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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Infinite distance in finite time

It is shown in a previous thread (AdS Space Boundary and Geodesics) that it's possible for null rays to travel to infinity and back in AdS space in finite coordinate time. That is to say, an observer ...
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16 views

Anti de Sitter Motion without matter

I've read that a non zero cosmological constant can lead to "motion without matter" in vacuum spacetimes such as AdS. Initially I didn't understand what the significance of this statement was since I ...
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92 views

Accelerated reference frame in Minkowski space vs pure gravitational field

I just finished reading Einstein's "Relativity: The special and the General Theory", and if I understand Einstein correctly, he says that an accelerated reference frame in Minkowski space (i.e., empty ...
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217 views

Derivation of one-form/vector equation in Carroll confusion

I don't understand the derivation of Equation 2.14$$\mathrm{d}f\left(\frac{d}{d\lambda}\right)=\frac{df}{d\lambda} \tag{2.14}$$ in Carroll's Lecture Notes on General Relativity ...
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459 views

Killing Vectors in Schwarzschild Metric

Given the Schwarzschild metric with $(-,+,+,+)$ signature, $$ds^2=-\left(1-\frac{2M}{r}\right)dt^2+\left(1-\frac{2M}{r}\right)^{-1}+r^2(d\theta^2+\sin^2\theta\,d\phi^2)$$ the lack of dependence of ...
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261 views

Typo or not in those GR notes?

Given $$ds^2=-A(r)dt^2+B(r)dr^2+2C(r)drdt+D(r)r^2(d\theta^2+\sin^2d\phi^2),\tag{23.1}$$ we want to eliminate that cross term $2C(r)drdt$ Upon change of variable such that. This can happen upon ...
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56 views

Covariant Derivative commutator on a Spinor [closed]

I am trying to prove 8.14 of Supergravity - Freedman. The equation that I am trying to show is $$\gamma^\mu \nabla_\mu \gamma^\nu \nabla_\nu \psi = (g^{\mu\nu}\nabla_\mu \nabla_\nu - ...
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1answer
69 views

Does a rigid box of gas cool over cosmological timescales?

According to standard cosmology theory the physical momentum $p$ of both massive and massless particles decay like: $$p \propto \frac{1}{a(t)}$$ where $a(t)$ is the scale factor as function of ...
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86 views

Why are Electromagnetism, Strong & Weak Nuclear and Gravitational Forces different?

If they are different then why the only thing that we 'see' in them, and that identifies them, the so called 'force' as we call and see it, is same among them all.
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1answer
46 views

Accelerating Frame and Gravity

I have recently learned briefly that an accelerating frame is equivalent to a gravitational field in the equivalence principle. I'm sitting on a chair and I am experiencing the force of gravity and ...
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1answer
83 views

Killing vectors in General Relativity?

I'm looking to derive the surface area of the event horizon of a Schwarzschild black hole. I was just wondering if it were possible for someone to explain to me this: $$ ...
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100 views

Observer inside event horizon of an extremely large black hole [duplicate]

Imagine a very large black hole, with a mass equal to a large number of galaxies. Assume a space station is in orbit around the black hole some distance from the event horizon at a point A. An ...
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46 views

Gravitational Time Dilation and Schwarzschild Coordinates

So I'm trying to use this equation for the time dilation of an object, but I don't know how to get the distance that I have (in meters) to a radial coordinate in terms of schwarzschild coordinates. ...
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21 views

How are mass and density treated in general relativity? [duplicate]

Background: I am confused by how mass relates to the equations in general relativity. For example, given a certain mass density distribution, I am unsure how to express a system in terms of GR. ...
2
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1answer
306 views

Does the Michelson-Morley experiment disprove gravitational waves?

I may be misunderstanding gravitational waves, but doesn't the idea of a gravitational wave imply that spacetime is a field or "medium" through which waves propagate at speed $c$? Was not this idea ...
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117 views

Are mass and angular momentum related at a quantum level?

Is the mass of an atom related to the amount of angular momentum it contains? It makes sense to me that since the waveform of an electron is much much larger than a particle in the nucleus that its ...
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67 views

What is $\mathcal{L}_M$?

Usually we derive the Einstein field equation in vacuum starting from E-H action $$S= \int{\sqrt{-g}d^4x(\frac{c^4}{16\pi G})R}.$$ But in case we wanted to get ...
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82 views

Is each succeeding dimension time? [closed]

I have been researching but I have found nothing on this topic (at least after basic google searching and some deeper searching on this site), I'm not sure if this is a common sense thing or it is ...
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123 views

Why does the Palatini formalism of GR work? [duplicate]

We can get the Einstein field equations of GR from the Einstein-Hilbert action via two distinct methods: First, by taking the metric as the only degree of freedom, and imposing right away that the ...
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83 views

Maintaining symmetry? [closed]

Minkowski metric is found to be $$ds^2=-dt^2+dr^2+r^2d\Omega^2$$ where $d\Omega^2$ is the metric on a unit two-sphere. Why should we keep track of the $d\Omega^2$ so that spherical symmetry holds ...
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630 views

Why do people put exponentials there

In his book, Sean Carroll, says p. 194 chapter 5: To impose spherical symmetry, we begin b writing the metric of Minkowski space in polar coordinates $x^{\mu}=(t,r, \theta, \phi)$: $$ ...
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415 views

Can we actually have null curves in Minkowski space?

I know that this sounds really stupid but, when I think of the Minkowski space I cannot imagine a null curve, only null lines. For me, the only possible way to have one is to change the basis of the ...
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149 views

Would the speed of an object keep increasing if it keeps falling infinitely? Please check details [closed]

Assuming "A" and "B" to be two wormholes (Einstein-Rosen Bridge) inside the Earth's atmosphere, and Warmhole B be the opening to Warmhole A, would the speed of an object keep increasing if it enters ...
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419 views

Does a clock oscillating in a friction-free hole through the center of a planet run slower than a stationary clock on the surface?

Assume a clock is dropped into a friction-free hole through the center of a symmetric, non-rotating planet, far from any other massive object. Clearly, the clock oscillates from one end of the hole to ...
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73 views

General theorems on tachyon propagation?

I was reading the quite nice answer of QMechanic on the topic of compact support tachyon fields not propagating faster than light, but this case is a rather simple one, free scalar field in flat ...
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1answer
194 views

Deriving the Poisson bracket relation of the Ashtekar variables

I'm trying to figure out how to calculate the orthogonality of Ashtekar variables with respect to the ADM hypersurface metric and conjugate momentum. $$\{{A_a}^i(x), {E^b}_j(y)\} = 8 \pi \beta ...
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1answer
228 views

Do free falling observers see gravitational blueshift?

Observers at rest in gravitational fields will see infalling light signals as blueshifted. Do inertial observers in free fall in a gravitational field see the same shift? If someone is standing on a ...
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79 views

Topology of Anti-de Sitter manifold with black hole

I'm interested in understanding the topology of space-time with a black hole. In other words how does having a black hole affect quantities such as the fundamental group, de-Rham cohomologies, Euler ...
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1answer
54 views

Do observers at rest at different positions in a gravitational field see the Universe expand at different rates

If we consider observers at rest outside a Schwarzschild black hole, the amount of proper time elapsed in terms of coordinate time is given by $\Delta\tau=\sqrt\frac{r-1}{r}\Delta t$ (where r is ...
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50 views

If the distance between two objects is increasing with increasing rate, can we determine which object is under influence of force?

Suppose two bodies, A and B, are together in free space. One of them, let’s say- A, accelerates away, then retards, stops, accelerates back and stops again when it reaches B. Although we can see the ...
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67 views

Bounded $L^2$ curvature conjecture [closed]

It seems a group of three have recently proven the aforementioned theorem. I was curious so I decided to look it up but the search wasn't very helpful. All that I could gather was that apparently the ...
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1answer
23 views

Lifting an analogy of a pond to question signals at natural or artificial boundaries in space-time [closed]

I conjured up an idea to lift an analogy into the language of QFT and GR. I thought up the universe as a pond with a liquid. If we imagine a liquid poured into some pond (sort of bang and inflation ...
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90 views

Coordinate velocity and free-falling past an event horizon

Ws can re-arrange the standard Schwarzschild metric as $$\left(\frac{d\tau}{dt}\right)^2=\frac{r-1}{r}\left[1-\left(\frac{r}{r-1}\frac{dr}{dt}\right)^2\right]$$ Where $\frac{r-1}{r}$ is the local ...
3
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1answer
58 views

Relativistic effects of an orbit around sun in a different direction than Earth

If I manage to orbit around the sun at the same speed but in a different direction than the earth, will I perceive the time on earth going faster or slower than my own time? And what about people on ...
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77 views

Why don´t we just do a Legendre transform for a GR hamiltonian?

In general, if one has a well defined lagrangian for a field theory, which depends on a field, say $A_{\mu}$ and on its first spatial and temporal derivatives, we can simply define the canonical ...
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84 views

If photons do not have mass, why does light get attracted such that it cannot escape a black hole? [duplicate]

Does gravitational force of black hole attract the light? Or is it something else?
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1answer
78 views

Is it possible to understand physics and make new discoveries using computer simulation? [closed]

I'm a computer science major and I want to learn Physics. I can create computer simulations of any type. I'm not good at math that is required to learn QFT or GR,but I'm thinking is it possible to ...
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2answers
132 views

The Michelson-Morley experiment

A fundamental assumption in special relativity is that the speed of light is constant in all inertial reference frames, which was first established empirically via the Michelson-Morley experiment. ...
2
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73 views

Isn't is far more likely that general relativity, and not QFT, is “wrong?” [duplicate]

At the risk/certainty of both sounding super ignorant and talking out of my arse, I have always wondered why there is some big mystery about why there are contradictions between the predictions ...
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77 views

3D-representation of space-time

When I read something about GR, I nearly always see some pictures that look like trampolines, like this one. I know that the curvature of space-time is described by the Riemann-Tensor $R$. I was ...
6
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1answer
182 views

Why must inertial mass and gravitational mass be equal, not just proportional?

I'm certain I'm just under a grave misapprehension. I really just don't understand how one can conclude that inertial mass is equal to gravitational mass. It seems to me that we've simply scaled our ...
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66 views

Transformation of Christoffel symbols [closed]

Friends I have little problem with transformations:) In General relativity is Christoffel symbol of second kind defined as: $$ \Gamma^{l}_{ij}=g^{lk}\left(\frac{\partial g_{ki}}{\partial ...
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17 views

Higher dimensional trapped surface and its condition?

In higher D-dimensional spacetime, a marginally trapped surface is a closed spacelike (D-2)-surface whose outer null normals have zero convergence. It is very like a marginally trapped surface in the ...
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1answer
163 views

How to measure Torsion and Non-metricity?

In General Relativity, we most often work with the Levi-Civita connection (metric and torsion-free). What kind of experiment can we make to be sure that our physical space-time indeed is torsion-free ...
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104 views

Is a local inertial frame of reference a Lorentz frame?

I started reading "Gravitation" (the big black book with the apple) and in the first chapter it is said that a local inertial frame of reference rocks. A little later it is said that Lorentz frames ...
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253 views

What is a Christoffel symbol?

What is a Christoffel symbol? I often see that Christoffel symbols describe gravitational field and at other times that they describe gravitational accelerations. Then, on some blogs and forums, ...
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123 views

Falling with same acceleration and meaning of gravity

My question is what does falling with same acceleration has to do with what Einstein concluded concerning the gravity in terms of the curvature?
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42 views

Hilbert Stress Energy Tensor for fermions + EM field and Yang-Mills theory (fermions + gluons)

@Qmechanic or anyone else who knows the reference. I am trying to find a references to the work(s) where thorough derivation of Hilbert Stress Energy Tensor for fermions + EM fields and Yang-Mills ...
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38 views

Variable $r$ in Dirac equation

Solutions of Dirac equation for an electron in orbit of an atom are usually expressed in terms of spherical coordinates $r,\theta$ and $\phi$. For a point ($r,\theta,\phi$) the variable $r$ represents ...
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760 views

How can we recover the Newtonian gravitational potential from the metric of general relativity?

The Newtonian description of gravity can be formulated in terms of a potential function $\phi$ whose partial derivatives give the acceleration: ...