $B$, with very small hawking radiation, but ...
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55 views

Physical and non-physical solutions to Einstein's field equations

Einstein predicted gravitational waves in 1916 as a solution to his field equations. Apart from doing experiments, is it possible to tell which solutions exist in the real world and which don't? Are ...
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46 views

Do gravitational waves produce real accelerations?

Do gravitational waves produce real accelerations? For example, if I have an electron and a gravitational wave passes by, will the electron emit electromagnetic waves according for instance to Larmor ...
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57 views

How much light is necessary to form a black hole

I suppose that enough light in a small enough volume could create a black hole. What is the good quantity that can tell when light can or cannot make a black hole? Energy density? But there must be ...
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45 views

Are objects like $a^{\mu \nu} a_{\mu \nu} b^{\mu \nu}$ consistent with Einstein summation?

I'm familiar with Einstein' summation notation and I understand objects like $a^{\mu \nu} a_{\mu \nu}$ just fine. But I'm wondering why I've never come across objects like this: $a^{\mu \nu} a_{\mu ...
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48 views

What is conformal symmetry physically?

I'm reading a paper by t'Hooft http://arxiv.org/abs/1410.6675. There is an argument in the paper that I could not understand: "Now that system, described by Maxwell’s equations, does have conformal ...
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47 views

Worldlines in Schwarzschild geometry

I have an observer and a photon on a hypersurface $ \theta=\pi/2$ . My observer has $e, l$ constants of motion (energy and angular momentum divided by mass) and photon has $e',l'$. What conditions ...
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23 views

Radiation collapse to black hole

I want to find the temperature at which radiation in AdS will collapse to form a black hole. I have even found a reference that gives the answer but I cannot understand it: ...