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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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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98 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
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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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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260 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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492 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
485 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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41 views

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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28 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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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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454 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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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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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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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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34 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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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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1answer
128 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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13 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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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 \\ ...
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2answers
871 views

How long is a second in zero gravity?

General relatively predicts that gravity creates time dilation and a relatively slower passage of time for the observer experiencing larger acceleration. For an observer experiencing zero ...
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49 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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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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1answer
56 views

Is this answer stating that an external observer can see a black hole mass grow, correct? [duplicate]

Is this answer from here stating that an external observer can see a black hole mass grow, correct? This question (is an external observer can ever see the mass of a black hole increase--motivated ...
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1answer
58 views

black holes and white holes

i have a question and i just couldn't get another way to get its answer. My question is regarding black hole and the possibility of a white hole. we know that even light cannot escape a black hole ...
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66 views

Circumference of a circle in a co-rotating frame of reference

According to Einstein it should be greater than $2 \pi R$ for a co-rotating observer, i.e. $L' = \gamma L$ where $L = 2 \pi R$ in a non-rotating frame and $\gamma$ is the usual Lorentz factor, which ...
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2answers
83 views

How is the Ricci scalar $R=0$ here?

Given the metric in the form: $$ds^2 =-A(r)dt^2 +B(r) dr^2 dr^2 +r^2(d\theta ^2 +\sin^2\theta d\phi^2)$$ Papapetrou in his book said that $R=0$ But when I performed it I didn't get zero. For ...
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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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127 views

General Relativity field equation solution and geodesic equation solution [closed]

I am currently learning partial differentials. I know ordinary differentials, as well as other parts of calculus. Here's my question: Say an electron is moving in the x1 direction only, at 60% the ...
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10 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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349 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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1answer
27 views

In layman's terms, why would frame dragging affect precession of nearby object?

My question is really about the gravitomagnetic frame-dragging and the Lense Thirring effect. My question is not whether the frame dragging effect exists but rather it's manifestation in affecting ...
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1answer
90 views

About Christoffel symbols in Riemann normal coordinates

According to the answer to this post, the Christoffel symbols in Riemann normal coordinates are approximated by $$\Gamma^{k}_{ij}(x)~\sim~\frac{1}{2} R^k{}_{ilj}(x_0) \xi^l \tag{5.10}$$ which came ...
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54 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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58 views

Falling into the black hole: a picture from the infinite distance [duplicate]

This question was bugging me for many years. Here it was argued that it would take an infinite time for somebody (suppose, an astronaut) to fall into the black hole, given that it is not his time, but ...
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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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2answers
147 views

Can hyperbolic space be bounded?

There are many visualisations of hyperbolic geometry using Poincaré disks. What are their purpose? Can hyperbolic space be bounded? Can we endow the disk with the structure described by the FLRW ...
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1answer
55 views

Calculation mistake some place in finding stress-energy tensor

If the Lagrangian in Maxwell's theory is $$L= R- \frac{1}{4}F_{\mu\nu}F^{\mu\nu}$$ I want to find $T_{\mu\nu} $ The procedure is that I vary the action: $$\delta S = -1/2 \int{d^4x ...
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31 views

Definition of Irreducible Tensor Parts in an Exercise

I am addressing exercise 23.9 on http://www.pma.caltech.edu/Courses/ph136/yr2011/1023.1.K.pdf. The exercise says that a fluid flowing through spacetime $\vec u(\mathcal P)$ can have its gradient ...
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1answer
72 views

Covariant derivative of stress-energy tensor for a scalar field [closed]

In order to prove that $$\nabla ^\mu T_{\mu\nu} =0$$ I want to find the covariant derivative of $$T_{\mu\nu} = \partial_\mu\phi \partial_\nu \phi -\frac{1}{2}g_{\mu\nu}(g ...
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1answer
59 views

Is the best data about Mercury's perihelion shift really 60 years old?

The advance of the perihelion of Mercury is one of the four classical tests of general relativity. I wonder what's the most precise modern measurement of it. However, while scanning the literature, ...
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2answers
65 views

Charge orbiting gravitational body [duplicate]

I am currently rather uneducated on the subject, but I was thinking of a general relativity thought experiment. Say I take a charge from infinity and give it velocity to orbit a planet in a circle. ...
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63 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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1answer
47 views

Moving From Schwarzchild Geodesic Equations to Equations of Motion

So I am a student and decided (for some bizarre reason) to attempt to tackle general relativity for my final astrophysics and computational physics project this term. I have been doing a lot of ...
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37 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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Conditions for a diagonal induced metric?

Let $M$ be a manifold of dimension $n$ with a (say Lorentzian) metric $g$, that is diagonal in some choice of local coordinates. Let $S$ be manifold of dimension $k<n$ , embedded in $M$ by some ...
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2answers
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length contraction in a gravitational field [duplicate]

As space-time is distorted in a gravitational field, relativistic effects such as time dilation and length contraction take effect. Time dilation is explained simply enough: closer to the source of ...
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2answers
511 views

Gravitational time dilation caused by a galaxy, and by

In a word, if you are sitting on the Earth, if I'm not mistaken you are experiencing Time Dilation compared to being in deep solar system space. Due to the mass of the Earth. However. We're all ...
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67 views

Relativity and acceleration-acceleration

Presummary to save expert's time! (pls see below!) "In GR, is jerk relative?" As I understand it, "Special Relativity" (special meaning, specific limited situations) applies only for (in a word) ...
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1answer
45 views

Newtonian tidal forces and curvature

Today in my physics class, my lecturer said something which confused me. He said: "Newtonian tidal forces are reinterpreted as a manifestation of curvature in General Relativity". Now I know what ...