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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What is the matter/energy flux on the cosmological horizons?

Consider the usual standard FLRW cosmology. Depending on the model, there may be two distinct horizons around any local comoving observer: the particles (or causality) horizon and the event horizon. ...
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How do clocks, at rest wrt to us, on a saddle-shaped 2D space tick relative to one another?

Clocks placed on a 2D flat space all tick at the same rate, if we look at them when we are at rest wrt to them. On a positively curved space, the clocks show different paces if we are at rest wrt to ...
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Complex scale factor for a model in cosmology [closed]

I was calculating the scale factor versus the time but I just realized that a scale factor is a complex number in my model. What is the mean complex number for the scale factor?
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Exercise 32 from Bernard Schutz

The equation mentioned in the exercise The exercise In Bernard Schutz's 'General Relativity, there is an exercise, I don't understand how to start with. To develop a TT Gauge, we should use the ...
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Coordinate of a point in AdS spacetime

Is there any way to get the coordinate of a point located on a plane, where the plane is in AdS spacetime with Lorentzian signature (-,+,+,+)? I'm thinking that Lorentzian geometry will be involved to ...
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Interchanging dummy indices to free indices [closed]

Is there any wrong in interchanging dummy indices to free indices or vice-versa.?
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Time and speed of light in Relativity

Time running slower near a massive object, but the speed of light does not really change near a massive object, according to Relativity - it just curves. Is not time directly related to the speed of ...
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On general covariance

If newton's theory could be formulated in the language of differential geometry (symplectic manifolds), what do we really mean when we say that the theory is covariant under the Galilean group when it'...
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Obtaining the KG equation from Action

After solving the field equation for $$S = \int \sqrt{-g}dx^4[f(\phi)R + h(\phi)g^{\mu \nu}\nabla_{\mu}\phi\nabla_{\nu}\phi - V(\phi)]$$ I have obtained $$2h\square \phi + \frac{\partial h}{\partial \...
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Does spacetime exist without matter? [closed]

A citation of Einstein is: “It was formerly believed that if all material things disappeared out of the universe, time and space would be left. According to relativity theory, however, time and space ...
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Cosmological constant divergence

The cosmological constant is measured to be of the order of $10^{120} $ smaller than the value which has been calculated from quantum mechanics. As far as I know, usually this divergence is attributed ...
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Variation for the Canonical Scalar Field in $f(\phi)R$

I am trying to find the Field equation for $$S = \int \sqrt{-g}dx^4[f(\phi)R + h(\phi)g^{\mu \nu}\nabla_{\mu}\phi\nabla_{\nu}\phi - V(\phi)$$ but I could not take the variation of $$\delta(\sqrt{-g}h(\...
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Is the volume in general relativity independent or dependent on the coordinates?

The volume in curved space is calculated as: $$V=4 \pi\int_{\Omega}r^2\sqrt{g_{rr}} d\Omega$$ Is this volume dependent or independent from the chosen coordinates? As I understand it should be ...
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Time dilation from constant speed of light? [closed]

The speed of light is constant. The energy-momentum-tensor leads to a curvature of spacetime regarding Einstein's field equations. I'm wondering whether the time-dilation-part in the curvature of ...
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State of the art on Modified gravity : going beyond the 2nd order differential equations, diffeomorphism invariance breaking, extra degrees of freedom

I am going to do a state of the art on Modified gravity models. I have found a talk that presents the problematic. In particular, it is said the following things : Modifying General Relativity How to ...
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Can the Lorentz force equation in curved spacetime be derived from the Einstein-Maxwell equations?

Given the Einstein field equations, $$R_{\mu\nu} - \frac{1}{2}R g_{\mu\nu} = \kappa T_{\mu\nu}$$ that imply in particular that $\nabla_\mu T^{\mu\nu}=0$, one can show, using the explicit form of $T^{\...
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Infinite volume gain of the whole universe due to curvature of spacetime from a finite mass?

The volume in curved space of a spherically symmetric metric calculates as $$V_{prop}=4 \pi \int_{0}^{R} r^2\sqrt{g_{rr}(r,\alpha)}dr$$ where $g_{rr}(r,\alpha)$ is the rr - component of the metric ...
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Are there types of spacetime that have no symmetries?

We derive the most basic laws of physics from several fundamental symmetries (those from Noether's theorems, gauge symmetries, Lorentz symmetry...). But are there any types of spacetime where no ...
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Cosmology from within a black hole

Suppose an astronaut is travelling "into" a black hole and has already passed the Schwarzschild boundary (as described in this video). What will the universe look like to this astronaut, ...
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Thought experiment in Mach's principle - Can a void universe be considered with special relativity?

Mach's principle is based on a thought experiment in which an astronaut floats in the middle of a space devoid of all matter and all landmarks. No star, no source of energy is present, whatever the ...
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Equation of motion in quadratic gravity

I am going through the paper https://arxiv.org/abs/1502.01028 which considers the quadratic gravity with the action \begin{align} S = \int d^4x \sqrt{-g} (R - \alpha C_{\mu\nu\rho\sigma}C^{\mu\nu\rho\...
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Could time be a secondary effect due to curvature of space?

In general relativity, four-dimensional spacetime is considered and curvature is calculated for spacetime, not only space alone. However, looking deeper into the equations, many sources of symmetry ...
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What is the general dependence of volume change from mass change due to general relativity?

The volume excess of earth due to general relativity in comparison to euclidean space has been calculated to $$ \Delta V = \frac{ G M \pi R^2}{5 c^2} = 113 km^3 $$ (this is done in this physics....
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Does a volume stay constant when freely falling?

In general relativity, if a volume of particles moves unrestricted through spacetime, is their volume always conserved? Say we let a collection of particles at rest wrt each other, fall freely in a ...
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Book/Article recommendation about modified gravity (scalar/tensor/scalar-tensor theories)

Is there a book or article that discusses the modified gravity theories scalar/tensor/scalar-tensor (maybe others as well) theories? (Look at this wiki page for a general overview of the theories that ...
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Could 2D spacetime be seen as an embedded manifold?

In a chart of a 2-dimensional spacetime manifold, we can write the rule giving separation between two points as: $$ ds^2 = - dt^2 + dx^2.$$ Could we use this to imagine how space time looks like a ...
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What does size of an inertial frame mean?

It is the equivalence principle that provides the bridge between the ideal $SR$ model and the real world. According to it, we can find at each event a set of local inertial frames (LIFS), which may be ...
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Does an observer experience stronger gravity on the way towards the singularity?

I have read this question: Clearly as you approach the singularity the tidal force on a body increases. Are the fundamental forces unified in a black hole? Based on the questions on this site, ...
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What is the real world interpretation of $E = mc^2$? [closed]

Why I am asking this question: There appears to be a logical contradiction in the notion that gravity is "one thing" mass moves in gravity much differently than light (a massless particle) ...
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How fast would a clock falling into a blackhole tick relative to the reflection of a clock stationed far away?

Lets say you have two clocks, you attach one to a mirror and drop in into a black hole, while you keep the other next to you, point it towards the black hole and view it's reflection on the mirror. ...
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Why would black hole rip me apart?

According to my understanding of General Relativity, gravity is not a force and an observer which is falling freely under the influence of gravity should be considered inertial. Now, I have come ...
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Given the time dilation at the event horizon plus black hole evaporation, can anything really ever enter a black hole? [duplicate]

There are many thought experiments about what it would be like to fall into a black hole, spaghettififaction, the singularity at the center and so on. But to me it seems that no object could actually ...
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Are there any other significant radii around Schwarzschild black holes besides the four I know of?

A Schwarzschild (non-rotating, non-charged) black hole has an event horizon with radius $r_s = \frac{2 G M} {c^2}$, where $M$ is the mass of the black hole, $G$ is the gravitational constant, and $c$ ...
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What is the component of gravity other than curvature?

This question started long, but it summarizes as follows: there is light there is mass These are 'many' things for the purpose of a single force, gravity. Yet there are 'many' components of gravity: ...
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Why the proper time of photon is zero? [duplicate]

I'm currently taking classes on General Relativity, and whilst working on Geodesis equation: Find out that for mass particle q is equivalent to proper time but in case of photon the proper time of ...
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2 votes
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How compact can a thin shell be without collapsing?

I've heard of https://en.wikipedia.org/wiki/Buchdahl%27s_theorem. It states that as the ratio between a spheres radius a it's Schwarzschild radius approaches $9/8$. the pressure at the center tends to ...
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Enquiry about the gravitational redshift in "The young center of the Earth" by U.I. Uggerhøj et al

I was reading "The young center of the Earth" by U.I. Uggerhøj et al., lately, and the standard gravitational redshift equation given in the paper is: The link to the paper: https://arxiv....
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Time taken to travel by light a minimum or maximum?

I'm stuck on the following. We know that the path taken by light to travel between 2 points A and B corresponds to the path which minimises time elapsed. However, from relativity we also know light ...
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Would this method work for generating sustained arbitrarily high time dilation in the center?

Let's say we have a series of a large number of spherical shells. Each shell has twice the mass and radius as the last. There may be thin poles or ropes to make sure inner shells don't move around. ...
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How to write down the metric explicitly?

I know that we can derive Schwarchild metric by imposing torsionless condition. if the torsion vanish, we can write down spin connection explicitly by veilbein. After variation to veilbein of Einstein-...
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Challenging General Relativity Problems to Complement Weinberg's "Gravitation and Cosmology" [duplicate]

I have gone through most of MTW's Gravitation along with most of the problems within it. I am currently reading Weinberg's "Gravitation and Cosmology" which sadly does not have problems for ...
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If two object moving away from each other, does one object see the other slower than their relative speed?

Let's say I am on spaceship A and it is moving with speed of 0.6c. Also, there's other spaceship B which is moving with the speed of 0.4c opposite direction from me. And after some time in our travel, ...
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6 votes
2 answers
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Dropping a mirror into a blackhole

Say you dropped a mirror into a black hole while observing at a distance and holding a clock such that the clock's face was pointing to the black hole. What is the latest time you would view on the ...
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How to make sense of the length of a rod in Special Relativity, using the mathematical framework of General Relativity? [duplicate]

This question asks how exactly Special Relativity (SR) emerges mathematically as a special case of General Relativity (GR). In GR, spacetime is modeled as a pseudo-Riemannian manifold with generally ...
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How do asymptotic symmetries help to get information about black holes?

I've heard that asymptotic symmetries (like BMS) are used to get information about black holes just by looking at their fields. How does that work?
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What if a cosmic string is eaten by two black holes?

What happens if you have a long cosmic string, each end of which is swallowed by a different blackhole, and the black holes have trajectories that will take them further away from eachother? WHat ...
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Normal to the hypersurface

I have a given metric and I want to choose a spacelike hypersurface and find the normal to that hypersurface. I know that if the hypersurface is spacelike, then the normal is timelike. The given ...
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Identity $\nabla_{j}\partial_{i} = \Gamma ^{k}_{ij} \partial_{k}$ involving covariant derivative

I am trying to understand the identity i have came across, but i am not being able to: $$\nabla_{j}\partial_{i} = \Gamma ^{k}_{ij} \partial_{k}$$ I thought that such equality would become obviously if ...
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What is the Ricci curvature tensor in a region of sparse matter?

In empty space, where the energy-momentum tensor $T_{\mu\nu} = 0$, any solution to the Einstein field equation has Ricci tensor $R_{\mu\nu} = 0$. So what does a solution look like in a region of space ...
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Has there been any experiment trying to measure the Ricci Curvature of the universe?

One of the major component of the Einstein equation is the Ricci Curvature. As of now, I understand it mathematically as some sort of trace of the Riemann Tensor, and geometrically as the factor by ...
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