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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Computation of spin connection 1-form [closed]

If stationary metric is given by $$ds^2 = e^{2U}(dt+\omega_idx^i)^2 - e^{-2U}dx^2$$ and I want to try to solve for this. After doing the effort to find the metric and its inverse, I used the tetrad ...
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99 views

Natario warp drive [closed]

There are two solutions to Einstein's equations that allow for warp drive. One is the Alcubierre warp drive and the other is the Natario warp drive. What is the difference? Is the Natario warp drive ...
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1answer
47 views

Calculate the mass of a Schwarzchild black hole with Komar integral

In Wald's GR, Komar integral is Eq. (11.2.9): $$M=-\frac{1}{8\pi}\int_S\epsilon_{abcd}\nabla^c\xi^d$$ $S$ can be chosen as a 2-sphere, the boundary of a spacelike hypersurface $\Sigma$ such that the ...
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2answers
449 views

Why does weak equivalence principle say gravity is equivalent to acceleration?

I am told that the weak equivalent principle, that $m_i=m_g$ (inertial and gravitational masses are equivalent) is equivalent to the statement that in a small system you can't tell whether you are in ...
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32 views

Books on special and general relativity? [duplicate]

I have idea about all the theories related to space and time and stuff. But I wanna dig deep into it and understand all the theories like special and general relativity to begin with for now. Can ...
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1answer
760 views

Does the heat equation violate causality?

I've ran across the idea that, besides simply writing partial differential equations in covariant form, they need to be hyperbolic with all characteristic speeds less than the speed of light. A ...
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1answer
59 views

Why is the value of the action integral in general relativity the same on all regions that are homologous?

In their famous paper Action integrals and partition functions in quantum gravity, Gibbons and Hawking argue that in order to avoid the singularity of a Schwarzschild black hole you can complexify ...
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132 views

Penrose diagram for spacetime which flows to $AdS_{2}$ at infinity

Consider I have the following 2 dimensional spacetime $(t,z)$: $$ds^2=\frac{4}{z^{2}}\left(1+\frac{1}{z}\right)^{-1}(-dt^{2}+dz^{2}).\tag{1}$$ When $z\rightarrow \infty$ we have ...
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1answer
64 views

Scalar field in a Schwarzschild metric

I have found this article recently published in Classical and Quantum Gravity giving the exact solution of a scalar field in the Kerr-Newman metric. These authors also derived Hawking radiation for ...
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2answers
187 views

Changing vector basis in AdS$_3$

I have AdS${}_3$ given as a surface embedded in a 4 dimensional pseudo-Riemannian space $$x^2+y^2-u^2-y^2=-l^2$$ With metric: $$ds^2=dx^2+dy^2-du^2-dv^2$$ I have Killing vectors of that space ...
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44 views

Is the orbit in Schwarzshild metric a path with maximal proper time?

In curved spacetime particles follow timelike geodesics, which should have maximal proper time (at least locally). I thought this path usually corresponds to a global maximum, and there are only ...
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391 views

How does time relate to mass and velocity

I understand that the larger the mass the greater gravity is and the slower time is, as well the faster an object is traveling the slower time passes. My question is that since the faster an object ...
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2answers
91 views

What would be the consequences of time not being “relative” [closed]

So far nobody proved Einstein wrong about Theory of relativity and time but I'm curious: What would be the consequences or problems if someone would prove him wrong when it comes to relativity of ...
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0answers
43 views

Gravity's effects on photons moving away from source

As a photon has no mass and must always have velocity c, if I were to shine a laser straight up (so Earth's gravity would be pulling straight back on it), what would the effect be on the photon? It ...
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2answers
73 views

How is strong time dilation consistent with weak tidal forces?

Nolan's latest film, Interstellar, takes pains to explain to lay audience members that the passage of time slows in the presence of strong gravitational fields (as per Einstein's theory of General ...
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3answers
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The Pioneer anomaly finally explained?

Pioneer 10 & 11 are robotic space probes launched by the NASA in the early 1970's. After leaving our solar system, an unusual deceleration of both spacecrafts has been measured to be approximately ...
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1answer
99 views

Explanation for “if all accelerated systems are equivalent, then Euclidean geometry cannot hold in all of them”

I'm doing an EPQ (mini college research paper) on gravity, and I found a site that explained things in simple terms. I am having trouble understanding how Einstein came to his revelation space-time ...
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1answer
161 views

$L^{1}$ energy-momentum tensors in general relativity; semi-classical gravity

I was unsure whether to pose this question in a physics or mathematics forum, but it is an interesting idea I have been thinking about for some time. In any (semi-)classical field theory it is often ...
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Is topology of universe observable?

There is an idea that the geometry of physical space is not observable(i.e. it can't be fixed by mere observation). It was introduced by H. Poincare. In brief it says that we can formulate our ...
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23 views

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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1answer
151 views

Massless Dirac equation is Weyl covariant

Does somebody know how to show that the following equation is Weyl invariant? $$\gamma^ae_a^\mu D_\mu \Psi=0$$ where: $D_\mu \Psi=\partial_\mu\Psi+A_\mu^{ab}\Sigma_{ab}\Psi$ is the spin-covariant ...
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2answers
99 views

What's the escape velocity of Naked Singularities?

Penrose's Cosmic Censorship Hypothesis doesn't hold for naked singularities which means that at least light can escape the singularity. But, if we calculate escape velocity with the given mass only, ...
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160 views

Movie Interstellar - Followup Question to Escape Velocity

Continuing the discussion on this thread: Movie Interstellar - Question about Escape Velocity The movie Interstellar shows people on a water planet where time is dilated so much that 1 hour is equal ...
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4answers
103 views

Twin paradox where the twins start at different locations

Suppose we have this scenario with twins A and B: 1) Instead of the twins starting at the same location, let's say the twins start out some distance apart, in the same reference frame. 2) The ...
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1answer
95 views

Why find the curl in this paper?

I was crossing over this interesting paper http://arxiv.org/abs/hep-th/9404006 when I couldn't realize what happened in the Second Section p. 3: They introduced the metric: $$ds^2 ...
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50 views

Finding the metric [closed]

If given the metric: $$ds^2=e^{2U}(dt+w_idx^i)^2-e^{-2U} d\overrightarrow{x}^2$$ where $w = w_idx^i$ is one form How to find the metric in order to find the inverse metric? The new thing about this ...
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486 views

Questions after watching the movie Interstellar [closed]

Awesome movie, but as a physics student, some questions do crop up When they travel to the watery planet, they say that 1 hour on this planet is 7 yrs om earth. How is this possible? Is the planet ...
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493 views

Are Wormholes predicted by the theory of general relativity?

Just like it predicted gravitational time dilation, gravitational lensing. What does it mean to predict something, Does it mean that we'll find wormholes in nature one day?
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1answer
263 views

Movie Interstellar - Question about Escape Velocity

The movie Interstellar shows people on a water planet where time is dilated so much that 1 hour is equal to 7 years back on Earth. Even though they lift off from Earth using a Saturn-V two stage ...
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1answer
42 views

Most general second-rank symmetric tensor in Einstein theory

I am reading MTW page 407, Exercise 17.1. (a) Show that the most general second-rank, symmetric tensor constructable from Riemann and $g$, and linear in Riemann, is $$a R_{\alpha\beta} + b R ...
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26 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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1answer
465 views

Surface gravity of Kerr black hole

I'm going through Kerr metric, and following the 'Relativist's toolkit' derivation of the surface gravity, I've come to a part that I don't understand. Firstly, the metric is given by ...
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No-hair theorems for naked singularities?

For black holes, we have no-hair theorems that say, under certain assumptions about the matter fields, that they are uniquely characterized by just a few parameters. Are there any such theorem for ...
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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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1answer
457 views

Is the fifth dimension of Interstellar the same as Block Universe theory? [closed]

Is the movie Interstellar (2014) referring to Block Universe theory of space-time with its concept of a fifth dimension?
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2answers
282 views

How are the Weyl & Riemann curvature tensors related to the stress energy tensor in GR?

Einstein's vacuum equations, that is without matter, allows the possibility of curvature without matter. For instance, we may consider gravitational waves. The question is: Is there some link ...
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Wormholes & Time Machines - for *experts* in GR/maths

EDIT: Further clarification in the context of answers/comments received to 20 Jan has been appended EDIT: 21 Jan - Response to the Lubos Expansion appended [in progress, not yet complete] EDIT: 23 ...
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1answer
140 views

Can light gravitationally affect itself?

Consider a electromagnetic wave in a vacuum. From my understanding of general relativity, The wave has momentum, and thus generates a gravitational field in all directions. The gravitational field ...
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0answers
49 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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5answers
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Can black holes form in a finite amount of time?

One thing I know about black holes is that an object gets closer to the event horizon, gravitation time dilation make it move more slower from an outside perspective, so that it looks like it take an ...
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0answers
41 views

Examples of warped product manifolds?

Bishop and O'Neil defined warped product manifolds. Space-times are good examples of such warped product manifolds. Is there a famous and important example of space-times $I×M$ where $M$ is itself a ...
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2answers
172 views

What is the physical meaning of the Eddington - Finkelstein coordinates?

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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1answer
357 views

What is the maximum time dilation factor when orbiting a rotating black hole?

Suppose one spaceship is stably orbiting a rotating black hole and another is far away from the black hole. What is the maximum time dilation factor between the two ships? Can it be made arbitrarily ...
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36 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 ...
2
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1answer
129 views

Rotating black holes and naked singularity

In the book The science of interstellar by Kip thorne can be found the following: There is a maximum spin rate that any black hole can have. If it spins faster than that maximum, its horizon ...
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2answers
55 views

How to identify a “measuring rod”, and how to compare separated “measuring rods” with each other?

The notion of "measuring rod" has appeared in PSE here and there, and outside PSE as well. As far as I understand (and as perhaps all who refer to this notion do agree on), important constituents of ...
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3answers
104 views

Understanding emergent phenomena in the block universe. (Reworded question)

Each person exists as an unchanging 4D worldtube in the block universe. At each slice of the worldtube there is a present, past and future. However, there is a black box* which appears to exist in ...
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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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1answer
59 views

Robertson-Walker metric and stable orbits [closed]

The RW metric is defined using 4 spatial dimensions, but stable planetary orbits require 3 spatial dimensions. Does this indicate a problem with the assumption of the RW metric to describe the cosmos? ...
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52 views

Is it possible to build a tensor with the following properties? [closed]

I am searching for a tensor in 4-dimensional space-time with two indices that satisfy: \begin{eqnarray} M_{;\mu }^{\mu \nu } &=&0 \\ M^{\mu \nu } &=&-M^{\mu \nu } \nonumber \\ ...