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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A clock in freefall

Time dilation calculated using Schwarzschild metric for a non rotating spherical body is: $$t_0=t_f\sqrt{1-\frac{2GM}{rc^2}}$$ For such a non rotating spherical body, what would the time dilation of ...
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382 views

Time dilation at the Big Bang

At the time the Big Bang happened the matter had enormous density. According the GR (I may be wrong here) such density dilates time. If so, could it be that the time periods just after Big Bang which ...
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856 views

Time Dilation in Orbits in the Schwarzschild Metric

I am wondering if there exist closed form-expressions for the time dilation experienced by an observer in different orbits around a Schwarzschild black hole, outside the event horizon, relative to ...
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188 views

the higher you go the slower is ageing [duplicate]

as per to einstein as we go far from the earth the TIME tends to slow down , so it means when I am one metre above the earth's surface , the time has slow down for me as per ...
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1answer
547 views

Space expansion looking like time dilation

Space looks like time depending on the motion of the observer so I was going to ask if space expansion was the same as the unfolding of time, but this was asked on physics.stackexchange before and the ...
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4answers
459 views

At which point of the universe $R_{\mu \nu}=0$ if there is a source of gravitation (point mass)

Schwarschild found his solution to Einstein's field equations for vacuum ($T_{\mu \nu}=0$) by placing a point-mass in the center of origin. Since the Ricci tensor $R_{\mu \nu}$ and the Einstein ...
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4answers
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What is the physical meaning of the connection and the curvature tensor?

Regarding general relativity: What is the physical meaning of the Christoffel symbol ($\Gamma^i_{\ jk}$)? What are the (preferably physical) differences between the Riemann curvature tensor ($R^i_{\ ...
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How does “warp drive” not violate Special Relativity causality constraints?

I'm talking about this nonsense: http://www.washingtonpost.com/news/post-nation/wp/2014/06/11/this-is-the-amazing-design-for-nasas-star-trek-style-space-ship-the-ixs-enterprise/ Now, I'm aware that ...
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5answers
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Could gravity be an emergent property of nature?

Sorry if this question is naive. It is just a curiosity that I have. Are there theoretical or experimental reasons why gravity should not be an emergent property of nature? Assume a standard model ...
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1answer
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Is String Theory formulated in flat or curved spacetime?

String Theory is formulated in 10 or 11 (or 26?) dimensions where it is assumed that all of the space dimensions except for 3 (large) space dimensions and 1 time dimension are a compact manifold with ...
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2answers
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Why does dark energy produce positive space-time curvature?

My understanding is that dark energy, or equivalently a positive cosmological constant, is accelerating the expansion of the universe and I have read that this gives empty space-time positive ...
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4answers
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Can general relativity be completely described as a field in a flat space?

Can general relativity be completely described as a field in a flat space? Can it be done already now or requires advances in quantum gravity?
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Why can't General Relativity be written in terms of physical variables?

I am aware that the field in General Relativity (the metric, $g_{\mu\nu}$) is not completely physical, as two metrics which are related by a diffeomorphism (~ a change in coordinates) are physically ...
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Why you need a graviton when you have the higgs boson?

Since I studied General Relativity I had this question running on my mind. As I see it (just taking lectures of Quantum Field Theory right now) "Why you need a gauge boson for gravity when the higgs ...
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3answers
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Does a Weak Energy Condition Violation Typically Lead to Causality Violation?

In the answer to this question: ergosphere treadmills Lubos Motl suggested a straightforward argument, based on the special theory of relativity, to argue that light passing through a strong ...
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4answers
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Can spacetime be non-orientable?

This question asks what constraints there are on the global topology of spacetime from the Einstein equations. It seems to me the quotient of any global solution can in turn be a global solution. In ...
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5answers
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Why does no physical energy-momentum tensor exist for the gravitational field?

Starting with the Einstein-Hilbert Lagrangian $$ L_{EH} = -\frac{1}{2}(R + 2\Lambda)$$ one can formally calculate a gravitational energy-momentum tensor $$ T_{EH}^{\mu\nu} = -2 \frac{\delta ...
14
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3answers
681 views

Extremal black hole with no angular momentum and no electric charge

A black hole will have a temperature that is a function of the mass, the angular momentum and the electric charge. For a fixed mass, Angular momentum and electric charge are bounded by the extremality ...
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4answers
554 views

Why gauge theories have such a success?

[This question was inspired by a identical question asked on a other forum] Note that we may morally include general relativity in the gauge theories. We may have several (some are deliberately ...
18
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3answers
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No hair theorem for black holes and the baryon number

The no hair theorem says that a black hole can be characterized by a small number of parameters that are visible from distance - mass, angular momentum and electric charge. For me it is puzzling why ...
14
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5answers
917 views

Does GR provide a maximum electric field limit?

Does GR provide a limit to the maximum electric field? I've gotten conflicting information regarding this, and am quite confused. I will try to quote exactly when possible so as not to confuse ...
11
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3answers
1k views

How to prove the covariant derivative cannot be written as an eigendecomposition of the partial derivative?

The Question How does one prove that Rindler's definition of the covariant derivative of a covariant vector field $\lambda_a$ as \begin{align} \lambda_{a;c} = \lambda_{a,c} - \Gamma^{b}_{\ \ ca} ...
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5answers
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Naive visualization of space-time curvature

With only a limited knowledge of general relativity, I usually explain space-time curvature (to myself and others) thus: "If you throw a ball, it will move along a parabola. Initially its vertical ...
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1answer
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Angular deficit

If one starts with a flat piece of paper, removes a wedge, and tapes the paper together, you get a cone. The angle of the removed wedge is called the "angular deficit". Now if this is done in 3 ...
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5answers
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How to measure the curvature of the space-time?

I know G.R. change our vision of space and time as a unique surface than can bend. We can associate the curvature of the space-time as the gravity created by the mass of planets, stars... But how can ...
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605 views

Stress-energy tensor for a fermionic Lagrangian in curved spacetime - which one appears in the EFE?

So, suppose I have an action of the type: $$ S =\int \text{d}^4 x\sqrt{-g}( \frac{i}{2} (\bar{\psi} \gamma_\mu \nabla^\mu\psi - \nabla^\mu\bar{\psi} \gamma_\mu \psi) +\alpha \bar{\psi} \gamma_\mu ...
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Visualizing GR spacetime distortion in 1+1D spacetime instead of 2D space

Usually spacetime distortion due to mass in GR is visualized as a rubber sheet distorted under some massive object, like this: source or as shown in this link. But what has always bothered me is ...
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4answers
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Is there a maximum possible acceleration?

I'm thinking equivalence principle, possibilities of unbounded space-time curvature, quantum gravity ...
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1answer
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Open problems in General Relativity [closed]

I would like to know if there are some open mathematical problems in General Relativity, that are important from the point of view of Physics. I mean is there something that still needs to be ...
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2answers
227 views

5D Ricci Curvature

As part of a hw problem for a class, we're supposed to be deriving the equivalence given in equation 2.3 of this paper http://arxiv.org/abs/1107.5563. I was wondering if there is some special ...
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2answers
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Faster-than-light communication using Alcubierre warp drive metric around a single qubit?

The Alcubierre warp drive metric has been criticized on the points of requiring a large amount of exotic matter with negative energy, and conditions deadly for human travellers inside the bubble. What ...
3
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9answers
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How does this thought experiment not rule out black holes?

How does the following brief thought experiment fail to show that general relativity (GR) has a major problem in regards to black holes? The full thought experiment is in my blog post. The post ...
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5answers
836 views

How are the comoving coordinates NOT a prefered reference frame?

Physics me this: The equivalence principle has rigorous physical definitions that say, for one, that the laws of physics are the same in all inertial reference frames. This is to say that the ...
19
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6answers
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How exactly does time slow down near a black hole?

How exactly does time slow down near a black hole? I have heard this as a possible way of time traveling, and I do understand that it is due in some way to the massive gravity around a black hole, but ...
4
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1answer
366 views

Would dense matter around a black hole event horizon eventually form a secondary black hole? [duplicate]

Possible Duplicate: Black hole formation as seen by a distant observer Given that matter can never cross the event horizon of a black hole (from an external observer point of view), if a ...
2
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2answers
609 views

Gravity on the International Space Station - General Relativity perspective

My question is an extension to this one: Gravity on the International Space Station. If all the outside views of the ISS was sealed, then the crew inside would not be able to tell whether they were ...
2
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4answers
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Inertial frames of reference

I'm struggling with the notion of an inertial frame of reference. I suspect my difficulty lies with the difference between Newtonian and relativistic inertial frames, but I can't see it. I've read ...
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6answers
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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 ...
8
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1answer
305 views

How long can a particle survive inside of the horizon of a black hole?

By examining the causal structure of a Schwarzschild black hole, one can see that a particle in region II is unable to escape to $r=\infty$. Such diagrams do not show, however, how long a particle ...
8
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2answers
904 views

Visualizing Ricci Tensor

By definition Ricci Tensor is a Tensor formed by contracting two indices of Riemann Tensor. Riemann Tensor can be visualized in terms of a curve, a vector is moving and orientation of the initial and ...
6
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1answer
681 views

When a neutral star with a magnetic field collapses to form a black hole, what happens to the magnetic field?

By the no-hair theorem, black holes are only characterized by mass, charge and angular momentum. If the star is neutral, the black hole will have only mass and angular momentum - and therefore it ...
4
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3answers
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Do photons lose energy due to gravitational redshift? If so, where does the lost energy go? [duplicate]

In the gravitational redshift, the frequency of photons radiated from some source is reduced. As the energy of a photon is given by $\hbar\omega$, if the frequency is reduced where is the lost energy? ...
4
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2answers
561 views

Introduction to relativity books for an engineer [duplicate]

Possible Duplicate: Getting started general relativity I am an engineer who loves to read science fiction books especially when there's more science than fiction but usually I see that I ...
4
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1answer
715 views
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2answers
679 views

Time-like Killing vector in FRW metric?

The spatially flat FRW metric in cartesian co-ordinates is given by: $$ds^2 = -dt^2 + a^2(t)(dx^2 + dy^2 + dz^2)$$ As I understand it there are Killing vectors in the $x$, $y$, $z$ directions implying ...
2
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2answers
657 views

Notation for anti-symmetric part of a tensor

I know that $A_{[a} B_{b]} = \frac{1}{2!}(A_{a}B_{b} - A_{b}B_{a})$ But how can write $E_{[a} F_{bc]}$ like the above? Can you provide a reference where this notational matter is discussed?
2
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3answers
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Ricci scalar for a diagonal metric tensor

I was wondering if there is a general formula for calculating Ricci scalar for any diagonal $n\times n$ metric tensor?
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why do x Schwarzschild radii equal time dilation effects of speed of light going y times faster than an object^2?

let me walk you through the math. First you start with the gravitational time dilation formula where: $$ T_1=T\sqrt{1-\frac{2GM}{rc^2}} $$ and rather than entering $r$ for the radius we replace $r$ ...
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2answers
524 views

How do gravitons impact on general relativity?

As I'm reading about GR a lot lately, I was wondering: how do gravitons (if they exist ofc) impact the general relativity? Since in GR, when we look at particles moving in space-time, we are only ...
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Is the speed of sound almost as high as the speed of light in neutron stars?

Have you ever wondered about the elastic properties of neutron stars? Such stars, being immensely dense, in which neutrons are bound together by the strong nuclear force on top of the strong gravity ...