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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Origin of time or origin of space-time? [on hold]

This might be a mere theoretical concept and I might even get down voted for asking this. I read in several sources that winding back general relativity equations leads to $t=0$, origin of time. ...
3
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2answers
49 views

Does the charge of a black hole affect its space-time geometry?

Does a black-hole of a given mass and angular momentum have the same space-time geometry regardless of its charge? I'm pretty sure that an electric field can accelerate a charged particle but doesn't ...
3
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0answers
42 views

Zeno effect in quantum gravity?

Given that "the quantum zeno effect can "freeze" the evolution of the system by measuring it frequently enough in its known initial state." Is there any equivalent/similar Zeno effect in quantum ...
5
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0answers
62 views

Can this relativistic hack allow one to see beyond an event horizon, in principle, else why not? [duplicate]

Consider a lone photon. As its frequency increases, its energy increases. Taken to the limit, a sufficiently-high-frequency photon could be a black hole unto itself. But the frequency of a photon is ...
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1answer
48 views

Why does one particle in Hawking radiation have negative energy? [duplicate]

So as I understand it, Hawking radiation occurs when virtual antiparticle-particle pair are created near the event horizon of a black hole due to vacuum fluctuations because of Heisenberg uncertainty ...
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35 views

Parenthetical tensor notation [on hold]

Just out of curiosity, what does it mean to be a type $(n,m)$ tensor? For instance in the context of special and general relativity, the Minkowski metric $\eta$ is considered a type $(0,2)$ tensor. I ...
1
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2answers
52 views

Riemann Tensor and Covariant Derivative in Carroll's Spacetime

In Spacetime and Geometry, Sean Carrol defines the Riemann Tensor in terms of the commutator of covariant derivatives: $R^\rho_{\sigma\mu\nu}V^\sigma = [\nabla_\mu, \nabla_\nu]V^\rho + T^\lambda_{\...
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0answers
23 views

Black Hole Scattering of Low-Frequency Light

What is the far-field interference pattern for low-frequency (i.e., the wavelength is much larger than the Schwarzschild radius) electromagnetic plane wave radiation about a point mass? I envision a ...
4
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3answers
754 views

Space-Time Curvature Depends on Relative Speed

When the mass of a planet causes the curvature of space-time we see that an approaching free-falling object deviates its path towards the planet. We also see the amount of that deviation depends on it'...
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1answer
49 views

Can revolving movement also generate gravitational waves? [on hold]

If an object revolves around a circular path at the speed of light could it still generate gravitational waves and what would be the simulation in inner area?
0
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1answer
41 views

Does gravity cause the gravity of another mass to curve?

For example say star 1 is at position x, however star 2 causes gravitational lensing on star 1's light that is traveling toward you and you now see star 1 at position y. Will star 1's gravity move you ...
1
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3answers
70 views

Ricci scalar for Black Hole

What is the value of Ricci scalar at $r=0$ inside Black Hole? Since $R_{\mu \nu}=0$ is vacuum solution and valid outside event Horizon of black hole where there is no mass energy density. But inside ...
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1answer
59 views

In relativity theory could we talk energy rather than frames of reference? [on hold]

In relativity theory, the space geometry, of space and time, is no longer absolute, if one observer is accelerating compared to the other. Could I say in other words that space geometry is changed if,...
0
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1answer
61 views

Is there energy output when mass moves between two spacetimes [on hold]

Is there energy output when mass $m$ moves between two spacetimes? Say, it starts in a flat spacetime and then falls into a black hole (other examples don't come to mind, but this doesn't mean they ...
2
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0answers
55 views

Solving the Friedmann Equation [closed]

Through substituting for values of $\rho$ and $k$, I have: $$H^2=\left(\frac{\dot{a}}{a}\right)^2=\frac{8\pi G C}{3a^4} + \frac{\Lambda c^2}{3}$$ $a=a(t)$, and $a(t=0)=0$. Note that $C$ is a ...
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0answers
115 views

What is the mass density distribution of a Schwarzchild black hole?

According to Schwarzschild metric the density element $$ \frac{\mathrm dm}{\mathrm dV} $$ becomes infinite on the event horizon if there is mass $$ \mathrm dm > 0 $$very near at the outside of ...
0
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1answer
43 views

Relativity, and Lenz's law with respect to the Lorentz force acting on a wire?

For this system: It's simple for me to predict the induced EMF, and if the wire were connected to a complete circuit(for current $I$ to flow), the opposing Lorentz force($-F$): However, if the ...
2
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1answer
63 views

How can the size of the universe change over time when time is part of the universe?

Bit of an awkward way to phrase it, but basically: Time in relativity is just one of four dimensions of space-time. Nothing really special about it. Yet the universe was once smaller than it is now ...
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1answer
53 views
0
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1answer
50 views

Trace of a Tensor

What is the significance of defining the trace of a tensor as $g^{\alpha\beta} R_{\alpha\beta}$ instead of $R_{\alpha\alpha}$ on a Riemannian manifold?
2
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1answer
82 views

GR says that time and space are aspects of the same thing, yet there is no observable for time in QM

I understand that the topic of a time operator in quantum mechanics has come up more than a few times so forgive me if this is a repeat question but I couldn't find anything specific to my question. ...
3
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1answer
52 views

Stress-energy tensor for Dirac fields, and its dependence on connection

In the stress-energy tensor (SET) for free scalar and vector fields, any references to the connection $\Gamma^\lambda_{\mu\nu}$ in the kinetic terms appear to either be absent ($\nabla_\mu \phi = \...
4
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1answer
24 views

Interpretation of components of energy-momentum flux near a null surface

Let $k^a$ be the normal to a null surface and $l^a$ be the auxiliary null vector satisfying $l^a k_a=-1$ (see, for instance, the textbook A Relativist's Toolkit by Poisson). I wanted to understand ...
19
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2answers
1k views

Chasing someone who has fallen into a black hole

Assume that my friend and I decided to explore a black hole. I parked the spaceship in a circular orbit safely away from the horizon. He puts on his spacesuit with a jet pack and carefully travels ...
0
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0answers
25 views

Studying relativity from Landau [duplicate]

I'd like to have an advice from you. I was thinking about studying for the exam of general relativity from Landau II: theory of fields. I already studied mechanics and fluid dynamics from Landau and I ...
0
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1answer
67 views

Riemann tensor for a diagonal metric [closed]

Is it correct that for a diagonal metric tensor, the Riemann tensor with one contravariant ( upper ) index, $R^\mu_{\phantom{a}\nu\theta\phi}$, is anti-symmetric for interchange of the two first ...
1
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0answers
23 views

Gravity of Masses in 4-D [closed]

I have developed a fairly stable understanding of the curvature of spacetime caused by a massive object (meaning with mass, not necessarily a lot of mass), though I have been wondering about a new ...
2
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3answers
114 views

How did the constant $\pi$ creep into Einstein's field equation? [duplicate]

The ratio of a circle to its diameter in Euclidean space appears in places that sometimes appear to be mysterious. I am wondering if in Einstein's field equations he is using Poisson's formulation of ...
3
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2answers
99 views

How does critical density affect the expansion of the universe if gravity is the curvature of space-time?

From what I know there are three scenarios about the end and expansion of the universe that all depend on the concept of critical density: If the matter of our universe is above critical density, ...
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2answers
214 views

Charged Accelerometer in Orbit

It is well known that an accelerometer (or any other object for that matter) in a gravitational orbit will register nearly zero acceleration. According to this answer, this is because the object is, ...
0
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0answers
25 views

Killing Horizon for a space-time metric

How many Killing Horizon (KH) are possible for a particular S.T. metric. Because there is a surface gravity associated to each KH, which is constant over KH surface. Do a Black Hole have many surface ...
1
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1answer
36 views

A question about metric tensor and their minors and cofactors in general relativity

In Einstein's book- 'the meaning of relativity', he says- The equation 55 mentioned is this one- I don't understand what the equation (62) means or how it can be proved. I know that the metric tensor ...
2
votes
3answers
160 views

Will the Graviton discovery mean the end of the General Relativity [closed]

I know that this question has been addressed in one form or the other however I would appreciate some other thoughts - other then "GR works so it doesn't matter what's behind it". In fact it does ...
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0answers
31 views

Does the general theory of relativity imply time dilation across the whole universe? [duplicate]

If not, why is my idea below not possible? The general theory of relativity tells us that time is slowed down by gravitational fields. We bounced radar signals off planets further from the sun, and ...
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1answer
61 views

Covariant Taylor Series

I am reading the following lecture notes of Avramidi https://www.researchgate.net/publication/255565392_Analytic_and_geometric_methods_for_heat_kernel_applications_in_finance I want to understand ...
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votes
1answer
76 views

Is the light in a Lorentzclock going slower when you travel with it with 0.9c? [closed]

In a Lorentzclock the light is bounced between the two mirrors with his speed of appr. 300.000km/s. Now when things speed up their time goes slower. But the light is always c, so in the Lorentsclock ...
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2answers
62 views

Source of Dark Energy.

In accelerated expansion dark energy play a crucial role because of negative pressure, but during expansion Dark Energy(DE) do not dilute. DE density is independent of scale factor unlike matter and ...
1
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1answer
104 views

Why not $\rho^{2}=T^{\mu\nu}T_{\mu\nu}$ as an effective mass density (squared ) in general relativity?

Why not $\rho^{2}=T^{\mu\nu}T_{\mu\nu}$ as an effective mass density (squared) in general relativity? It's covariant, and as far as I can tell is zero for any electromagnetic field tensor. \begin{...
1
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1answer
38 views

Does the Komar mass density act like a four density?

The Komar mass is a means of measuring gravitational mass in spacetime. Via Wikipedia (https://en.wikipedia.org/wiki/Komar_mass) it is stated as (for a stationary metric): $$m=\int\rho d\mathrm{vol}=\...
1
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2answers
46 views

Space-Time Geometry that shortens time intervals?

So we've all heard of the concept of time dilation and length contraction (from both general and special relativity). Suppose we work with a metric of a black hole, and person A is far, far away and ...
1
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2answers
56 views

How can I slow down? Or, How can I speed up time? Reverse twin paradox

Everyone know the standard Twin Paradox. I have my clock synchronized here on Earth with my twin. I leave Earth, Travel for a time at 0.9c, turn around, come back at .9c and then my clock is slow ...
0
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0answers
56 views

On the definition of Lagrangian

I have a question about "the definition of Lagrangian" in spacetime manifold. In general relativity, the energy-stress tensor and the vacuum energy stress tensor can be written as below: $$T_{\nu\mu}=...
0
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1answer
56 views

What is the intuitive concept of the action of a relativistic point particle? [duplicate]

The action of a relativistic point particle is its negative rest energy along its worldline, the parameter being its own proper time. $$ S = - mc^2 \int d\tau $$ (see Wikipedia) Action is energy ...
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0answers
23 views

Why the action of a relativistic point particle is considered to be negative? [duplicate]

The action of a relativistic point particle is its negative rest energy along its worldline, the parameter being its own proper time. $$ S = - mc^2 \int d\tau $$ (see Wikipedia) Is there a ...
6
votes
4answers
780 views

Can general relativity be explained by equations describing a fabric of space embedded in a flat 5-dimensional Minkowski space?

Does such a set of equations exist or does our universe have an intrinsic curvature that can't be explained by an embedding in a flat Minkowski space of 1 higher dimension? Even if general relativity ...
0
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2answers
54 views

Does the expanding universe prove the theory of relativity wrong? [duplicate]

I recently read an article which said the the universe is expanding with a very high velocity, which is even a lot faster than the speed of light. So, doesn't this prove Einstein's theory wrong which ...
1
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1answer
55 views

Black Hole: mass density or energy density? [closed]

Recently, I read a quora post in which the OP asked the following question: Can a black hole be formed from accelerating a body and increasing its relativistic mass to the level of a Schwarzschild ...
3
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1answer
52 views

Effective Potential in General Relativity

I would like to clarify a concept about the Effective Potential in General Relativity when the kinetic energy term is not unitary. Suppose (in spherical coordinates) one has a generic line element of ...
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2answers
130 views

How exactly does string theory make general relativity and quantum mechanics compatible?

Correct me if I'm wrong, but the reason that quantum mechanics and general relativity are incompatible is because the quantum foam at Planck scales renders space-time discontinuous and doesn't allow ...
0
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1answer
77 views

Showing $m_I = m_g$ follows from the equivalence principle

The inertial mass of an object is defined as its resistance to acceleration by $\vec{F}_{net} = m_I\vec{a}$. The gravitational mass of an object is defined as the scaling of the gravitational force an ...