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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The arrow of time and the cosmology of a black hole interior

When solving the Einstein field equations in Schwarzschild metric for an observer falling into a black hole the radial coordinate r of the black hole and time t switch roles in the equations when ...
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Have red shifted photons lost energy and where did it go? [duplicate]

I think the title says it. Did expansion of the universe steal the energy somehow?
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5answers
688 views

Space Expansion vs. Relative Motion

Given 2 objects moving at some velocity $v$ relative to one another, is it possible to determine whether they are moving or whether the space between them is expanding?
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What is meant when it is said that the universe is homogeneous and isotropic?

It is sometimes said that the universe is homogeneous and isotropic. What is meant by each of these descriptions? Are they mutually exclusive, or does one require the other? And what implications rise ...
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5answers
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What methods can astronomers use to find a black hole?

How can astronomers say, we know there are black holes at the centre of each galaxy? What methods of indirect detection are there to know where and how big a black hole is?
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229 views

Bending of light - photon's inertia instead of mass

Using classical mechanics, the formula for gravitational attraction is $$F = G\frac{m_1m_2}{r^2}.$$ This formula does not work for photons, and we need to use Einstein's theory of gravity to ...
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401 views

What is the general relativity explanation for why objects at the center of the Earth are weightless?

The idea that as you move through the earth you get a symmetric cancelling of gravitational acceleration which approaches zero acceleration due to gravity at the center of the earth makes a lot of ...
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781 views

How general relativity gets to an inverse-square law

I understand that a general interpretation of the $1/r^2$ interactions is that virtual particles are exchanged, and to conserve their flux through spheres of different radii, one must assume the ...
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382 views

Gravitational waves and time

Two questions. It is said that time can only go slower in gravity fields and if you move faster. I have heard that when a gravitational wave pass earth then the space/time vibrate and time change ...
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1answer
232 views

Regarding the possibility of Closed Timelike Curves

I've been looking a lot at Closed Timelike Curves, and how if a theory allows for these curves it doesn't respect causality. I understand that about the curves themselves (Grandfather Paradox), but ...
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1answer
647 views

Why is matter drawn into a black hole not condensed into a single point within the singularity?

When we speak of black holes and their associated singularity, why is matter drawn into a black hole not condensed into a single point within the singularity?
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3answers
764 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?
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Speed of light originating from a star with gravitational pull close to black-hole strength?

Imagine you have a star which is on the brink of turning into a black hole. Lets say it is infinitely close to become a black hole, but not there yet. Since there is no event horizon, but a great ...
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461 views

Watching something fall into a black hole from far away

I am observing (theoretically) an object falling into a black hole from a safe distance away. My understanding is that from far away it appears as if the body will asymptotically approach the event ...
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2answers
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Evidence for quantum gravity from gravitational waves

The rumor spreads that physicists will make their big gravitational wave announcement this thursday. I am far from being an experimentalist, but I want to know if there is any chance that the ...
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1answer
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Local translations in curved spacetime

A global Poincare transformation on a scalar field induces $$\delta(a, \lambda)\phi(x) = [a^{\mu}+\lambda^{\mu\nu}x_{\nu}]\partial_{\mu}\phi(x). \tag{11.46}$$ In curved spacetime we replace $a^{\mu} ...
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2answers
488 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 ...
0
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1answer
194 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
587 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
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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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2answers
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Layman's explanation and understanding of Einstein's field equations

Most of us have heard of Einstein's amazing equations which describe the universe around us, yet only some of us understand what the equations are actually saying. What are these equations ...
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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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1answer
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Euclidean derivation of the black hole temperature; conical singularities

I am studying the derivation of the black hole temperature by means of the Euclidean approach, i.e. by Wick rotating, compactifying the Euclidean time and identifying the period with the inverse ...
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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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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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2answers
713 views

Global Properties of Spacetime Manifolds

When solving the Einstein field equations, $$R_{\mu\nu}-\frac{1}{2}g_{\mu\nu}R = 8\pi GT_{\mu\nu}$$ for a particular stress-energy tensor, we obtain the metric of the spacetime manifold, ...
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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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8answers
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How precisely does a star collapse into a black hole?

I think we all heard general statements like "once big enough star burns out there is nothing to prevent the gravitational collapse ending in a black hole". But I can't remember even seeing the ...
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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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What is the exact gravitational force between two masses including relativistic effects?

I was wondering if there is a closed-form formula for the force between two masses $m_1$ and $m_2$ if relativistic effects are included. My understanding is that the classic formula $G \frac{m_1 ...
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3answers
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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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3answers
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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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5answers
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Could gravity accelerate light? [duplicate]

Gravity causes anything with energy to accelerate toward the source. Black holes, for example, have such strong gravity that they pull in light and don't let any escape. But can acceleration still ...
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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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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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2answers
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is there a way to split a black hole?

Classically, black holes can merge, becoming a single black hole with an horizon area greater than the sum of both merged components. Is it thermodynamically / statistically possible to split a black ...
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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 ...
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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 ...
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3answers
698 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
583 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 ...
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5answers
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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 ...
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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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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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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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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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1answer
346 views

Infinitesimal transformations for a relativistic particle

The action of a free relativistic particles can be given by $$S=\frac{1}{2}\int d\tau \left(e^{-1}(\tau)g_{\mu\nu}(X)X^\mu(\tau)X^\nu(\tau)-e(\tau)m^2\right).$$ If we then make an infinitesimal ...
5
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2answers
785 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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608 views

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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Is there a maximum possible acceleration?

I'm thinking equivalence principle, possibilities of unbounded space-time curvature, quantum gravity ...
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1answer
1k views

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 ...