# Tagged Questions

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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### Does the concept of curved spacetime for spatial distances hold only inside of the observable universe?

What is the spatial distance of two stars, if each of them is outside of the observable universe of the other? Even by the means of a thought experiment, we could not synchronize the two clocks of ...
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### 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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### Visualizing gravity

When you see graphics trying to help people visualize what gravity in Einstein's relativity "looks" like it will often be a mostly two-dimensional plane with a concave warp where a massive object is ...
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### Capacitors in space [closed]

I'm new here and I have a question for all of you. What happens to a capacitor in open space? There are different kind of them, which one of these is better to use there? And... We know that if we ...
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### Acting for a covariant derivative on charged spinor [closed]

For field, theory what i know $i.e$,complex scalar QED \begin{align} D_\mu \phi = \partial_{\mu} \phi - i Q A_{\mu} \phi \end{align} and \begin{align} D_\mu \phi^{\dagger} = \partial_{\mu} \phi^{\...
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### Photon pair production at relativistic speeds?

This is probably an obvious question, but I don't see it answered anywhere. Imagine we have an object in the Universe that is traveling, relative to the Milkyway at about .99999999999999999999999999c ...
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### Can a black hole fall into another black hole's innermost stable orbit?

Can a black hole, in principle, fall into another black hole's innermost stable circular orbit?
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### Fast moving black hole with low rest mass [duplicate]

Sorry for probably very stupid questions but.. If the massive body with small mass (one of the twins, for example) accelerates until the speed close to the speed of light, the mass of this body as ...
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### Textbook on Differential Geometry for General Relativity [duplicate]

I'm going to start self-studying General Relativity from Sean Caroll's Spacetime and Geometry: An Introduction to General Relativity. I'd like to have a textbook on Differential Geometry/Calculus on ...
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### Can an inhabitant of a spacetime region measure its curvature tensor?

So, lets say that I am an ant living on a 2-D spherical surface that is stretching to the equator...like half a sphere. I can not describe this surface in terms of the outside coordinates only someone ...
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### Local frame of reference

I am currently simulating particle trajectories in Kerr spacetime numerically with $M=1$ and $a=1$. In the picture above, I am calculating the geodesic in Boyer-Lindquist coordinates. I was messing ...
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### Geometrical point of view of the harmonic constraints ($\Delta g_{ij}=0$) in General Relativity

What does it mean, from the geometrical point of view, use (in General Relativity) of the constraints on the metric tensor's coefficients such that $\Delta g_{ij}=0$? (where $\Delta$ is the Beltrami-...
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### Hughston, Todd General Relativity Problem 5.2

Hey everyone I am trying to solve the following problem in Hughston Tod: A manifold is endowed with a connection such that $$(\nabla_a\nabla_b-\nabla_b\nabla_a)V_c=T^d_{ab}\nabla_d V_c$$ For any ...
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### Difference or relation between ADM mass, Brown-York Quasi-local mass, Komar mass

Can you give me some explanations for difference or relation between ADM mass, Quasi-Local mass and Komar mass? What i know about is there is some relation between ADM mass and Quasi-local mass. (i....
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### Nambu-Goto and Polyakov Actions

This might be a little bit of a technical question, so bear with me. Ok, so from string theory we know that the action for a relativistic string is found from the worldsheet when we embed the string ...
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### Metric transformation, polygons and gravitons

I'm trying to understand the paper by Hitchin called: ''Polygons and gravitons". I'm stuck at page 471. At this point, he does some computations and obtains a metric:  \gamma dz d\bar{z}+\...
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### Position / velocity / acceleration vs time graphs when falling towards a black hole

In Newtonian physics, as far as I understand it, for a small object falling towards a massive object, the graphs of position, speed and acceleration vs time look like this: (If the massive object ...
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### Can molecules/atoms/any subatomic particle cause space time curvature?

Space-time curvature is caused by huge objects in space like black holes, merging black holes, or planets. This curvature is what causes gravity. Can molecules cause at least a really tiny curve ?
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### View of the sky from inside a black hole

Consider an observer located at radius $r_o$ from a Schwarzschild black hole of radius $r_s$. The observer may be inside the event horizon ($r_o < r_s$). Suppose the observer receives a light ray ...
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### Confusion with conclusion to positive mass theorem

I am trying to understand the positive mass theorem as it is presented in the survey paper by Corvino and Pollack http://arxiv.org/abs/1102.5050 I am fundamentally confused by the structure of their ...
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### What is the difference between $\theta^{0}_{n}$ and $\theta_n$ in Strong gravitational lensing?

I am currently studying the strong gravitational lensing effects by general relativity. However, when studying these effects I came across several paper (especially these two papers, Paper One and ...
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### Is critical mass of fissile material the same in gravitational fields with different force?

Let's take plutonium-239 for example. $10\, Kg$ (sphere $9.9\, cm$) need for a nuclear reaction. Are we talking about these numbers in Earth environment with $\approx 9.8\, m/s^2$ gravitational ...
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### Lorentz surfaces, conformal metrics and eigenvalues

From what I understand of Lorentz surfaces (spacetimes of dimension 2), it seems that, according to Kulkarni's theorem, two reasonable enough Lorentz surfaces (I am only interested in surfaces with ...
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In general relativity, we can write the geodesic equation as a contraction $v^\alpha \nabla _\alpha v^\mu = f(\lambda)v^\mu$ along a path defined by coordinates $x^\mu(\lambda)$, and where $v^\mu = \... 1answer 252 views ### Geometric formulation of the equivalence principle Let$(M,g)$be a$4$-dimensional Lorentzian manifold. It is well know that given$(U,\psi=(x^1,\ldots,x^4))$local chart around some$p\in M$, it is posible to find a change of coordinates given by$(...
I am trying to calculate gravitational time dilation with the following formula: $\exp\left(\dfrac{1}{c^2}\cdot-\dfrac{GM}{h}\right)$, where $-\dfrac{GM}{h}$ is the integral of the g function, and \$\...