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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Meaning of general covariance

Quoting from Wald's GR: In the context of special relativity, the principle of general covariance states that the spacetime metric $\eta_{ab}$, is the only quantity pertaining to spacetime ...
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Time should run slower near massive body

We have considered that time should run slower near massive body like Earth, BH. There is no gravity in space, means time is faster in space compare to earth. Then How is it possible that man who ...
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(Scalar) Ricci flatness of a metric

What is the physical meaning to vanishing Ricci scalar $R=0$ of a metric in general relativity? Note that this is not the same questions as the geometric meaning of $R_{\mu\nu}=0$ which has been asked ...
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42 views

Increase in momentum of a particle falling into a black hole

From the point of view of an external observer at a fixed distance above a black hole, the linear momentum a free falling particle increases exponentially with Schwarzchild time. (This happens when ...
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145 views

Relation between $f(R)$ gravity and Tensor–vector–scalar (TeVeS) gravity

We know that there is a relation between f(R) gravity and scalar-tensor gravity. By applying the Legendre-Weyl transform, we can receive brans-dicke gravity from $f(R)$ gravity. If we start with the ...
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1answer
91 views

Is the event horizon also the boundary region of the mass contained by a black hole?

I was recently playing around with classic Newtonian mechanics and calculated that the Earth would have to be compressed to a spherical region of $8.8 \ mm$ (Its Schwarzchild radius) to turn its ...
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Einsteins gravity Space time

I'm having a difficulty in understanding Einstein's version of gravity as "space time curvature" (I could be a total physics idiot, please point out !). How does an object on the surface of earth ...
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1answer
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Would a wormhole in space look like anything at all?

In movie "Interstallar", the wormhole is elaborately depicted as a sphere, complete with explanation about why it is spherical, and as it is approached, it looks like a sphere containing fabulous ...
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Can all fundamental forces be fictitious forces?

After reading many questions, like this and this, I wonder: is it possible to consider also the other fundamental forces, the electroweak interaction and the strong interaction or ultimately the ...
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Length of Day and year on massive Earth

Say, a planet has the same orbital periods as Earth (365 days in a year, 24 hours in a day, etc. with respect to Earth-bound clocks), but the planet has double the mass. So, time must pass more slowly ...
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1answer
322 views

Calculate the mass of a Schwarzchild black hole with Komar integral [closed]

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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159 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
109 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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1answer
187 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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1answer
69 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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2answers
139 views

Does inbound light slow down (for an external observer) as it approaches the event horizon?

As I understand, for an external observer nothing even enters a black hole because it takes infinite time in his frame of reference for something to actually reach the event horizon. I also read that ...
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0answers
102 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
146 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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82 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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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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641 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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1answer
171 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
124 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 =(V\bar{V})(dt+\...
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0answers
172 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
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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
63 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 g_{...
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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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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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75 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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75 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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1answer
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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
145 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
138 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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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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277 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
876 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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0answers
126 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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63 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 \\ M_{;\...
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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 acceleration,...
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211 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
98 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
144 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
107 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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3answers
259 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 ...
3
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2answers
118 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 ...
13
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1answer
2k 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
76 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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2answers
345 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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0answers
67 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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0answers
71 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 ...