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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Gravitational Redshift and Length Contraction

Gravitational redshift is based on the time-time component of the metric (e.g., http://en.wikipedia.org/wiki/Redshift). Why does length contraction not contribute to redshift?
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35 views

Advantage and disadvantage of weak field approximation

Many textbooks related with GR, covers weak field approximation, (also called Linearized gravity). Since so far, i have been calculated many this with this $i.e$ $g_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu}$ ...
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32 views

Do all the spacelike curve terminate at the spatial infinity $i_0$ in the Penrose Diagram of a Schwarzchild black hole?

Let's restrict to the radial direction, so the metric can be expressed as $ds^2=-(1-r_S/r)dt^2+(1-r_S/r)^{-1}dr^2$ with $r_S$ the Schwarzchild radius. Expressed in Kruskal coordinates, the metric is ...
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39 views

Retarded Green function and the gravitational field of a point particle

I'm trying to understand a calculation by Aichelburg and Sexl of the gravitational field of a point particle. Linearizing the Einstein field equations in the usual way (that is, supposing a metric of ...
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16 views

Applying Weak Energy Condition for a specific energy-momentum tensor

So, I have a particular energy-momentum tensor, for a specific line element, and I want to check if this obeys the weak energy condition ($T_{ \mu \nu} U^\mu U^\nu \geq 0$ where $U^\mu$ and $U^\nu$ ...
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61 views

Is the gravitational acceleration at the event horizon constant?

If the escape velocity at the event horizon of a black hole is equal to the speed of light, does this imply that the gravitational acceleration at the event horizon is also constant? For example, ...
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50 views

Extracting something from Schwarzschild metric

In Papapertrou's lecture book on General Relativity he said in p 137 that from the metric $$ ds^2= e^\nu dt^2-e^\mu dr^2 -r^2(d\theta^2 +\sin^2\theta d\phi^2)$$ one deduces that $$\sqrt{-g} ...
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12 views

Can “uniform motion” (or “mutual rest”) be determined intrinsically, by members of Synge's “five-point curvature detector”?

In his description of a "five-point curvature detector" [1], J. L. Synge exhibits a Cayley-Menger determinant in terms of "optical distances" between five distinct participants; and he states that the ...
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58 views

That the gravitational mass equals to inertial mass can imply that only Einstein-Hilbert action is satisfied

I read Spacetime and Geometry by Sean Carroll. In p. 166 there is a comment that GR's action is nonlinear because if it is linear like the EM field, then graviton will not interact with each other, ...
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68 views

de Sitter–Schwarzschild metric in the Kretschmann Gravity?

The Kretschmann Gravity (Gauss-Bonnet Gravity,Lovelock Gravity) results when the Ricci scalar is replaced by the Kretschmann invariant in the Lagrangian of the General Relativity. We consider here a ...
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51 views

Schwarzschild metric in Isotropic coordinates

As one wants to jump to Isotropic coordinates in order to write the Schwarzschild metric in terms of them, one does this coordinate transformation: $$r=r'(1+\frac{M}{2r'})^2$$ So we start with the ...
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32 views

Covariant Fluid Flow approach

I am doing Cosmological perturbation. Currently reading a paper by Bruni et al. In that it is mentioned that they are using covariant fluid flow approach to cosmology. Can any body give me a rough ...
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61 views

Topological implications of symbolic represenation of the relativity

I have seen in the online Stanford Encyclopedia of Philosophy in the entry on Copenhagen Interpretation of Quantum Mechanics that Niels Bohr had argued that the theory of relativity is not a literal ...
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20 views

how to specify eigenfunctions(eigentensors) of Lichnerowicz operator?

Lichnerowicz operator is an operator which acts on transverse trace-free symmetric tensors. If this statement is correct, my question is that any transverse trace-free symmetric tensor is an ...
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63 views

Why doesn't this proof change indices?

In this pdf, in the second line of the proof, $\sigma$ was plugged in where it appears as $$\frac{\partial x^\sigma}{\partial y^{\rho'}}$$ Meanwhile in converting the coordinates of $g^{\mu'\rho'}$, ...
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29 views

Relation between the curvature of a manifold and the number of covariantly constant vector fields that it admits

Suppose that on a four dimensional manifold we are able to explicitly construct four linearly independent covariantly constant vector fields $K^a_{\mu}$: $$D_{\mu}K^a_{\nu}=0,$$ $a=1,2,3,4$ then it ...
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78 views

How strong is the force of space expansion?

There are many questions about space expansion, its cause, or its effects. But I have the feeling we never get straight and simple answers. I do not expect answers to be simple in general, but I ...
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52 views

Weak Equivalence Principle and universality of free fall

I know how we can derive geodesic equation from varying the action of a test particle with respect to coordinates and i know the fact that particles follow geodesics means that free fall is universal. ...
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34 views

problem with spin connection term

While working out Kaluza Klein compactification, I am getting the unwanted spin connection term $\omega_{c}^{ac}$ .I have tried to show that this is zero.But I am not quite sure of it. What I tried ...
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46 views

Relation involving the Lorentz transformation and the inverse of its transpose

The relation I was referring to in the title is $${\Lambda_a}^b= \eta_{ac} {L^c}_d \eta^{db}$$ where ${\Lambda_a}^b$ is the inverse transpose of $L$, the Lorentz transformation. I was wondering ...
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37 views

What causes the unexpected change in acceleration for flybys of spacecraft?

If the vehicle is not operating on RTG, then thermal recoils of photons shouldn't be considered as in the case of PIONEER. Then what actually accelerate the spacecraft from expected value (expected by ...
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90 views

Is there a general stress-energy tensor for vector fields?

I've been reading about scalar fields in the context of general relativity, and I found this page: https://en.wikipedia.org/wiki/Stress-energy_tensor#Scalar_field. It says that the stress-energy ...
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81 views

Minkowski to Euclidean

When dealing with solutions to Einstein's equations given by a 4d metric with signature $(-,+,+,+)$, we're able to move to Euclidean space using some transformation so that our signature is now ...
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46 views

Caustic and Singularities in General Relativity

What is the relation between the formation of caustics of a family of null geodesics and the existence of an incomplete null geodesic?
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17 views

Is there some other name used for “ping rigidity”?

In MTW, p. 398, "Box 16.4 (continued)", there's an interesting sketch (which can also be seen on p. 15 of this excerpt (www.pma.caltech.edu/~ph236/yr2008/readings/MTW_Chapter16.pdf). (It's not the ...
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166 views

Frequency of a photon as related to the change of its frequency

I think that bob maybe already, at least partially, has answered my following question: "Is it true or false that the frequency of a photon is not related to the change of its frequency caused by ...
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70 views

Null geodesics and rotation in stationary axisymmetric space-times

It is well known that in Schwarzschild space-time, a torque-free gyroscope in circular orbit at any permissible angular velocity at the photon radius will, if initially tangent to the circle, remain ...
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28 views

freedom of choice of 1-form in canonical representation of generic local field corresponds to gauge choice?

So it is a question in Gravitation Wheeler, Thorne and Misner 4.2 Exercise. Given F=$dp_{i}\wedge dq^{i}$. Using canonical transformation from p to $\bar{p}$ and q to $\bar{q}$, one gets ...
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23 views

Angular diameter distance in an inhomogeneous universe?

Computing the angular diameter distance $D_{A}$ is a well known academic exercise in an homogeneous Universe. But now suppose that we are in an inhomogeneous Universe and that I am interested in ...
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15 views

Why the position of apparent horizon depend on choice of Sigma t of foliation?

Whether a 2d surface is a trapped surface is independent of choice of Sigma t of foliation. Why its outer boundary (apparent horizon) depends on choice of Sigma t of foliation?
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52 views

Conditions that the coordinate must satisfy in order to become local inertial

Consider the coordinate transformation $$ \tilde x^a=x^a+\frac{1}{2}\Gamma^a_{bc}x^bx^c $$ I have shown that at the origin $O=(0,0,0,0)$, $$ \frac{\partial\tilde g_{ab}}{\partial\tilde x^c}=0 $$ ...
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33 views

(Special Relativity) Points that can be seen by an observer

Let the metric be $$ ds^2=(1+gz)^2dt^2-dx^2-dy^2-dz^2 $$ where $g$ is a positive constant. Let an observer be stationary at $x=y=0$ on the surface $z=0$ and look upwards at an angle $\theta$, how ...
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56 views

Exercise Lorentz Transformations

I have 2 inertial frames, both are in relative motion along the x axis moving with constant velocity $v_x$. It is called with Standard figuration where the Lorentz transformations relate the ...
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143 views

Wormholes with event horizons?

Under General Relativity, Lorentzian wormholes (the kind that are traversable) require exotic matter (a kind of unobtainium which is not known to exist). On the other hand, we know black holes exists ...
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39 views

Can we design the orbit of a satellite with Einstein’s curved space?

I think that the most successful theory of gravity is that the orbit of planet can be explained with this theory and the orbit of satellite was designed with this theory. To design an orbit of a ...
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30 views

gravitational waves and orders of magnitude

I have a question about numerical magnitude in eq. 6.110 of this reference. So, using this reference sheet for this PSR1913+16 binary, I get the following numbers: $$M = 2.8 \times 10^{30} ...
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21 views

Angular and luminosity distance in general?

Consider a non-Friedmannian Universe in which we know the trajectories of photons, ie in which we know null geodesics $\left(\eta, x^{1}, x^{2}, x^{3}, a, z\right)$ where : $\eta$ is the conformal ...
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52 views

The border of the System

In General Relativity, if the system accelerates, the inside of the system and the outside of the system will have different speed of time. Where is the boundary of the system? If a human ...
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46 views

Questions about four-momemtum

I am reading a note about Kerr metric, following is some screen shot where I have problems. First of all, I think the author made a mistake. It should be $$ E=-u_\mu k^\mu=u^t\;\;\;L=u_\mu ...
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83 views

Why such hypersurface orthogonal vector leading to $g_{0i}=0$ for $i=1,2,3$?

Suppose that the hypersurface orthogonal co-vector $W$ us perpendicular to the family of hypersurface defined by a function $\varphi$ with $\varphi=constant$. If we choose a coordinate in which ...
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56 views

Degrees of freedom in physical equations

Say we have the field equation: \begin{equation} f^{\prime}(R)R+3\square f^{\prime}(R)-2f(R)={\kappa}^{2}T, \end{equation} why is the non-vanishing of the second term means that there is an extra ...
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79 views

Einstein frame vs. Matter frame

What is the difference between Einstein frame and Matter frame in General Relativity? -A brief comment on each could be useful too. These two frames were used in this manuscript ...
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51 views

Lorentz transformed Scharwzschild solution

A question that has always intrigued me is: "Imagine a star moving as it evolves into a black hole, Ignore the effect of debris from the supernova. Assume also that before the collapse, the star was ...
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31 views

Do early-time black-hole infallers ruin effective field theory at the horizon for late-time observers?

I have an elementary confusion about black hole physics. The standard consensus is that if I fall into a black hole, at the horizon I don't see any violations of effective field theory for a large ...
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140 views

Has the Reissner-Nordstrom metric ever been experimentally verified?

In contrast to the solution of the conventional Reissner-Nordstrom problem, where the Schwarzschild metric takes on an additional $1/r^2$ term due to the added electric charge, P. Mannheim has in ...
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80 views

Timelike Shell Collapsing into a Black Hole

Does anyone know where I can find the solution for a spherically symmetric thin shell of timelike matter falling into a Schwarzschild black hole? The matter should be pressureless, so that each ...
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94 views

Curvature based derivation of Schwarzchild Metric

I'm a third year maths undergrad and I'm trying to find (and follow) a curvature based derivation of the Schwarzchild metric, if there exists such a proof?
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71 views

How to move from Special to General Relativity

I have understood special relativity nicely, and right now I am trying to learn general relativity from D'Inverno's book. I an finding it rather difficult to understand the pre-requisite math (i.e. ...
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62 views

About divergence of a vector field and geodesic sphere

I have a question. I want to know the difference between the sphere and the geodesic sphere. Another question: given a vector field, $Y$, on a manifold $M$ defined by: $Y(p)=p$ for every point $p \in ...
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87 views

Light cones and reference frames

I'd like to know what does it mean exactly to find a reference frame in which two events occur at the same time or in the same space coordinates. As I picture it if we have two events A and B in a (x, ...