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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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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127 views

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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1answer
63 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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1answer
51 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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1answer
29 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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85 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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15 views

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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1answer
117 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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54 views

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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196 views

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
211 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
70 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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173 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 tensor ...
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1answer
41 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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37 views

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
215 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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24 views

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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1answer
73 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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215 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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450 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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45 views

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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0answers
46 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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0answers
68 views

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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1answer
99 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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79 views

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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1answer
58 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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67 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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109 views

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
61 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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1answer
70 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
254 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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1answer
43 views

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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1answer
39 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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1answer
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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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1answer
104 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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1answer
127 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
99 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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25 views

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 ...
2
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1answer
105 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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0answers
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
178 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
408 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 ...
0
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1answer
100 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 ...
2
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1answer
59 views

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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1answer
55 views

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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3answers
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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 ...
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Particle energy in conformal FRW spacetime?

Let us start with the flat-space FRW metric in Cartesian co-ordinates for simplicity: $$ds^2=-dt^2+a(t)^2(dx^2+dy^2+dz^2).$$ In GR the energy of a particle is given by: \begin{eqnarray*} ...
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2answers
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How to define $\delta{g_{\mu\nu}}$?

In general relativity, when deriving the field equation using the variational principle we use $\hat{g}_{\mu\nu}=g_{\mu\nu}+\delta{g_{\mu\nu}}$. Does $\delta{g_{\mu\nu}}$ mean the measurement of how ...
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68 views

What is the status of the area theorem in AdS?

The area theorem, by Hawking (in "Gravitational Radiation from Colliding Black Holes", also found in Wald), states that the area of an event horizon cannot decrease with time. As I understand, there ...