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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Problems of General Relativity on small and large scales [duplicate]

As far as I know, the most important problem of GR on large scales is the cosmological constant problem which in some manner can be thought of as a dark energy problem (please correct me if I am ...
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39 views

If there is a point in a past set, does its chronological future interset a future set?

This post concerns the causality of spacetime $\mathcal M$. A future set $F$ is defined to be the chronological future of some set $S\in \mathcal M$, ie., $F=I^+[S]$. Similiarly, a past set ...
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Confusion about 1-forms as introduced in “Gravitation” (Kip S. Thorne,…)

In the book Gravitation in chapter 2, paragraph 5, they introduce the concept of 1-forms by thinking about the momentum 4-vector differently. They first introduce the de Broglie 1-form as follows (I ...
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89 views

Hermiticity of Dirac operator in curved spacetime

The Dirac Lagrangian in curved spacetime is usually given by \begin{equation} \mathcal{L} = i\bar{\Psi}\gamma^a e^{\mu}_a(\partial_\mu + \frac{1}{4}\omega_{\mu bc}\gamma^b\gamma^c)\Psi \end{equation} ...
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GR time dilation cares only about local curvature, right?

Regarding this remark on Worldbuilding SE and the discussion leading up to it: Can someone properly knowledgeable on the subject please explain whether the time dilation due to being in a gravitation ...
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52 views

Event horizon from the metric

Let us suppose we have a metric of this form $$ds^2=-A(r)dt^2+\frac{dr^2}{B(r)}+r^2d\Omega^2$$ In all documents I can read, I've seen that the event horizon is defined by considering $A(r)=0$ But I ...
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44 views

Does General Relativity say that the Laws of Physics are the same in all Reference Frames?

Most texts on General Relativity seem to imply that Einstein generalized the Relativity Principle (that all reference frames are equivalent) to include changes in velocity (accelerations); but then go ...
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27 views

The equivalence principle and experiments concerning it?

Imagine that we are in a rocket accelerating with some magnitude $a_1 = dx^2/d^2t$, also imagine that we have a stationary rocket ship in close proximity to ours, stationary relative to our reference ...
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66 views

Does $R_{\mu \nu \sigma \rho} R^{\mu \nu \sigma \rho} \propto R$ hold?

For $R_{\mu \nu \sigma \rho}$ the Riemann-tensor and $R$ the Ricci-scalar: Does $R_{\mu \nu \sigma \rho} R^{\mu \nu \sigma \rho} \propto R$ hold? Or is there any way to relate $R$ approximately ...
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Cosmological constant in General Relativity [duplicate]

According to my GR notes the cosmological constant can be thought of as a vacuum energy much in the same way as the ground state of the harmonic oscillator. The notes claim that the regularised energy ...
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82 views

What is the conformal mode of a metric?

I have a problem in terminology. This article talks about the conformal mode of a physical metric. I know what a conformal transformation is. But what is the conformal mode of a metric?
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Interpretation of black hole area

I'm studying properties of Kerr spacetimes and a lot of fuss is made about area of BH. It is defined to be integral of area element on event horizon $r=r_+$, $t=const.$ where $r_+$ is radial ...
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Does the spin of a particle change if observed from an accelerating reference frame?

If we consider a spin-$\frac12$ particle at rest in the absence of any potentials, we can use the Pauli spin operators and an associated basis to describe the observable. Let's arbitrarily choose the ...
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4answers
122 views

How do gravitational waves work without internal tension?

One implication of general relativity is the concept of gravitational waves or gravitational radiation, ripples in spacetime thought to travel at speeds close to the speed of light. As far as I have ...
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2answers
64 views

Is it possible that one of the quasars we see is an ancient Milky Way?

As I understand it, even though our current measurements of the Riemann curvature of the universe overlaps with flat spacetime, this doesn't restrict the shape of the universe to being infinite. It's ...
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66 views

Gravitational lensing on galaxy cluster with given potential

I am having a problem with gravitational lensing question where we are interested in deflection angle of light traveling in potential of galactic cluster, described with ...
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1answer
28 views

Why can only asymptotically flat and AdS black hole have the thermodynamics? What's about asymptoticaly dS black hole?

Almost all advanced GR textbooks will have the content of black hole thermodynamics for asymptotically flat black hole. And this paper solve the asymptotically AdS (Anti-de Sitter) black hole ...
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Equation of state of a universe full electrons

If I have a universe full of nothing but (slow moving) electrons, what would the equation of state ($w$, from $p=w\rho$) be? I think it would be incorrect to say that the electrons should be treated ...
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2answers
73 views

Does acceleration warp space?

I know that mass warps spacetime and gravity and acceleration are equivalent so does acceleration warp spacetime too?
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Gravitational boson violating relativity [duplicate]

Currently doing a introductory degree level physics course, they were talking about how changes in gravity/gravitational field cause changes so quickly that if you assigned it the "graviton" said ...
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65 views

Is it possible to directly test whether of not the vacuum gravitates?

According to GR, all sources of stress-energy (e.g. everything on the $T_{\mu\nu}$ side of the EFE) should gravitate (e.g. affect the curvature/$G_{\mu\nu}$ side of the EFE). We observe the expansion ...
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97 views

Einstein-Yang-Mills Connections

I am playing around with coupling a classical $SU(2)$ Yang-Mills theory to Einstein's equations. Assuming spherical symmetry, the $SU(2)$ connection can be written \begin{equation} A = ...
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419 views

Casimir effect for spinning Casimir plates

I recently thought of the following experiment. Let's say I have two plates in vacuum facing each other. Now, due to the Casimir effect, there will be some internal attraction between the plates. Now ...
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Thomas precession, Lie algebra of the Lorentz group and the conservation of energy

If you read this post Thomas Precession, you will see a very good answer by WetSavannaAnimal, on the subject of Thomas Precession, which I am currently working my through, in conjunction with some ...
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45 views

Any applications of kinetic physics on cosmological scales?

On galaxy cluster scales, one is usually forced to use approximate theories such as hydrodynamics or magnetohydrodynamics for modelling cosmological phenomena. I wanted to ask if kinetic theory is ...
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Existence of affine parametrization [closed]

This is a question from General Relativity by Wald Chapter 3, problem 5. Given either pseudo-Riemannian or Riemannian metric $g_{ab}$ and manifold $M$. Assume the $\nabla$ is compatible with the ...
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73 views

How does a world line of an Alcubierre drive look like?

In my recent question ”Speed of light and warp drives in general relativity” I asked exactly how an Alcubierre drive worked and exactly what "FTL travel" meant. One of the comments I got stated that: ...
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Any textbook about non-renormalizability of gravity?

I have learned general relativity in a graduate-level. My knowledge about QFT is very rudimentary. But, I need to learn about non-renormalizability of gravity. I have these questions. Is there any ...
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53 views

Can everything be described without anything needing to actually “bend”? [closed]

Is space bending because gravity actually causes small particles to move differently? If large source of gravity is somewhere are particles extending towards it, creating a "bend" in space? So "bend" ...
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43 views

Variation of quadratic term in modified Einstein-Hilbert actions

In the context of mimetic gravity at some point one try to add to an already modified Einstein-Hilbert action also a term like $$ S_\chi=\int\,d^4x\,\sqrt{-g}\frac{1}{2}\gamma\chi^2,\qquad(\star) $$ ...
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Angle sum of triangle in Schwarzschild solution

Curvature of space is often intuitively explained as angles of a triangle not adding up to 180 degrees. My questions concerns that. Suppose you have a perfectly spherical star of uniform density - so ...
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1answer
40 views

Does spacetime curvature increase when an attractor's potential energy is converted to kinetic energy?

Imagine an asymptotically flat spacetime with nothing but two stars at a certain distance. They fall into each other and form one big star, so their potential energy is converted to kinetic energy. ...
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49 views

Mass and Schwarzschild Radius [duplicate]

Do free massless particles have a Schwarzschild radius? I'm curious about the mass in the equation for the Schwarzschild radius. I know that you can calculate a Schwarzschild radius for any massive ...
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4answers
187 views

Is a black hole's mass uniformly distributed?

If you were to fly around a black hole, would the gravitational pull be uniform and centered on the singularity, regardless of your relative location? If yes, how can this be consistent with models ...
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Can you recover the values of spacetime intervals $s^2$ from given causal relations between events?

Given a suitable set $\mathcal S$ of events together with their (pairwise) causal relations, i.e. for each pair of distinct events $\mathsf A, \mathsf B \in \mathcal S$ the assignment whether ...
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32 views

Short Gamma Ray Bursts from black hole mergers

I have read in passing that short gamma ray bursts can be caused by the merger of 2 black holes in a binary system. I have Googled but can't seem to find any good sources describing the phenomenon ...
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63 views

Can you recover a spacetime from its null geodesics?

So, I know that you can learn a lot about a spacetime from its causal structure, but can one completely recover the metric of a spacetime, just knowing the equations for the null geodesics in it? If ...
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64 views

What force causes massive objects to bend space? [duplicate]

The visualization of gravity as shown by this video is pretty good at explaining how massive objects bend space, and such bending causes objects around it to fall towards it (a.k.a: gravity). ...
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49 views

A question about the physics involved in tracking satellites such as those used in the GPS system [duplicate]

I know that besides the effects of Newton's theory of Gravitation on the satellite's motion, one has to take account of the retardation of the satellite's clocks when compared to earth-fixed clocks. ...
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1answer
55 views

“Proper mass” and “gravitational binding energy” in general relativity

I'm reading Robert Wald's "General Relativity" and after the discussion of the Schwarzschild Solution it goes on to talk about interior, static, spherically symmetric solutions. Wald says that "M" in ...
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What component of the stress–energy tensor contains the kinetic energy of heat? [duplicate]

As I understand it, the component $T_{00}$ of the stress-energy tensor contains the energy density (which equals the mass density), $T_{0i}$ are the impulse flows (intuitively speaking, the ...
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1answer
54 views

Gravitational redshift in a general stationary metric

Suppose you have a general metric $g_{\mu \nu}(t,r,\theta,\phi)$ which don't depend explicitly on $t$ coordinate, i.e a stationary metric. Light travels along a geodesic from A (at which the frequency ...
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31 views

How to explain the homogeneity of the universe through a physic model [duplicate]

If in general, two objects homogenize themself by combining it's parts, why the horizon effect, based on a big bang model, excludes such an important physical interaction process? I wonder if this ...
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3answers
131 views

If time is relative, how could time pass? [duplicate]

EDIT: I appreciate people who answered below. But it does not answer the question, so I will clarify my questions: -It seems like everyone is saying that time passing is actualized by physical ...
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3answers
144 views

What is the binding energy of a neutron star?

Neutrons which constitute a neutron star have a rest mass that is greater when separated from the star because they are bound with a certain potential energy. This potential energy causes the system ...
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4answers
3k views

Why do physicists trust black hole physics?

Based on popular accounts of modern physics and black holes (articles, video lectures), I have come to understand the following: Black holes are predicted by General Relativity, a classical theory ...
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1answer
79 views

Does an object traveling near the speed of light create a gravitaional field? [duplicate]

Does a particle traveling near the speed of light create an observable/measureable gravitational field around it? I know most elementary particles travel near the speed of light and have no ...
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What $f(R)$ models pass most of the known constraints? [closed]

In most papers and talks about $f(R)$ gravity authors repeatedly state that the model proposed by Starobinsky 2007 $$ f(R)=R+\lambda\,R_{0} \bigg[\bigg(1+\frac{R^{2}}{R_{0}^{2}}\bigg)^{-n}-1\bigg] ...
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3-cylinder surface element (Poisson's “A Relativist's Toolkit”)

From Poisson's "A Relativist's Toolkit": he introduces the non-dynamical term $$ S_0=\frac{1}{8\pi}\int_{\partial\Omega}\epsilon K\sqrt{\lvert h\rvert}d^3x $$ in the GR action, where $h$ is the ...
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Can a Dyson Sphere around a Black Hole be built so that it would not radiate significant IR?

This is related to this question If the sphere surrounded a BH and used it as a heat dump (as well as extracting energy from it by dropping in mass) could its exterior be engineered to match the ...