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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Angle sum of triangle in Schwarzchild 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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4answers
2k views

How energy curves spacetime?

We know through General Relativity (GR) that matter curves spacetime (ST) like a "ball curves a trampoline" but then how energy curves spacetime? Is it just like matter curvature of ST?
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301 views

Does the actual curvature of spacetime hold energy?

My understanding of GR is that curvature of spacetime reflects the density of energy-matter. Does the curvature itself have energy? Or if energy is assigned to curvature it simply reflects the energy ...
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136 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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30 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
47 views

Mass and Schwarzschild Radius

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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132 views

How warped spacetime bends trajectories of light and moving objects?

I fail to see why the light follows something like the blue line and not the green line on the attached image. Figure 1 - light bends around warped spacetime Afaik. something similar happens ...
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1answer
38 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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22 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
49 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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1answer
41 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
44 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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351 views

What is the minisuperspace Lagrangian for gravity plus a scalar field?

In this paper by Sean Carroll and Grant Remmen, in equation (11) they write a Lagrangian of the form $$\boxed{\mathcal{L}=3a\left(k-\dot{a}^2\right)+a^3\left[\frac{1}{2}\dot\phi^2-V(\phi)\right]}$$ ...
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1answer
46 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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1answer
106 views

How to derive the Schwarzschild metric?

I'm having trouble differentiating the following when making a change of co-ordinates to determine the Schwarzschild metric. $$r'^{2}=r^{2}C(r)$$ Then taking the total derivative of both sides, the ...
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1answer
102 views

Schwarzschild Solution

I'm able to derive the Schwarzschild solution under the assumptions that the metric is (1) static (2) spherically symmetric and that the space is the vacuum. However, I have read that the ...
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116 views

Curvature based derivation of Schwarzschild Metric

I'm a third year maths undergrad and I'm trying to find (and follow) a curvature based derivation of the Schwarzschild metric, if there exists such a proof?
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35 views

Does the effect of spaghettification mean that (speculative) traversable wormholes can only exist from supermassive black holes? [on hold]

Assumption that wormholes really exist. Even if humanity could produce wormholes from quantum black holes. These would be never traversable due to the effect of spaghettification? Or does the exotic ...
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1answer
175 views

Thermal radiation in the Unruh Effect

The following formula has been given in 't Hooft's black holes notes ($|\Omega \rangle$ is the vacuum state of Minkowski space, O is a operator): $$\langle \Omega| O|\Omega \rangle = \sum_{n \ge 0} ...
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3answers
115 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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0answers
20 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 ...
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1answer
53 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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3answers
88 views

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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1answer
51 views

What $f(R)$ models pass most of the known constraints?

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
164 views

Non-trivial scalar quantity

Is there any scalar quantity made of only the Christoffel symbols, determinant of a metric and tensors, not derivatives? In other words, can we construct a scalar quantity which cannot be written in ...
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136 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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28 views

How to explain the homogeneity of the universe through a physic model

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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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
124 views

Closed timelike curves in the spin-2 gravity formalism

Let's say we take some topologically trivial CTC spacetime, like the Gödel metric: $$ds^2 = -dt^2 - 2e^{\sqrt{2}\Omega y} dt dx - \frac{1}{2}e^{\sqrt{2}\Omega y} dx^2 + dy^2 + dz^2$$ And then I ...
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1answer
114 views

Spin connection and covariant derivative

How to prove explicitly (i.e., to don't postulate it) that by including Lorentz indices $a$ the covariant derivative $D_{\mu}$ looks like $$ D_{\mu}A^{\nu a} = \partial_{\mu}A^{\nu a} + ...
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1answer
56 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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1answer
40 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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49 views

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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86 views

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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2answers
174 views

Why general relativity over other similar theories?

Since all theories where gravity is seen as a result of space curvature automatically satisfies the equivalence principle, why should one prefer GR over all other alternatives? Surely you can make the ...
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1answer
44 views

Distance between two galaxies of different redshift

Let $Q_1$ and $Q_2$ two different objects in the Universe (we can think to two galaxies or quasars), that we observe from the Earth at different angular position $(\alpha_1,\delta_1)$, ...
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54 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 ...
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23 views

Does every particle in a neutron star accretion disc undergo Thomas precession?

Assuming, based on this wikipedia article Accretion Discs That accretion discs surrounding neutron stars are diffuse (I take this to mean they are composed of a gas and / or plasma). That the ...
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2answers
936 views

Why is the stress-energy tensor symmetric?

The relativistic stress-energy tensor $T$ is important in both special and general relativity. Why is it symmetric, with $T_{\mu\nu}=T_{\nu\mu}$? As a secondary question, how does this relate to the ...
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2answers
49 views

If the measurements of a clock above the earth depend on orientation, then what measurements are correct?

Take a clock in space above the earth (assuming a Schwarzchild spacetime) that works by relaying a light signal a small distance radially; ticking each time the light signal returns. Compare this to ...
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2answers
77 views

Special and general relativity and space time

I have a question. I'm reading The Elegant Universe and it's talking about the special and general theory of relativity. One of the things it mentions is that time and the three dimensions of space ...
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76 views
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33 views

Are there any experimental data for light bending angle? [duplicate]

The gravitational lensing formula is given by equation $a=4M/r$. Is there any experimental data for this equation. I am trying to plot a curve for this equation and the real experimental data and ...
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1answer
159 views

Spinning micro blackholes power conversion

In the context of energy extraction of spinning black holes, there are two known mechanisms: the Penrose process and the Blandford-Znajek process. The former relies on fragmentation of accreting flow, ...
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400 views

Energy-Momentum Tensor in QFT vs. GR

What is the correspondence between the conserved canonical energy-momentum tensor, which is $$ T^{\mu\nu}_{can} := \sum_{i=1}^N\frac{\delta\mathcal{L}_{Matter}}{\delta(\partial_\mu f_i)}\partial^\nu ...
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1answer
67 views

The relativity of gravity: If mass is relative how much gravity do I experience?

Now let's say the I am on a spaceship. The spaceship is not accelerating, i.e., it is not firing its rockets. Most of the ship's mass is in the back of the ship. Let's say it is moving arbitrarily ...
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1answer
76 views

When is Einstein summation implied by Lorentz indices?

I would like to ask if it is possible to find out whether Einstein summation is used in an equation. For example, $$A^{\mu \nu} = 1$$ can either mean $\sum_{\mu\nu} A^{\mu \nu}=1$ or $A^{\mu \nu}=1$ ...
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1answer
94 views

Speed of light and warp drives in general relativity

Velocities can be a tricky thing in general relativity. A cool concept seemly consistent with the Einstein field equations) is an Alcubierre drive, described by the Alcubierre metric. However, I ...
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60 views

What is the value of the variation stress energy tensor?

If we are living in a portion of space-time where the metric is very close to flat space and we know that the stress energy tensor is negligible at this portion of space-time is it ok to assume that ...
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Compactly generated vs. compactly constructed causality violating region?

I am currently trying to grasp the nuance between a compactly generated future Cauchy horizon (as per Hawking's chronological protection conjecture) and a compactly constructed causality violating ...