# Tagged Questions

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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### Gibbons-Hawking Variation

I know there already exist some questions about this and some very good answers. However, I am still having trouble understanding one part of the calculation. The GHY term is given by ...
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### What is the sum of the angles of a triangle on Earth orbit?

Gauss went out and measured triangles made up of mountain peaks to show that the angles sum up to 180 degree. However, general relativity leads to non-Euclidian space and I would like to get a better ...
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### Non-time orientable quotient of de Sitter space

Examples of non-time orientable spacetimes are pretty scarce, but it seems the big one is quotients of de Sitter space of the form $dS^n/\pi_1$, where $\pi_1$ is some subgroup of the isometries of de ...
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### 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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### Two dimensional spacetime and the Gauss Bonnet theorem

Generally two dimensional spacetimes are deemed to be static, as the Gauss Bonnet theorem implies that the Einstein Hilbert action would be a constant independent of $g$. But as far as I can tell, ...
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### Which property do the word Pressure refer to in General Theory of Relativity?

In this course by MIT Alan Guth while delivering the lecture stated " Both Pressure and Energy densities can produce gravitational fields. Negative pressure creates repulsive gravity and positive ...
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### Is boundary well defined if variation of metric don't vanish on the boundary?

Suppose that you want to calculate the variation $\delta S$ of an action induced by some arbitrary variation $\delta g_{\mu \nu}$ of the spacetime metric : S = \int_{\Omega} ...
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### An argument that massive particles don't redshift?

I start with the spatially flat FRW metric in conformal co-ordinates: $$ds^2=a^2(\eta)(d\eta^2-dx^2-dy^2-dz^2)$$ This metric has the following non-zero Christoffel symbols: \begin{eqnarray} ...
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### If curved paths imply that the vehicle is accelerated, how come do we assume that light gets curved whilst its speed is constant?

I don't understand how we can accept these two sentences at the same time: Light speed is constant, therefore experiences no acceleration. On the presence of a gravitation field, light path is ...
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### What are some ways to justify the Einstein field equations?

Since they are a postulate of general relativity, it is not really possible to "derive" the Einstein field equations $$R_{ab} + \left(\Lambda - \frac{1}{2}R\right)g_{ab} = -8\pi T_{ab}$$ in any very ...
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### Can a Set of “Maxwell's Equations” for Newtonian Gravitation be Derived from Newton's Force + Special Relativity?

When I learned about electromagnetism in my first year of undergraduate school, Maxwell's equations were derived roughly in the following way (see also here or in [1]): Gauss's law for a static ...
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### Local inertial frame

In general relativity we introduce local inertial frames to be such frames where the laws of special relativity holds. Let $\xi^{\alpha}$ the coordinates in the local inertial frame, so we get ...
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### Form of Spin Four-vector

The spin angular momentum of a gyro is represented, in special and general relativity, by a spin four-vector $S^{\mu}$. In the rest frame of the gyro, the spin four-vector takes the form ...
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### Integral curves in null hypersurfaces [closed]

Let be $(M^{n+1},g)$ a spacetime (Lorentz manifold, connexe and time-oriented), $n\ge 2$, and $S\subset M$ a null hypersurface (codim $S=1$ and the restriction of $g$ to each tangent space $T_p S$ ...
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### Thought experiment on space curvature due to gravity

Let's say you built a huge, straight rigid beam out in space, far from the sun (outside the orbit of Pluto). It is very long, say 200,000 miles long, but can be very narrow. Then you move it to the ...
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### Why gravitational collapse always end up in a black-hole singularity? [closed]

I know the positive energy condition and the singularity theorems by Penrose and Hawking. But still, why people didn't work on gravitational collapse to some exotic matter with an event horizon?// My ...
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### If gravity isn't a force, then why do we learn in school that it is?

I have studied some of Einstein's Theory of General Relativity, and I understand that it states that gravity isn't a force but rather the effects of objects curving space-time. If this is true, then ...
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### Are some gravitational wavelengths forbidden by causality?

Consider a gravitational wave in linearized gravity $d_{\mu \nu}(X_{\eta}) = D_{\mu \nu} e^{i X_{\eta} K^{\eta}}$ with $K^{\eta} = (-\omega t, \textbf{k})$. Let $d=| \textbf{D}|$ the scalar maximum ...
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### Gravity's force on space

Here is a quote from Brian Greene, The Fabric of the Cosmos: Space, Time, and the Texture of Reality, p. 273: “The early universe provided an arena in which gravity exerted its repulsive side with ...
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### Is there proof gravity bends space or is it just the most convenient explanation?

I have read this sentence in an article: The theory [of general relativity] holds that gravity is geometry: particles are deflected when they pass near a massive object not because they feel a ...
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On page 2 of this paper (http://arxiv.org/abs/1106.6073), Maldacena explains (and has a very nice picture) showing the trajectories that a timelike and null particle would take in AdS space. Of ...
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### Operational Definition of Reference Frame in General Relativity

Most treatments of GR begin with the assumption that spacetime is a pseudo-Riemannian manifold (or, sometimes, that it is a more general manifold). But this entails quite a few tacit assumptions about ...
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### What are the definitions and the differences between string “background” and string “vacuum”?

In cosmology one studies perturbations around FRW metric classically (pure GR, we say that we perturbe the FWR "background"). In QFT we have perturbation theory quantistically (we expand around a ...
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### What do quantum theory and general relativity have in common? [closed]

What areas of commonality are there between quantum theory and general relativity? Is it even possible to use the the two when calculating the same physical behaviour? Is there a correlation between ...
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### Suppose I apply a force to a ball that can then only be slowed down by gravity or, perhaps, relativity. What happens to the ball? What would I see? [closed]

Suppose I'm on planet Earth. I have a ball that, once set in motion, can only be slowed down or stopped by gravity. What will happen to this ball? What would I (an observer on Earth) see? Here's what ...
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### Life of a photon in gravity?

I have a simple thought experiment and I am not sure about the answer: What would happen to a photon that is emitted by an excited hydrogen in an otherwise empty universe? Would gravity of the atom ...
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### Does rest mass increase in the FRW metric?

The flat FRW metric can be written in conformal co-ordinates: $$ds^2=a^2(\eta)(d\eta^2-dx^2-dy^2-dz^2)$$ where $\eta$ is conformal time. Let us assume that $a(\eta_0)=1$ when $\eta_0$ is the present ...
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### Tensor decomposition

I came across what a Physicist called "decomposing a tensor with respect to a congruence", something I simply cannot grasp. I searched a lot and I couldn't find any reference on that. I know that ...
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### Black Holes should take infinite time to form with the increase in mass to form one [duplicate]

How can black hole form because as the density begins to increase gravity also start to increase and time starts to slow. wouldn't it take infinite time to form a black hole. how can anything fall ...
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### Quasilocal stress tensor

I have been reading through the paper hep-th/9902121 and have a few questions about the first five lines of the introduction: 1) "In a generally covariant theory, it is unnatural to assign a local ...
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### Why the $g_{00}$ of the Robetson-Walker metric is 1? [closed]

Why it not depends on another variable?
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### Can space have angular momentum that can be transfered to/from physical objects?

This is related to another question that discusses whether space can have momentum and energy. Apparently gravitational waves or ripples in spacetime is how space stores and transfers energy/momentum. ...
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### Variation of det metric tensor

I have the metric tensor $g_{\mu\nu}$. I want to make the variation of $\sqrt{-g}$ where $g=detg_{\mu\nu}$. Can I make this work? ...
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### Traveling to the future is possible, but not to the past? [duplicate]

I understand how going to the future is possible: If you go really fast, time around you slows down for observers. But is it true that time traveling into the past isn't even theoretically possible?
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### Why not all timelike world lines have infinite total length?

I don't understand this stament by Geroch(1968), when discussing the definition of singularity: We could not have required that all timelike world lines have infinite total length, for this ...
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### How can the speed and the mechanics of light be similar to the speed and the mechanics of gravity? [duplicate]

How can the speed and the mechanics of light be similar to the speed and the mechanics of gravity? Most say that light cannot escape a black hole. Then gravity cannot escape a black hole either, so ...
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### How is electromagnetic binding energy introduced in the stress-energy tensor

Take the hydrogen atom. It is easy to imagine that the gravitational pull it creates is smaller than the sum of those of the proton plus the electron, because a photon of 13.6 eV was created when the ...
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### Why can't we fix the metric and its derivatives at boundary, with the variational method?

In general relativity and for its Einstein-Hilbert action, we usually ask that the metric variations $\delta g_{\mu \nu}$ cancel on the boundary $\partial \, \Omega$ of some region $\Omega$ of the ...
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### Definition of Energy in Friedmann equations?

The first Friedmann equation for a flat Universe is given by: $$\bigg(\frac{\dot{a}(t)}{a(t)}\bigg)^2 = \frac{8 \pi G}{3} \rho(t)$$ The energy density $\rho(t)$ is given by: \rho(t) \propto ...
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### 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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### If Alice is moving at relatavistic speeds compared to Bob, is collapse still simultaneous?

I have read some papers about experimental proof of non-locality involving a laser that goes through a beam-splitter and then each "half" goes to an observer (traditionally "Alice" and "Bob"). It has ...
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### Distortion of body in Schwarzschild black hole

Suppose I toss a cloud of matter into a Schwarzschild black hole; for the sake of argument, have it be timelike dust. As we know, the dust is "spaghettified" by tidal forces: simultaneously compressed ...
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### Conservation of energy and Killing-field

In general relativity we have no general conservation of energy and momentum. But if there exists a Killing-field we can show that this leads to a symmetry in spacetime and so to a conserved quantity. ...