A theory that describes how matter produces and responds to 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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Time slowing down vs. universe expanding

Einstein said that it is impossible to distinguish between the effect of gravity and acceleration (so if you stand in an accelerating elevator in space it would not feel any different than if you were ...
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49 views

Candidates for holographic QFT of 4D Einstein gravity

If we are to believe that holographic principle holds over a wide number of dimensions, and gravitational theories, but specially, those that are relevant to our universe, then there must be some 3D ...
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46 views

Exercise Lorentz Transformations

I have 2 inertial frames, both are in relative motion along the x axis moving with constant velocity $v_x$. It is called with Standard figuration where the Lorentz transformations relate the ...
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2answers
116 views

Does gravity actually contract space-time?

In the Big Crunch Theory it says that gravity (curvature in space-time) will stop the universe's expansion and gravity will cause the universe to contract on itself. My question is if gravity is a ...
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2answers
72 views

Is the acceleration at the event horizon of a black hole independent of the magnitude of its radius?

Is the acceleration of a free-falling observer at the Schwarzschild radius of a black hole the same regardless of the numerical value of the radius (i.e. outside of a black hole, is the acceleration ...
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1answer
61 views

What are the consequences of a body of mass moving at speed of light? [closed]

What would happen to someone who could move at the speed of light? I know that at the speed of light bodies gain mass and decrease in size. But what would happen to a body gaining mass tending to ...
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3answers
105 views

Could a photon travel faster than the speed of light in vacuum?

If the cosmic speed limit is the speed of light in vacuum, then what happens when a photon traveling through space meets gravity? Wouldn't gravity pull on the photon that's already traveling at max ...
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1answer
75 views

Infinitesimal transformations for a relativistic particle

The action of a free relativistic particles can be given by $$S=\frac{1}{2}\int d\tau \left(e^{-1}(\tau)g_{\mu\nu}(X)X^\mu(\tau)X^\nu(\tau)-e(\tau)m^2\right).$$ If we then make an infinitesimal ...
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38 views

Wormholes with event horizons?

Under General Relativity, Lorentzian wormholes (the kind that are traversable) require exotic matter (a kind of unobtainium which is not known to exist). On the other hand, we know black holes exists ...
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26 views

Are combined masses in space, such as galaxies, considered to be uniform bodies? *In addition, a related question about force

If we were to calculate the force that one galaxy exerted onto another, would we consider the individual masses within the galaxies, or the masses of the galaxies as a whole? Do the individual stars ...
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0answers
87 views

Simple General Relativity Relation [closed]

Given the identity $$\nabla_a(R^{ab}-\frac{1}{2}R g^{ab})=0,$$ how do I then show that $R_{ab}=0$ implies $$\nabla_a R^a_{\space \space \space bcd}=0$$
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4answers
186 views

Where does the idea gravity=curvature of spacetime really come from?

I have been searching for quite a while but mostly found the answer: Einstein's genius. Quite unsatisfactory. I know and understand that the idea gravity=curvature of spacetime works. Furthermore I ...
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28 views

Specific problems with the quadrupole formulation of gravitational radiation

the quadrupole formula has some counterintuitive consequences, when analysing the power output averaged over a period $$ P = \langle \frac{d^3 Q_{ij}}{dt^3} \frac{d^3 Q_{ij}}{dt^3} \rangle $$ ...
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1answer
57 views

Spacetime line elements and proper time (specific problem)

Sometimes, when we have a certain line element and we are given a worldline parametrised by a path parameter that is not necessarily proper time I don't completely understand some of the standard ...
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0answers
32 views

Can we design the orbit of a satellite with Einstein’s curved space?

I think that the most successful theory of gravity is that the orbit of planet can be explained with this theory and the orbit of satellite was designed with this theory. To design an orbit of a ...
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0answers
26 views

gravitational waves and orders of magnitude

I have a question about numerical magnitude in eq. 6.110 of this reference. So, using this reference sheet for this PSR1913+16 binary, I get the following numbers: $$M = 2.8 \times 10^{30} ...
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0answers
68 views

How is foliation of manifolds' theory useful in General Relativity?

I am interested on getting some hints on how Foliations Theory of Manifolds can be used fruitfully on General Relativity. I just started my Ph.D on Mathematics this semester focusing on studying ...
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1answer
87 views

Square of a tensor

I think, $$\sigma_{ij}\sigma^{ij} = \sigma^2.$$ However, on the Wikipedia page on Raychaudhuri equation, It was mentioned: $$\sigma^2=\frac{1}{2}\sigma^{ij}\sigma_{ij}$$ I am confused, but I think ...
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0answers
30 views

What is the effective physical difference between a massive region of a polarized vacuum and a region of curved space-time?

What is the effective physical difference between a large region of curved space-time and an equally large region of a polarized vacuum? Consider the fact that vacuum polarization amounts to an ...
2
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1answer
100 views

Stuck following derivation of geodesic equation

In the book "Reflections on Relativity" by Kevin Brown, there is a chapter called "Relatively Straight", in which he derives the geodesic equations using the Euler equation. Online version Just ...
5
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1answer
97 views

Differentiating the gravitational redshift and the cosmological redshift?

If general relativity accounts for a redshift, independent of inflation, how can we still know that inflation is viable? Moreover, how do we differentiate the the gravitational redshift and the ...
9
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1answer
332 views

Justification for new theories of Particle Physics and General Relativity

In reference to arxiv:1212.4893v3 and arxiv:1206.5078v2 papers of Ma and Wang, they have proposed new theories in particle physics, the weakton model where quarks and leptons are formed using these ...
4
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0answers
75 views

Dirac equation in curved spacetime - found second derivatives of the metric, violation of the principle of equivalence?

I am working on the Dirac equation on curved spacetime. A Foldy-Wouthuysen transformation was applied to obtain the semiclassical limit of the equation to study the dynamics of the spin of the ...
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4answers
1k views

Is there experimental evidence that massless particles such as photons attract massive objects?

For instance evidence that a highly energetic laser beam attracts objects nearby? In the framework of Einstein's general relativity all energy curves spacetime and hence exerts an attraction, but my ...
4
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2answers
170 views

What does it mean to “convert energy into time”?

In a recent article about creating electron-positron pairs by colliding photons in a laboratory, Andrei Seryi, director of the John Adams Institute at Oxford University, was quoted to said: It's ...
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1answer
36 views

Properties of event horizon for incoming matter

In one of his lecture,Prof. Susskind mentioned that the event horizon "bulges" forward to meet any incoming radiation or matter; and it is a property of Einstein field equations. I have not come ...
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102 views

An error in Gravitation by Misner Thorne and Wheeler?

I was studying on Gravitation the PPN formalism. Since in equation (39.41) pag. 1087, the term $1 + \dfrac{v^2}{2}+(2+\gamma)U = 1 + \dfrac{v^2}{2}+3U$ (the second in GR) looked odd, I tried ...
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3answers
72 views

How can the electromagnetic stress energy tensor be restricted to flat space-time

The Wikipedia article describing the electromagnetic stress energy tensor seems to suggest that this tensor can only be defined in flat space-time. How is it possible to define an electromagnetic ...
3
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1answer
220 views

Gregory-Laflamme Instability of Black Strings and $p$-Branes

In a paper by Gregory and Laflamme (http://arxiv.org/abs/hep-th/9301052) in 1993, it was demonstrated that black strings and $p$-branes which were solutions to certain low energy string theories were ...
5
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2answers
287 views

Perturbation metric problem

I know this is an already answered question, but I couldn't make head or tail of it, and it's bugging me. I know I'm probably asking a silly question, but please bear with me as I'm 14 and this is my ...
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1answer
69 views

Time travel to the past in binary black hole system

I just saw this YouTube video (only 3 mins long) of Neil deGrasse Tyson explaining what happens when two black holes collide. He says that when the black holes are rotating around each other, there ...
2
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4answers
166 views

GR matter-free equations and Schwarzschild geometry

I am reading some lecture notes on General relativity (undergraduate level) and I do not understand a sequence of statements about the topics in the title. After stating that the for matter-free ...
3
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2answers
145 views

The wave equation in general relativity, special relativity, and Cartesian coordinates

The relativistic wave equation is $$\square\varphi=\rho$$ where $\varphi$ is the field, $\rho$ is the source, and $\square$ is the D'Alembert operator, defined by ...
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1answer
55 views

Where is the way on a rotating black hole to another Universe? [closed]

Where is the way on a rotating black hole to another Universe? Where and how should it be entered by to get away from here?
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4answers
229 views

What was the Law of Gravity better explained by?

In mechanics, our professor made the declaration that "all laws of physics" have been disproven. He mentioned several examples including the Law of Gravity, mentioning briefly that it is better ...
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1answer
27 views

Luminosity distance from angular diameter distance

Consider that I know the cosmological angular diameter distance at a given redshift : $$D_{A}\left(z\right)=\frac{x_{object}}{\theta_{observer}}$$ Is there a general formula to compute the ...
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1answer
67 views

Knots and singularities

Can space-time singularities be treated as mathematical knots occurring in dimensions greater than four? I just drew an analogy with knots in one-dimensional strings. When a rubber-band is looped over ...
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0answers
56 views

How to draw the Poincaré patch of ${AdS_3}$?

My main reference for this question are these notes (maximally symmetric spaces.pdf) by Kurt Hinterbichler. I'm using Global Coordinates: \begin{align} x^0&=\sec{R}\cos\tau\\ ...
3
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1answer
106 views

Metric Perturbations in General Relativity and quasi-normal modes?

I am familiar with the tools that appear in (linear) perturbation theory for general relativity, that is namely that one writes: $$g_{\mu \nu} = g^{(0)}_{\mu \nu} + \epsilon g^{(1)}_{\mu \nu} + ...
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0answers
49 views

Stationary and Static

I have some confusion about the concept of stationary and static. A metric $g$ is called stationary if there is a time like Killing vector $K$. $g$ is called static is further HSO (hyper surface ...
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3answers
79 views

Speed/direction of gravity for a moving source [duplicate]

Consider the Earth, and a bowling ball held 186,000 miles (1 light second) above it. When the ball is released, it will start to fall vertically downwards towards the Earth. Now consider the case if ...
9
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3answers
246 views

Which clock is the fastest inside an accelerating body?

The picture shows an accelerating spaceship with two clocks inside it. It is so far away from all other bodys that gravity is of no importance. Will the bottommost clock be slower than the topmost ...
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0answers
19 views

Angular and luminosity distance in general?

Consider a non-Friedmannian Universe in which we know the trajectories of photons, ie in which we know null geodesics $\left(\eta, x^{1}, x^{2}, x^{3}, a, z\right)$ where : $\eta$ is the conformal ...
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52 views

Dark Matter and Modified Gravity

Could someone please explain briefly or refer me to an article or manuscript that shows how f(R) modified gravity theories can be used to explain the problem of Dark Matter, particularly Galaxy ...
3
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1answer
109 views

Taylor expansion of the metric

Consider a coordinate change $$ x^a\mapsto \tilde x^a=x^a+\epsilon y^a $$ In the note I am reading, the author calculate the change of metric by $$ g_{ab}(x) = \tilde g_{ab}(\tilde x)=\tilde ...
5
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2answers
181 views

Confusion about Lie derivative on metric

According to this site, the Lie derivative of a $(0,2)$-tensor is $$ \mathcal{L}_XT_{ab}=\partial_XT_{ab}+T_{cb}\partial_aX^c+T_{ac}\partial_bX^c $$ However, according the same website, the Lie ...
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0answers
67 views

About the proof of the second Bianchi Identity

The second Bianchi Identity is $$ \nabla_{[a}R_{bc]de}=0 $$ As far as I know, the proof (say, Walfram Mathword) start by stating the representation of Riemann tensor in local inertial coordinates $$ ...
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2answers
61 views

Understanding emergent phenomena in the block universe. (Reworded question)

Each person exists as an unchanging 4D worldtube in the block universe. At each slice of the worldtube there is a present, past and future. However, there is a black box* which appears to exist in ...
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2answers
100 views

Confused about the concept of time and time dilation [duplicate]

I am having a hard time understanding what is time. If scientists define time as a multiple of caesium frequency, then time itself is dependent on motion, so what if I have a number of particles that ...
5
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1answer
151 views

Schwarzschild Metric coordinate sign change in $0\leq r \leq 2GM$

In the event horizon of the Schwarzschild-metric not only the time coordinate but also the radial space coordinate seems to change sign: ...