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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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 ...
3
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3answers
243 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 ...
12
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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
74 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
323 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
66 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 ...
7
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1answer
176 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
225 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 ...
0
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1answer
90 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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0answers
77 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
279 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 ...
3
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1answer
145 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, ...
4
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2answers
86 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. ...
1
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1answer
135 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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0answers
795 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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0answers
124 views

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
1k views

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 ...
2
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2answers
1k 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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2answers
173 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
143 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 ...
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6answers
665 views

Can energy be created and destroyed?

The indroduction of the principle of conservation of mechanical energy has been tremendously useful from the practical point of view. But .. Consider the case in which we shoot an electron up in the ...
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3answers
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How can a black hole reduce the speed of light?

If the speed of light is always constant then light should escape from a black hole because if directed radially outwards it only needs to travel a finite distance to escape, and at a speed of $c$ it ...
3
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1answer
553 views

How to explain centripetal force in terms or relativity

At the end of a video of dropping a ball and feathers in a vacuum, Brian Cox explains that the Ball and Feathers, as understood in terms of General Relativity, aren't falling. (apologies I can only ...
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45 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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76 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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1answer
85 views

What happens as the stable orbital velocity approaches the speed of light?

Based on my understanding of the relationship between planetary mass, orbital radius and the velocity for stable orbit, a satellite orbiting a mass equivalent to Earth with an altitude of ~5mm would ...
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2answers
105 views

Why does Einstein's equation of relativity exclude space and time? [closed]

Taking $E={m}{c^2}$, we have mass and energy but no space and time. What is the best way of understanding the ways that space and time are passive and therefore unaccountable as mass and energy?
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8answers
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What is a rocket engine thrusting against in space?

I know Newton's third law of motion might be the answer for this but still I am wondering how the rockets could thrust in the empty space and move in the opposite direction. I guess an astronaut ...
1
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1answer
319 views

Is black hole singularity a single point?

General relativity expressed in terms of differential geometry. And it lets you to do interesting things with the coordinates: multiple coordinates may refer to a single point, eg. the equirectangular ...
2
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4answers
390 views

Conservation of potential energy for a wormhole

So you managed to build a stable traversable wormhole. Somehow you managed to acquire the exotic negative-tension materials with sufficient densities to make it all work. Now you place opening A of ...
3
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0answers
89 views

Path of light in Kerr metric? [closed]

How can one find the trajectory of light in various direction in the Kerr metric? Just wondering if there are some classes of solutions, I don't need exact formula. Are there different classes than ...
4
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1answer
226 views

Gibbons-Hawking-York (GHY) boundary term for Schwarzschild metric

What is the simplest way to calculate Gibbons-Hawking-York boundary term for Schwarzschild metric? \begin{align} \int ...
2
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0answers
222 views

How does matter interact with spacetime? [closed]

It's easy to see how matter interacts with itself but how does it interact with spacetime which is "not" matter? Einstein showed us that mass and energy cause a curvature in spacetime, which intern ...
5
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1answer
347 views

Ray tracing in General Relativity

I would like to find out what one would see at the Schwarzschild radius of a massive non-rotating black hole, if the black hole is surrounded by a bright ring. For that, I would place the observer at ...
0
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1answer
245 views

Verifying a solution to Einstein's vacuum field equations

I need to verify a solution to Einsteins vacuum field equations. I have the solution as follows $$ds^2=a\,dt^2+b\,dr^2+\cdots$$ Is the following the right approach? Einsteins equation reduces to ...
4
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1answer
309 views

Is General Relativity based on a Symmetry?

In short: Is there any kind of symmetry one can start with to derive general relativity (GR)? Longer: Einstein had the opinion that GR was the generalisation of special relativity, because instead of ...
1
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1answer
97 views

Circular orbit in Schwarzschild coordinates [closed]

This was an example in a general relativity textbook which I've been trying to work through myself. A spaceship uses its rocket engine to maintain a circular orbit around a Schwarzschild black hole ...
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0answers
22 views

What is the rate at which the field of an electron spreads? [duplicate]

There are 2 steps in the creation of a force field: (1) first the object comes into existence (2) then the field appears. In the case when a photon splits into an electron and an antielectron, these 2 ...
1
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1answer
81 views

Can we define the effective mass or the moving mass of a photon?

I know that the rest mass of a photon is zero. but the photon can be bent by gravity (which can also be explained by the curvature of space-time due to the effect of mass), this implies that it must ...
1
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0answers
124 views

What is the derivation of $E=mc^2$? [duplicate]

How did Einstein derive his most famous equation: $$E=mc^2$$ Is the above equation a special case of $$E^2=m^2c^4+p^2c^2$$ Its derivation? What is the difference between them?
4
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1answer
418 views

Angular momentum in curved spacetime

It is known that the angular momentum components are also a representation of the $SU(2)$ generators. Given a non-trivial spacetime, say a black hole of some kind or AdS space, how can one define the ...
7
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3answers
420 views

Recommended books for a “relativity for poets” class?

I teach physics at a community college and have developed a new course titled "Relativity for Poets," which I will be teaching for the first time in spring 2015. As implied by the title, it's a ...
0
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1answer
253 views

What is Laplace operator of Schwarzschild-Spherical coordinates? [closed]

This is the Laplace operator of Spherical coordinates: What is the Laplace operator of Schwarzschild-Spherical coordinates? where the Differential displacement of Schwarzschild-Spherical ...
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0answers
55 views

Some books to bridge the gap before GR [duplicate]

I am extremely interested in GR, but somehow feel that the books I read are not really enough. Frankly, I find many question on this site and elsewhere completely bewildering, which makes me think ...
3
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2answers
436 views

Correct tetrad index notation

There seems to be some different conventions on the indexes of the tetrad. I am wondering which is the standard, which is correct, and which is an abuse of notation. In Sean Carroll's notes and in ...
2
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0answers
91 views

Metric with 5D signature: +---+

From a paper that a friend sent to me (on inflation theory which I am still in learner mode) a 5D signature +---+ was specified with the 5th dimension being a velocity dimension. I didn't know that ...
5
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3answers
260 views

Gravity - Force or Result?

I am no Physicist, but I enjoy reading about Physics. However reading about leading theories such as M-Theory and others they speculate about the existence of the Graviton. In my past reading of ...
5
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2answers
2k views

Is my interpretation of how a gravitational wave is formed correct?

I'm sure many here are familiar with the following image showing the 2D representation of how the fabric of spacetime is warped by the presence of mass:- Can this fabric be interpreted as an ...