Questions tagged [general-relativity]
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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Isn't Gravity at least "sort of" predicted by QFT? [closed]
Let me say to begin with that I'm not a crackpot and don't think I've discovered anything new here. I'm a physics graduate student but not in quantum gravity but I still like the idea of unification ...
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Can 3 objects with same mass dropped from 10,000ft land in the same region/area together? [closed]
I mean specifically VERY close together, like in the same spot next to each other? And specifically, for example, objects such as 3 separate elastic band-bound bundles of €20 bills amounting to €2,000 ...
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Is there any measurement of all the observable angular momentum in the Universe?
Has the sum of all observable angular momentum in the Universe ever been evaluated? There has been a lot of efforts dedicated to the missing mass and energy problem, but has any experimental work ever ...
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Expressing curvature invariants ($K_1, I_1, ... $), at any one event, through Synge's WF $\sigma$ (given of each event pair, in a suitable region)
Considering a set $\mathcal S$ of events such that for each pair $p, q \in \mathcal S$ Synge's world function $\sigma$ is defined and the corresponding value $\sigma[ ~ p, q ~ ]$ is given, and such ...
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Three Questions on Black Holes in Penrose Diagrams [closed]
Three black hole questions for Penrose diagrams:
If we launch a particle away from a black hole that's far enough away with enough escape velocity, then obviously it will float off into space. How ...
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Recession of Galaxies vs. Black Holes [closed]
Light surrounding black holes is redshifted due to the local warping of space and its velocity relative to other objects. Why is it not possible that objects gaining infinite momentum (including mass) ...
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The Weird Interpretation for Contravariant and Covariant Vector
I have seen the answer for related topics, and it makes sense to me for the trivial contranvariant expression for a vector,
$$\pmb{v} = v^i\hat{e}_i\tag{1}$$
and it is said that if the base $\hat{e}_i$...
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What is the difference between GPE and gravitational self energy in GR?
What is the difference between gravitational potential energy and gravitational self energy in General Relativity? Are they both the same in Newtonian gravity?
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Tensor/Vector decomposition/representation & DOF arguement [closed]
In fluid mechanics, for irrotational flow it is sometimes useful to present the velocity, $U$ in terms of a scalar potential $\Phi$ as:
$$\vec{U}=\nabla \phi$$
$\vec{U}$ has 3 dof. $\phi$ has 1.
Why ...
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Is a Klein-bottle-like topology allowed for GR?
As the spacetime of the universe seems to be quite flat, a torus topology comes mind easily. How about others?
Is it issue if manifold is non-orientable? I see challenges to find 3- or 4-Klein-bottle-...
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What would happen if the aether did exist and there was no such thing as relativity? [closed]
I'm curious as to the purpose of relativity and why the universe would function this way as opposed to a universe with an aether. So what would be different if we had an aether?
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Is the term $-1/2g_{\mu\nu}R$ in the field equations of Einstein a constant energy?
Einsteins field equations are
$R_{\mu\nu} -\frac{1}{2}g_{\mu\nu}R = \kappa T_{\mu\nu}$
I'm wondering about the meaning of the term
$\frac{1}{2}g_{\mu\nu}R$.
I bring it to the right side:
$R_{\mu\nu} =\...
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Relationship between spacelike and timelike distances in General Relativity vs. Special Relativity
In Minkowski spacetime, the distance $d_S$ between two space-like separated events $x$ and $y$ can (up to constant) be given by a distance between the two time-like separated events $z$ and $w$ where $...
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Is the equation $g_{\mu\nu} = const. + T_{\mu\nu}$ equivalent to Einstein's field equations? [closed]
Is the equation
$g_{\mu\nu} =$ diag (-1,1,1,1)$\cdot$ const. + $T_{\mu\nu}$
equivalent to Einstein's field equations?
$g_{\mu\nu}$ is the metric tensor and describes the curvature and $T_{\mu\nu}$ ...
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Spatial separation in analogy to time separation in Lorentzian geometry?
O'Neill (Semi-Riemannian Geometry With Applications to Relativity, 1983, p. 409) defines time separation between two events as follows:
"If $p, q \in M$, the time separation $\tau(p, q)$ from $p$...
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Can a body escape a black hole by being thrusted? [duplicate]
I am told many time that nothing can escape black-hole because black-holes escape velocity is more than speed of light. But we know object don't necessarily have to exceed speed of light to escape a ...
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The linear growth factor of perturbations today should be 1 but I am unable to derive it
The definition of the linear growth factor $D(z)$ of perturbations in a cosmological setting is usually normalized to unity at redshift $z=0$. So,
$$\delta(z) = D(z)\times \delta(z=0) \tag{1}$$
where $...
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Extrinsic curvature, Gauss equation and Christoffel symbol contribution
This question is in the context of geometry of hypersurfaces and ADM formalism. In a $4$-dimensional manifold, we define a $3$-hypersurface with space-like tangent basis $e_a$, $a=1,2,3$, and a normal ...
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Questions about E. Minguzzi's article on Synchronization (arXiv:1009.3005)
Only recently I learned of E. Minguzzi's article
"Clocks' synchronization without round-trip conditions", [gr-qc: arXiv:1009.3005] ...
(Notably, the article available for download is dated ...
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Reduced mass vs. Total mass in gravitational wave estimations
When people do back of the envelope calculations about GW physics, they always use a very abstract mass scale $M$ and I want to figure out the identity of said scale for different relevant magnitudes ...
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Is the "capacity to do work" of a body equivalent to the concept of "resistance to change in motion"?
For any body we have $E = mc^2$, where $E$ is the capacity of the body to do work on its surroundings and $m$ is the resistance the body has to move from its state of rest. Therefore, the capacity to ...
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Meaning of Einstein's equation (Baez & Bunn) - derivation question
See this page, and this paper.
I am mostly happy with the steps from equation (7) onward.
Just before equation (6), the authors make a choice of sign that carries through the rest of the derivation. ...
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GR Action and Ashtekar Connection
Palatini action $S_{Pal}$ is (assuming Cosmological constant $\Lambda=0)$:
$$ S_{Pal}[e,\omega]=\int e\wedge e\wedge R[\omega].$$
Motion equations (varying this action) gives us Einstein Equation and
...
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Chose coordinates where $g_{01}=g_{02}=g_{03}=0$ to disentangle space and time?
$g_{\mu\nu}$ is the metric tensor. It describes the curvature of spacetime in general relativity. The choice of coordinates is completely arbitrary. It should be possible to find and chose coordinates ...
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Twin paradox - how much energy does it take to travel to the future? [closed]
In the usual twin paradox in Minkowski space, we have twins Alice and Bob. Alice stays at home. Meanwhile, Bob visits a distant planet and returns. On return, Bob has aged less than Alice. So, in a ...
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Question about relativity [duplicate]
I know when mass becomes massive we need general relativity. My question is why do we need to incorporate special relativity since the mass is not in high speed .Cant we have Newtons law of ...
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Why can't the answers to equations be infinity?
When talking about black holes and singularities, most books say that combining relativity and quantum mechanics gives the answer of infinity in some equations. They also say that:
Infinity is the ...
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When doing general relativity in practice, how do we choose the appropriate manifold describing the scenario?
The theory only deals with the local curvatures, not the global topology. Hence any manifold with an allowed metric is allowed. These can be infinitely many, especially for negative curvature space-...
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Is it possible to describe every possible spacetime in Cartesian coordinates? [duplicate]
Curvature of space-time (in General Relativity) is described using the metric tensor. The metric tensor, however, relies on the choice of coordinates, which is totally arbitrary.
See for example ...
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The limit of GR with infinite speed of light $c$
Just answer what you can. I don't mean the zero curvature flat space time version. I know that the Einstein Field equations use $c$ as a constant, but what would the universe be like if gravity was ...
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What vacuum should be defined for a observer in Kerr spacetime?
A scalar field in Kerr spacetime can have two kinds of modes, one labeled by "in", and the other by "up". The "in" modes originate from the past null infinity, while the &...
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Can either of LISA, NanoGrav or LIGO measure the polarization of gravitational wave background(GWB)?
Polarization in GWB should carry as much important information as in CMB. However, I've done some superfluous literature research and found little discussion. Is there any planned project for ...
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Hypersurface orthogonal congruences
In his book "General Relativity" on p. 226 Wald writes that the congruence of all timelike geodesics through $p$ is hypersurface orthogonal. I dont't really understand why. Can anybody help ...
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Books/resources for the study of non-flat spacetime shadows
I'm preparing a research paper (and possible review) on shadow calculation in asymptotically non-flat spacetime. I have been searching the internet for some references and the only thing I found was ...
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Allowed Topologies for General Relativity
Studying the ADM formulation of General Relativity the ADM splitting comes out from the assumption that the spacetime is globally hyperbolic.
From that assumption thanks to Geroch's theorem, it is ...
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What aspects of GR should be taken into consideration for realistic visualizations of a Kerr black hole? [closed]
I am not 100% sure if these kinds of questions are allowed, if not sorry in advance.
For the past year, me and a friend have been working on a render engine to visualize a Kerr black hole. We have ...
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Could black holes be a three dimensional object breaking through space time and falling 4th dimensionaly [closed]
I was thinking about general relativity and I was thinking about it in two dimensions where a heavy metal ball would be placed on a mesh fabric (this is just how I’m imagining it) and if the ball was ...
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Why can't we gauge the Lorentz group? (Or can we?)
One of the (many different, somewhat independent) routes to gauge theory is to start from a global symmetry of some kind and "gauge" it, which involves promoting it to a local symmetry and ...
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According the theory of general relativity, what is the role of causality in the changes of the curvature of spacetime? [closed]
In Einstein's equations the curvature of spacetime and energy-momentum-pressure density are correlated. Is it clear when changes in matter energy density affect causally to curvature and when changes ...
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Inclination angle of a ray in a static spacetime
In accordance with Synge (equation 8) of the ray with respect to the radial direction in a static Schwarzschild spacetime is
$$ \cot \psi = \left(1 - \rho^{-1} \right)^{-1/2} \rho^{-1} \frac{d \rho}{d ...
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How do changes in energy distribution update the curvature of spacetime? [closed]
Let's give the name "gravitational signaling" to the information that affects changes in curvature. For example, the Moon draws changes in the curvature controlled by the Sun as it orbits ...
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Shapiro Time Delay and Elliptic Integrals
I have been trying to determine Shapiro's Time Delay in terms of Elliptic Integrals, but getting apparently ERRONEOUS results. I start with the following integral, where b is the impact parameter, c ...
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Christoffel symbol / scalar product of co- and contravarient basis vectors
I am currently learning about the Christoffel symbole.
Given is the following equation:
$\Gamma_{nm}^{l} = e^l \cdot \Gamma_{nm}^{k} e_k$
with $e$ being an arbitrary co-/contravariant basis vector in $...
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Schwarzschild line element in Eddington-Finkelstein coordinates
I'm studying Eddington-Finkelstein coordinates for Schwarzschild metric. Adopting the coordinate set $(t,r,\theta,\phi)$, the line element assumes the form:
$$
ds^2 = \left(1 - \frac{R_S}{r}\right)dt^...
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Solve Einstein equation with self-dual field strength
I have this action
$$
S = \int d^6x \sqrt{g} \Big(R-\frac{1}{3}G_{\mu\nu\rho}G^{\mu\nu\rho}\Big)
$$
on a $D=6$ dimensional manifold with the following metric
$$
dS^2_6 = dx^-dx^+ - \sum_{i,j=1}^4 A_{...
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Explanation about black holes
As a newbie I was reading the book "The Theory of Everything", and came about these two paragraphs which I just don't understand:
I had already discussed with Roger Penrose the idea of ...
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How to prove This Equation between Riemann Tensor and Killing Vector?
How to prove This Equation between Riemann Tensor and Killing Vector?
$$
[\nabla_\mu, \nabla_\rho]\xi_\sigma = R_{\sigma\nu\mu\rho}\xi^\nu
$$
I know
$$
R(\vec{X},\vec{Y},\vec{Z})=[\nabla_{\vec{X}}, \...
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Time Dilation And Comparing Inertial And Non Inertial Reference Frames
Can we calculate the total observed time dilation on a spaceship and a planet by combining the planet's relativistic spin velocity and the spaceship's approach or recession velocity from the planet it ...
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Is curvature localised in General Relativity?
Is the curvature of spacetime in General Relativy localised?
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Tensor Index Manipulation
I am trying to study General Relativity and I thought about starting with some index gymnastics. I found a worksheet online and I am stuck with a simple problem. I have to prove that
$$\partial_{\mu} ...
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