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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Simple Question About Repulsive Potential Field Time Dilation

A space-time with a point mass gravitational potential given by $\Phi(r)$ has a metric described by, $$ds^2=-\left(1+\cfrac{2 \cdot \Phi(r)}{c^2} \right) \cdot c^2 \cdot dt^2+\left(1-\cfrac{2 \cdot ...
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1answer
61 views

Does Alcubierre drive allow time travel? [closed]

In Alcubierre drive, one can travel apparently faster than the speed of light by "compressing" space in front in the direction of travel. So let's say we have a stationary observer at point A, and an ...
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2answers
86 views

Difference between gravity and standing on a platform accelerating upwards at 9.81 m/s^2

So, according to Einstein's theory of general relativity, gravity is not a force instead it is a consequence of objects with mass deforming spacetime, right? And so, according to him, there is no ...
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2answers
57 views

Wald's General Relativity, section 6.3 Page 144

I cannot understand how he reaches the conclusion in equation 6.3.36 and 6.3.37; even the terminology is somewhat confusing. This is a problem of bending of light under gravitational field. This is ...
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2answers
59 views

Power of blueshifted light falling on observer in circular orbit around Schwarzschild black hole

This answer explains that the time dilation for an observer in a circular orbit around a Schwarzschild black hole, relative to a distant observer at rest relative to the black hole, is given by the ...
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1answer
83 views

The dimension of the energy-momentum tensor and the Einstein-Hilbert action

I have been thinking recently what will happen if one uses the energy momentum tensor of the Dirac field as a source in the Einstein Field equations. It is well known that in this case $$ ...
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4answers
285 views

Why didn't LIGO wait for a second observation of a gravitational wave? Are not reproducible results fundamental to science? [closed]

Wikipedia states, "Reproducibility is one of the main principles of the scientific method." So why did LIGO ignore a main principle of the scientific method? My whole life I have been taught that ...
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0answers
31 views

Einstein-Infeld-Hoffman-Lagrangian for a Test-Particle as Limit of Schwarzschild-Geodesic

Consider a test particle of mass $m$ which is in orbit around a spherical-symmetric body with mass $M$. It therefore has a position as described by the coordinates $r,\phi$, and its motion can be ...
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2answers
79 views

Are gravitational force and gravitational time dilation proportional?

Particles in gravitational fields are subject to gravitational time dilation. The closer a particle is near a gravitational source, the slower is running its clock. I would like to know more about the ...
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2answers
53 views

Bending of Light in General Relativity using Perturbation

It is standard textbook calculation (e.g. Schutz's First Course in General Relativity page 294) that we can find a total angular change in light deflection due to gravity to be ...
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1answer
232 views

What happened to the black hole firewall theory?

What happened to the black hole firewall theory? Back in 2012, some physicists apparently came up with strong evidence that one of three things must be wrong for black holes to work the way we thought ...
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1answer
44 views

Coordinate form of divergence of anti-symmetric tensor field [closed]

just a quick question on something that might save me a little bit of time and effort. In a general curved metric, the divergence of a vector field, $A^\mu$, can be written as: $ \nabla_\mu A^\mu = ...
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1answer
50 views

Classical Limit of Schwarzschild Metric

The orbit of a test particle orbiting a black hole can be described by the Lagrangian $$\mathcal{L} = -\frac{1}{2}\left(-\left(1-\frac{2 G m}{c^2 r}\right) \dot{t}^2 + \left(1-\frac{2 G m}{c^2 ...
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2answers
88 views

Gravity and spacetime bending [duplicate]

Something that puzzles me if gravity is just bending of space time near a mass then what is gravitational force? If say two massive bodies were perfectly at rest relative to each other they would ...
1
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0answers
25 views

Why don't big bang photons conserve mass and energy? [duplicate]

A photon from the big bang has lost most of its momentum and energy. What does it push against? Does it break the 'laws' of conservation of energy and momentum? Is there any possibility that momentum ...
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34 views

What is a zero temperature horizon?

While reading the paper "Disorder horizons: Holography of randomly disordered fixed points" by Hartnoll and Santos, I came across this: We are interested in solutions with a zero temperature ...
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1answer
163 views

What is the problem with quantizing GR in the Effective Field Theory approach?

In the modern view due to Wilson, the cut-off $\Lambda$ is an intrinsic property of a theory and renormalization just means that the theory is invariant under scale transformations below $\Lambda$. ...
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1answer
51 views

Could particle wave duality be caused by gravity? [closed]

We know that light (and other particles) displays particle wave duality, or the ability to be a particle and a wave at the same time. After that it becomes confusing. We also know that gravity is a ...
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2answers
92 views

How is this conflict about age of the universe resolved?

In a previous Phys.SE question, Does a spaceship travelling at near lightspeed see the universe aging slow or fast?, the answer (which was followed by a proof involving co-moving reference frames) was ...
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2answers
179 views

Implementing Category Theory in General Relativity

I was thinking if it may be possible to implement category theory in general relativity. I don't mean writing simply in terms of categories, but actual fundamental ideas (i.e. physics of the theory ...
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0answers
35 views

Radiative equilibrium in orbit of a black hole

According to Life under a black sun, Miller's planet from Interstellar, with a time dilation factor of 60,000, should be heated to around 890C by blue-shifted cosmic background radiation. How they ...
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0answers
33 views

Is there a direct relation between gravitation and gravitational time dilation? [duplicate]

The following calculation seems to show that gravitational time dilation is not only due to gravitation, but that there is a close relation between both of them: Gravitational time dilation seems to ...
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1answer
37 views

Do we exist in warped space and time?

Does the Suns altering of space and time (as evidenced at an eclipse) extend to the Earth such that we exist in warped space and time or are we outside those effects.
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1answer
67 views

Deriving a Schwarzschild radius using relativistic mass

Introduction I have shown below two different approaches to deriving the Schwarzschild radius. I know these are less rigorous than the derivation of the Schwarzschild solution however the ...
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4answers
6k views

Are black holes very dense matter or empty?

The popular description of black holes, especially outside the academia, is that they are highly dense objects; so dense that even light (as particle or as waves) cannot escape it once it falls inside ...
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1answer
105 views

Do gravitational waves travelling through a medium produce sound?

Say Alice decided to orbit dangerously close to a couple of black holes circling each other. She is in a heavily enclosed astronaut suit, as is Bob, who is floating much further away. Assuming Alice ...
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0answers
56 views

Einstein equations from the Palatini action [closed]

I am trying to obtain the usual form of vacuum Einstein's equations $$ R_{\mu \nu} - \frac{1}{2} R g_{\mu \nu} + \Lambda g_{\mu \nu} = 0 $$ from the first-order (Palatini) tetradic action $$ ...
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1answer
65 views

If we could perfectly control gravitational waves, could we play music with them? [closed]

Sound is just a kinetic wave propagating through a medium, right? In that case, if we had the ability to make gravitational waves exactly as we want them, could we play music to an observer some ...
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1answer
35 views

Function to model deformed spacetime in 2D visualization of an Alcubierre drive

In the Wikipedia article on Alcubierre drive there is a top image. It is 2D visualization of an Alcubierre drive, showing the opposing regions of expanding and contracting space-time that displace the ...
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1answer
90 views

Why do we need connections, if we have the Lie derivative?

When I learned about the covariant derivative, it was motivated as a way of defining a good differentiation operation on tensors. To do this, we had to define a connection on the manifold, which was a ...
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2answers
310 views

Gravitational imaging

Gravitational Imaging So as we know from the famous theory and equations of Einstein is it possible to track the individual gravitational pull?
3
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2answers
173 views

If space can expand faster than light why can't gravitational wave?

I heard that gravitational wave is the measure of stretchiness of space time, so since there is no limit to how fast space can stretch what about gravitational wave?
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1answer
89 views

Why is the speed of gravity the same as that of photons? [duplicate]

Why is it that the speed of massless particles in space is the same as propagating disturbances of space? We can´t send human information (with photons) faster than the speed of light. But we can ...
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1answer
65 views

Derivation of the relativistic equation of energy conservation for a perfect fluid

I'm currently attempting to struggle through the first chapter of Sean M. Carrol's spacetime and geometry. I'm a bit stuck, most likely because of not understanding the mathematical operation. ...
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66 views

What is the explicit form of $\tau^{\alpha\beta}$ in the linearized Einstein field equations $\Box h^{\alpha\beta}=-16\pi\tau^{\alpha\beta}$?

If we let $h^{\alpha\beta}=\eta^{\alpha\beta}-g^{\alpha\beta}\sqrt{|det(g)|}$ then, according to wikipedia, the Einstein Field Equations become $$\Box h^{\alpha\beta}=-16\pi\tau^{\alpha\beta},$$ where ...
3
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2answers
89 views

Why does an evaporating black hole always stay a black hole?

Stars can only collaps and form black holes if their masses are above the Chandrasekhar limit, $M>M_{\rm Pl}^3/M_{\rm hydrogen}^2$. When the universe eventually cools down enough, the black holes ...
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0answers
17 views

Gibbons-Hawking-York boundary term expanded at second order in the fluctuation

Does anyone know a general form for the Gibbons-Hawking-York boundary term expanded at quadratic order in the fluctuation of the metric? Assume to define the fluctuation of the metric $g_{\mu \nu}$ ...
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2answers
72 views

The influence of gravity on the energy levels of atoms

There´s an ongoing debate if gravity waves (or gravity?) contains energy. But what if a very strong wave of gravity hits an atom. Let´s for simplicity say a hydrogen atom. Not a wave that is ...
2
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0answers
52 views

Closed timelike curves in the Kerr metric

I just read in Landau-Lifshitz that the Kerr metric admits closed timelike curves in the region $r \in (0, r_{hor})$ where $r_{hor}$ is the event-horizon ( I am talking about the case $|M|>|a|$ ...
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0answers
22 views

Hidden character in EPR paradox [duplicate]

I am a beginner in Quantum Mechanics so i am pretty new to the EPR paradox although i have heard about it a long time ago but finally studying in detail. And came across a doubt: Why the hidden ...
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2answers
36 views

Curvy space in and around massive objects [closed]

If space curves around massive objects, what happens to the space within the massive objects?
4
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1answer
104 views

Why is Newtonian cosmology correct for curved space?

The Newtonian model of an expanding Universe gives Friedmann's equation exactly for non-zero spatial curvature $k$ (see http://hyperphysics.phy-astr.gsu.edu/hbase/astro/expuni.html). Instead of using ...
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0answers
42 views

Can a lightlike singularity have nonzero mass?

The effective mass of the Schwarzschild solution is valid at $r=0$. For $m>0$, we have a spacelike singularity, while for $m<0$ we have a timelike singularity. Suppose, instead of a spacetime ...
4
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2answers
82 views

What's the metric of the Standard Non-Time-Orientable Spacetime

If you've read any spacetime topology, you know that spacetime. It is the amazing rotating lightcone identified after half a rotation. And outside of De Sitter space with some identifications, it is ...
2
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0answers
61 views

Should we consider space and time as separate entity?

In general relativity, we think of space and time in spacetime framework. As some people say, metric tensor sign difference, along with our inability to go backward in time suggests that space and ...
4
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1answer
75 views

Negative mass thin shell collapse

Suppose we have a collapsing light-like (ingoing) shell with negative mass and decreasing further. The shell is radiating and so the exterior region is that of the outgoing Vaidya solution. $$ds^2 = ...
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0answers
127 views

The integration of Einstein's equations [closed]

Einstein's equation is $$G_{\mu\nu} + \Lambda g_{\mu\nu} = {8 \pi G \over c^4} T_{\mu\nu}$$ where $G_{\mu\nu} = R_{\mu\nu} - (1/2)g_{\mu\nu}\,R$ is the Einstein tensor, which combines the Ricci ...
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0answers
33 views

Can we distinguish between two mass distributions in spacetime having the same effect over a test partlicle [duplicate]

Einstein's equation is $$8πT_{ab}=G_{ab}$$ where the left side contains the stress-energy tensor and the right side contains the Einstein tensor. Is there exactly one unique stress-energy tensor ...
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1answer
33 views

Elementary question about non-Euclidean geometry in general relativity: “cannot move about without changing shape”

One basic result of general geometry (from math) in curved spaces or on curved surfaces is that if you are in a surface of variable curvature, things like the Euclidean congruence postulates and ...
2
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1answer
122 views

Is every solution of Einstein field equations unique?

Einstein's equation is $$8 \pi T_{ab} = G_{ab},$$ where the left side contains the stress-energy tensor and the right side contains the Einstein tensor. Is there exactly one unique stress-energy ...