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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Behavior of black holes in higher- and lower-dimensional space-times

The behavior of black holes in 3+1 dimensional space-time as our own is rather well known: formation, event-horizon size, mass, spin, radiation etc. However, my question is what would black holes ...
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Question on inflation

I have two particular questions regarding the inflationary scenario. They are: 1.) What is the physical origin of the inflaton field? 2.) Why has the potential of the inflation field its particular ...
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What do you feel when crossing the event horizon?

I have heard the claim over and over that you won't feel anything when crossing the event horizon as the curvature is not very large. But the fundamental fact remains that information cannot pass ...
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198 views

How does nature prevent transient toroidal event horizons?

How does nature prevent transient toroidal event horizons?.. and does it really need to? Steps to construct a (transient) toroidal event horizon in a asymptotically flat Minkowski spacetime: take a ...
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What role does electrical charge play in black holes?

Not having studied General Relativity, I have sometimes been puzzled by references to the behaviour for "classic" black holes — as they are popularly portrayed — as being true for black ...
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684 views

White Holes and Time-Reversed Oppenheimer-Snyder collapse

So, the canned explanation that I always hear about why the white hole solution of the extended Schwarzschild solution is non-physical is that "The matter distribution cuts off the white hole ...
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Would quantum fluctuations cause problems for scalar-field inflation?

Wheeler once said that spacetime would be highly curved at very small scales because of the uncertainty principle for energy-momentum. In which case the spacetime becomes very bumpy and not smooth ...
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I think I am misunderstanding Einstein's equivalence principle and his elevator

I'm having difficulties understanding why a gravitational acceleration can be guaranteed to be locally equivalent to an accelerating frame. Doesn't it matter on how the force is being applied? If the ...
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254 views

Is there an algorithm for N body simulations in General Relativity [duplicate]

I am new to general relativity but have a background in computer science. Why is it so hard to do n-body simulations in GR? For example, there could be a program which takes the properties (mass, ...
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90 views

Do two bodies spinning about the same axis in the opposite direction repel each other?

I recently read about the GEM equations, which look very much like the Maxwell's equations. Does this mean the behavior of mass is like the the behavior of the electric charge? So for example if you ...
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298 views

Dirac operator in curved spacetime in 2 dimensions – hermitian?

I'm currently trying to learn about the Dirac equation in curved spacetime and have come across an odd remark in Nakahara's well-known textbook "Geometry, Topology and Physics" that I would like to ...
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236 views

Curved space-time VS change of coordinates in Minkowski space

I'm looking for a rather intuitive explanation (or some references) of the difference between the metric of a curved space-time and the metric of non-inertial frames. Consider an inertial reference ...
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119 views

A true singularity at $t=0$, coordinate independent Big Bang

Consider a flat Robertson-Walker metric. When we say that there is a singularity at $t=0$, clearly it is a coordinate dependent statement. So it is a "candidate" singularity. In principle there is ...
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594 views

Movie Interstellar - Followup Question to Escape Velocity

Continuing the discussion on this thread: Movie Interstellar - Question about Escape Velocity The movie Interstellar shows people on a water planet where time is dilated so much that 1 hour is equal ...
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464 views

How to explain centripetal force in terms or relativity

At the end of a video of dropping a ball and feathers in a vacuum, Brian Cox explains that the Ball and Feathers, as understood in terms of General Relativity, aren't falling. (apologies I can only ...
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168 views

Modifying Newtonian gravity to fit observed precession of Mercury's orbit

The idea is to modify Newtonian gravity so that it fits measurements of orbits around the sun. For example the precession of Mercury's orbit unlike Newtonian $n$-body simulations. I'm currently not ...
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295 views

Photon “stuck” on the event horizon of a black hole

According to what I've read on special relativity, $c$ is the speed limit for every object in the universe, and according to Einstein, an object's speed through the three spatial dimensions plus its ...
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341 views

Massless fields in curved spacetimes

I read the following statement in one of Penrose's paper zero rest-mass field equations can, with suitable interpretations, be regarded as being conformally invariant. I take this to imply that ...
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816 views

Geodesic equations

I am having trouble understanding how the following statement (taken from some old notes) is true: For a 2 dimensional space such that $$ds^2=\frac{1}{u^2}(-du^2+dv^2)$$ the timelike geodesics ...
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568 views

Hawking Radiation: how does a particle ever cross the event horizon?

The heuristic argument for Hawking Radiation is, that a virtual pair-production happens just at the event horizon. One particle goes into the black hole, while the other can be observed as radiation. ...
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Does electric charge affect space time fabric?

I am confused with this question. Does electric charge affect the space time fabric? If so, why? Also if electric charge does not affect the space time fabric, how can we interpret the origin of the ...
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Formulation of general relativity

EDIT: I think I can pinpoint my confusion a bit better. Here comes my updated question (I'm not sure what the standard way of doing things is - please let me know if I should delete the old version). ...
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How to connect Einstein's Special Relativity (SR) with General Relativity (GR)?

How Einstein's SR becomes GR? $$ds^2=dr^2-c^2dt^2,$$ $$ds^2=g_{\mu\nu}dx^{\mu}dx^{\nu}.$$ When the $s$ is constant $ds^2=0$, isn't it true? How to connect Einstein's SR with GR? What is the ...
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How do gravitational waves sustain and propagate large scale spacetime curvature?

I understand that gravity in GR is a manifestation spacetime curvature dictated by the field equations by the principle that objects follow the geodesic path in spacetime. And, I get how ...
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How do you explain the observed fact that “black hole” objects move?

As per Newton objects with mass attract each other, and per Einstein this is further explained by saying that mass warps space-time. So a massive object makes a "dent" into space-time, a gravity well. ...
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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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Can a GPS system detect the decline in the rotational velocity of the Earth?

From Wikipedia: Rotation in Angular Velocity of Earth Earth's rotation is slowing slightly with time; thus, a day was shorter in the past. This is due to the tidal effects the Moon has on Earth's ...
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112 views

Is the stress energy tensor continuous at the interface between an object and vacuum?

The stress energy tensor has (as I understand) zero value in the region where there is no matter and non-zero value where there is matter. Suppose there is one matter object in space, now how does the ...
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242 views

What would a closed timelike curve look like?

What exactly are closed timelike curves. In a metric in which they would exist, what would they look like. What would it be like travelling through them? It obviously wouldn't look like a door. Would ...
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137 views

How can I use Einstein's field equations to find the metric tensor? [duplicate]

I have watched and read a lot on the topic of General Relativity and the geometry behind it. I am confident that I can derive an approximation of the the stress-energy-momentum tensor with just the ...
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286 views

Is the accelerated expansion of the universe consistent with conservation of energy? [duplicate]

If energy can neither be created nor destroyed, how come the universe is expanding at an accelerating rate? Where does this energy come from?
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106 views

Does the escape velocity of a black hole exceed $c$ *before* a singularity is created?

As an offshoot of the question Can we have a black hole without a singularity? I'm curious if the point of no return at which the massive object is condemned to become a singularity happens before its ...
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Derivation of f(R) field equations, problem with integration by parts

I am following the derivation of the field equations on the the Wikipedia page for $f(R)$ gravity. But I do not understand the following step: $$ \delta S = \int \frac{1}{2\kappa} \sqrt{-g} ...
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What does it mean by complex frequencies? (Quasinormal Modes)

Something I've taken for granted and not yet thought about physically, is how the frequency of quasinormal modes related to a black hole are $\textit{complex}$. I know that it's something to do with ...
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proper distance and proper length

I am wondering if I mix up the notion of proper distance and proper length. I have two cuves in Schwarzschild space-time describing the flight of two photons (think of it as photons guided in by ...
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290 views

How come that an Infinite universe will collapse under gravity?

In this PSE post the issue is about the stability of an infinite universe under Newtonian gravity. Here I'will drop the Newtonian constraint because we know of the finite speed of interactions and I ...
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303 views

Does the concept of a wormhole violate the law of mass-energy conservation?

If my understanding of wormholes is correct, anything that moves into a wormhole can be transported from one region of space-time to another. Consider a situation where an object of mass $m$ in space ...
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283 views

Do physicists believe the singularity theorems to be accurate?

This question is largely based on the last post by reddit user RobotRollCall who gave some fantastic explanations of phenomena in relativity on a layman's level. About a year ago, she said: The ...
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How to calculate Riemann and Ricci tensors for a sphere? [closed]

Let's have the metric for a sphere: $$ dl^{2} = R^{2}\left(d\psi ^{2} + sin^{2}(\psi )(d \theta ^{2} + sin^{2}(\theta ) d \varphi^{2})\right). $$ I tried to calculate Riemann or Ricci tensor's ...
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1answer
317 views

LIGO Gravitational Waves [closed]

Has LIGO detected any gravity waves yet, or any hints of them? Is it just that LIGO is not sensitive enough or are we now entering disconfirmation territory? If we never detect gravity waves with any ...
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2k views

What is the equation of the gravitational potential in general relativity?

How is the gravitational potential replaced by the metric tensor in general relativity? $$U_G=\frac {GMm}{r}$$ What is its equation?
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407 views

What's the relationship between quantum entanglement and the relativity of time?

Apologies in advance for what may be a stupid question from a layman. In reading recently about quantum entanglement, I understood there to be a direct link between entangled particles, even at ...
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848 views

Blandford-Znajek process: Why/how does the current flow along the magnetic field lines

Related: How would a black hole power plant work? I have put a bit of commentary enumerating my confusions in parentheses I read in Black Holes and Time Warps (Kip Thorne), that quasars can generate ...
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3answers
254 views

Is there a single metric for a given system?

Let imagine a tunnel that connect two distant places at the globe (eastern-western or north-south) There are a lot of posible "distances" or metrics, defined by maps, routes, "as the crow flies", ...
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161 views

Does the positive mass conjecture indicate a necessity of interactions in our universe?

The positive mass conjecture was proved by Schoen and Yau and later reproved by Witten. Total mass in a gravitating system must be positive except in the case of flat Minkowski space, where energy is ...
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161 views

Particle energy in general relativity?

Assume that a particle is moving with four-velocity $u^\mu$ through a spacetime with metric $g_{\mu\nu}$ ($-+++$ signature). Let us also assume that there exists a time-like vector field ...
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170 views

Path of light as it travels between two black holes

What would happen to light passing through a narrow space between the event horizons of two equal-mass black holes? Would it deviate or follow a straight path?
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678 views

How to derive the Schwarzschild radius? [duplicate]

I know that the Schwarzschild radius is given by $$r=\frac{2GM}{c^{2}}.$$ but I never seen a derivation for this equation. 1- Does anyone know how to derive this equation from general relativity? ...
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What is a “local” lorentz transformation of vielbein? How does it transform?

I'm struggling with Anthony Zee's chapter on differential forms in Einstein Gravity in a Nutshell, page 600. He asks us to prove that $$\omega= \Lambda \omega' \Lambda^{-1} - (d\Lambda) \Lambda^{-1}$$ ...
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Curvature of Weyl-rescaled metric from curvature of original metric

I'm trying to go from the low-energy effective action in the string-frame to the corresponding action in the Einstein frame. The action in the string frame has the form $$S = \frac{1}{(2\pi)^7 ...