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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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 ...
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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 = \...
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Does time and time dilation exist in a black hole?

Since being near stronger gravitational fields causes time dilation, can this be generalized to the region beyond the event horizon? i.e , is it meaningful to say that someone outside the black hole ...
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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. ...
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854 views

Stress-energy tensor for a fermionic Lagrangian in curved spacetime - which one appears in the EFE?

So, suppose I have an action of the type: $$ S =\int \text{d}^4 x\sqrt{-g}( \frac{i}{2} (\bar{\psi} \gamma_\mu \nabla^\mu\psi - \nabla^\mu\bar{\psi} \gamma_\mu \psi) +\alpha \bar{\psi} \gamma_\mu \...
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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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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 ...
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685 views

Visualizing GR spacetime distortion in 1+1D spacetime instead of 2D space

Usually spacetime distortion due to mass in GR is visualized as a rubber sheet distorted under some massive object, like this: source or as shown in this link. But what has always bothered me is ...
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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 ...
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3answers
115 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 ...
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216 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, ...
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1answer
284 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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Are neutrinos affected by gravity?

Layman here, but EE and BS physics. I know that light is affected by gravity. But are neutrinos? During the collapse of a star into a neutron star, as the electrons join protons to form neutrons (e....
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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 ...
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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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26 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 ...
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1answer
170 views

Ernst potential from Kaluza-Klein reduction of axisymmetric space-time

Following appendix A of "Ergoregions in Magnetised Black Hole Spacetimes" by G. W. Gibbons, A. H. Mujtaba and C. N. Pope, starting from the Lagrangian $$\mathcal{L} = \hat{R} - \hat{F}_{\mu\nu}\hat{...
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Counting the number of linearly independent Killing vectors for some N-dimensional geometry of space

In symmetric spaces(for spacetimes of Einsteinian General Relativity) we would like to find the vector space of Killing vectors($\xi^{(n)}_\mu(x)$) for the given metric tensor($g_{\mu\nu})$ at some ...
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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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What is the conserved quantity of a scale-invariant universe?

Consider that we have a system described by a wavefunction $\psi(x)$. We then make an exact copy of the system, and anything associated with it, (including the inner cogs and gears of the elementary ...
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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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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{...
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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 ...
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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 ...
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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}=\...
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Why you need a graviton when you have the higgs boson?

Since I studied General Relativity I had this question running on my mind. As I see it (just taking lectures of Quantum Field Theory right now) "Why you need a gauge boson for gravity when the higgs ...
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Can we apply Schrödinger equation in Newton gravitational potential and derive the deterministic Newton's gravitation as a special case of it

We know the solutions for wave functions of a an atom of hydrogen, and the energy values as given by spectral analysis of radiation emitted by hydrogen confirms the possible energy states as predicted ...
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1answer
109 views

How to get null tetrad by metric?

How to get null tetrads ${l^a,n^a,m^a,\overline{m}^a}$ for this metric? This on is from Ryder's book (Introduction to general relativity) page 268 $g^{\mu\nu}=\begin{pmatrix} 0 & \frac{1}{c} &...
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2answers
151 views

What kind of fundamental interaction is gravitation?

Einstein showed that gravitation is not a force but a effect caused by curvature of space time. Then why does theories of quantum gravity treats gravitation as one of fundamental force?
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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}=...
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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 ...
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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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132 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 ...
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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 ...
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3answers
556 views

Locally flat coordinate and Locally inertial frame

I am having some doubts on myself regarding the above concepts in General Relativity. First, I want to point out how I understand them so far. A male observer follows a timelike worldline ($\gamma$) ...
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2answers
56 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 ...
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1answer
78 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 ...
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2answers
252 views

Confusion about gravity

I understand the “rubber sheet” model of Relativistic gravity is just an illustration, and beyond the initial issues of mixing three-dimensional objects with a two-dimensional representation of 3D ...
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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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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 ...
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The “force” of gravity is an illusion: things follow geodesics in space-time warped by mass-energy - can other forces be explained by similar models? [duplicate]

As I understand it, the force of gravity between two objects is not really a force, but appears to be so. It behaves in such a way that the Newtonian force explanation works in many cases, but the ...
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2answers
77 views

Expanding Universe [closed]

So an expanding universe has the metric $$ds^2 = g_{\mu \nu} dx^\mu dx^\nu = -dt^2 + a(t) ( dr^2+r^2 d\Omega^2)$$ where $d\Omega^2 = d\theta^2 + \sin^2\theta d\varphi^2$ as the usual spherical ...
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3answers
129 views

Two Robertson-Walker observers, at what time will a light signal be received?

Here is a question I have that is inspired by this question here. The spacetime metric of a radiation-filled, spatially flat ($k = 0$) Robertson-Walker universe is given by$$ds^2 = - dT^2 + T[dx^2 + ...
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1answer
191 views

If a point r lies in the boundary of the chronological future of another point p, why does the chronological future of r belong to that of p?

I am studying the global causality of the spacetime. Here, I come across a problem. Suppose a point $r\in \partial I^+(p)$. $I^+(p)$ is the chronological future of a different point $p$ in spacetime....
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72 views

What exactly is the relationship between gravity and acceleration?

I know that one of Einstein's key steps towards General Relativity was the realization that gravity and acceleration were related. I understand the free-falling elevator analogy, but the relationship ...
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124 views

What happens to objects sucked into a black hole after the black hole evaporates away?

Suppose an object falls into a black hole that's so massive that it wouldn't get torn apart at the event horizon. What happens to it after the black hole evaporates away? According to the theory ...
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1answer
44 views

Time dilation along a curved path

I was thinking about Einstein's elevator, more specifically, a box, say with one side labeled A and the opposite labeled B. On side A, a laser sends pulses of light to side B at equal time intervals. ...
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15 views

Flat Universe and Evolving Geometry [duplicate]

I have heard in multiple locations that in the case of a flat universe, the universe is infinite. This seems to present multiple issues: a) If a flat universe were infinite, would would the space of ...
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2answers
539 views

Doesn't the Schwarzschild metric combined with Hawking radiation imply that nothing ever gets past the event horizon of a black hole?

According to the General Theory of Relativity, the coordinate time distance per spacetime distance traveled by a particle freely falling into a black hole gets closer and closer to $0$ as the particle ...
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3answers
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What is “a general covariant formulation of newtonian mechanics”?

I am a little confused: I read that there are general covariant formulations of Newtonian mechanics (e.g. here). I always thought: 1) A theory is covariant with respect to a group of transformations ...