Cosmology Lecture 2

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Recommends Yukterez · 2016-02 · Physics Stack Exchange · on “Universe expansion and general relativity”

Because relativistic mass only arises because of motion through space, not motion with space. For more details google "peculiar velocity" and "recessional velocity". Susskind explains this here [this video] .

Recommends Stijn D'hondt · 2017-06 · Physics Stack Exchange · on “Newtonian interpretation of the Friedman-equation”

I'm a first year physics student so I cannot yet understand general relativity, yet the Friedman-Lemaître-Robertson-Walker (What's in a name?) equations are used in my introductory course in astronomy, and I'm trying to understand them as best as I can. I have watched some of Leonard Susskinds video's on Cosmology which are available on Youtube ( [this video] ) where he derives the FLRW equation. He does so in a Newtonian way - which is the same way how it is done in my course book. The equation I'm talking about is: $$ \dfrac{\dot{a}^2}{a^2}=\dfrac{8\pi G}{3}\rho-\dfrac{kc^2}{a^2},$$ and since this is in conventional notation, I suppose whoever reads this is familiar with the variables. My quest

Recommends Yukterez · 2020-02 · Physics Stack Exchange · on “Validity of Newtonian gravity inside the Hubble radius”

For the "radious" you would deserve a fat downvote, but nevertheless: in cosmology we assume that everything is homogenous, isotropic and the galaxies to be flowing with the hubble flow, so locally at rest. If you want to calculate the trajectories for objects with high peculiar velocities (relative to the CMB) then you have to use relativity, but otherwise you can derive the evolution of the universe with Newton as well, see [this video]

Recommends FleetFoot · 2022-01 · Physics Stack Exchange · on “Ambiguity in applying Newton's shell theorem in an infinite homogeneous universe”

The spaceship doesn't accelerate in either direction but the gravitational effect between points can be thought of as slowing down the expansion of the universe. There is a lecture here by Susskind using precisely this approach to derive the Friedmann Equations: [this video]

Cites Yukterez · 2017-01 · Physics Stack Exchange · on “If the universe is very nearly flat how can space be curved?”

As the WMAP and other satellite data have shown that universe is very nearly flat. But the theories like general theory of relativity assume curved space to describe gravity. That is not correct. GR describes gravity as curved spaceTIME. The curvature of space itself is a completely different story [this video] ! Does it mean that space is curved around massive bodies and the whole universe is flat. It means that the whole universe is measured to be practically flat, so you can go in any direction and will never end up where you started like you would on the 2d analogy, the surface of a 3 dimensional sphere. Around massive bodies you have curved spaceTIME which manifests itself as acceleration (w

Cites Yukterez · 2017-07 · Physics Stack Exchange · on “What Is The Reference Frame For The Velocity Of An Object In The Universe?”

In an expanding universe you have the peculiar velocity [LINK] which is measured relative to the cosmic microwave background (in the frame of a comoving observer [LINK] the CMB has the same wavelength in all directions, while an object with peculiar velocity sees a dipole in the CMB [LINK] ). If you measure an object's velocity relative to a distant observer you also have to add the recessional velocity [LINK] that can sure enough exceed the speed of light [this video] , which is of course allowed by general relativity [LINK] . So the total velocity between 2 objects is their peculiar velocities added like in special relativity [LINK] and the recessional velocity between both added classicaly. Ex

Cites Yukterez · 2020-07 · Physics Stack Exchange · on “Does light travel faster when it is in moving spacetime?”

The speed of light relative to a local observer is always c, but relative to a far away observer it can indeed receed faster than c; for example, a photon receding at the hubble radius has a speed of 2c relative to the observer in the center of the frame, and a photon travelling in your direction at that distance has a speed of 0c relative to you (the proper distance relative to you stays fixed), but still 1c relative to a local observer who is also located at the hubble radius, see Susskind, Cosmology 2 [this video] at timestamp 1:30:30. The same goes for the ergosphere or the horizon of a black hole, relative to a local observer it still has exactly 1c.

Cites Yukterez · 2022-08 · Physics Stack Exchange · on “If the escape velocity for a body that is very close to a BH is near $c$ but not $c$ can it move away a little bit before it falls inside the BH?”

Krešimir Bradvica asked: "But what about a spot close to the BH but far enough for the escape velocity not to be c? Would a body,at least theoretically,pushed away from the BH at that spot travel a piece of space before it eventually encounter the BH core after passing through the event horizon?" Since the gravitational time dilation is finite above the horizon, the shapirodelayed velocity (in the frame of the far away observer) of the escaping object which moves radially outwards relative to a local stationary observer might be small, but not zero, so yes, it will move away from the black hole also in the frame of the far away observer aka the Schwarzschild coordinate bookkeeper, but slower

Cites Yukterez · 2023-04 · Physics Stack Exchange · on “Can the speed of light be measured only in a local inertial frame of reference?”

Spigel asked: "Is there a possibility for that observer to measure the speed of light in some other frame of reference, where there is also a different gravity and flow of time? If there is, does the difference appear in the measurement of the speed of light?" Locally light always has c, but far away it can have less, see the shapirodelayed [LINK] velocity in the vicinity of a mass where light can even stay stationary at the horizon of a black hole, or more, see the recessional [this video] velocity to which it is added in an expanding universe. The laws of special relativity only hold in the immediate spatial and temporal neighbourhood.

Cites Yukterez · 2023-12 · Physics Stack Exchange · on “Spacetime that allows matter to rotate faster-than-light”

You already have to corotate with more than the speed of light if you are inside the ergosphere [LINK] of a rotating black hole, so that is not a boundary in relativity. The only thing you can't do is fly past someone else with more than the speed of light, so relative to all the objects you meet inside the ergosphere you will still have less than the speed of light since they are also forced to corotate, but relative to the far away stars more [this video] .