A theory that describes how matter produces and responds to 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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Setting $\delta R =0$ on boundary of hypersurface

Does requiring $\delta R=0$ on the boundary of hyper-surface create any restrictions or problems in deriving the field equations from Einstein-Hilbert Action?
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183 views

Space and the size of infinity [duplicate]

If you could build a spaceship and keep travelling in one direction, what would finally happen? One answer is that you would never ever reach the end. But this sounds purely platonic space and comes ...
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1answer
100 views

Time Dilation Effects from simply being on a spinning planet orbiting a star in a rotating galaxy in an expanding universe.

I am a layman, so take this with a grain of salt. I saw a TV show the other day which showed a Russian Cosmonaut who had spent more time in space than any other human. The relativistic effects of ...
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1answer
110 views

Energy-momentum tensor for dust

We all know that the energy-momentum tensor for dust is just $T^{\alpha\beta}=\rho_0v^\alpha v^\beta,$ where $\rho_0$ is the mass density in the dust's rest frame and $v^α$ is the dust's ...
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423 views

How does time dilate in a gravitational field having a relative velocity of v with the field?

Consider a Mass on earth. The time dilation on the surface of Earth is $$T' = T \sqrt{1 - \frac{2GM}{rc^2}}$$ Now if the mass is moving around the earth at velocity of v w.r.t Earth, what will be ...
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736 views

Can Flow of time become still?

According to theory of time dilation, flow of time slows down significantly at the speed of light.Is there any conditions practically or theoretically when flow of time is reduced to zero means it ...
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1answer
131 views

How Would an Alcubierre Drive “ride” a Wave of Spacetime?

The colloquial explanation is that the spacetime in front of a ship contracts and the spacetime behind expands. I see how one could think that this would bring you closer, but I don't see that it ...
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1answer
339 views

How to prove that a spacetime is maximally symmetric?

In Carroll's book on general relativity, I found the following remark: In two dimensions, finding that $R$ is a constant suffices to prove that the space is maximally symmetric [...] In higher ...
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249 views

If NASA could send a camera into a black hole, could we then see what's inside the black hole?

Inspired by Stephen Hawking I recently tripped upon an idea of what is really inside a black hole. I thought if NASA (or any other space agency) could send a super protected camera into a black hole, ...
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83 views

Klein Gordon eq. expressed with Killing fields

I have a question on the reformulation of the Klein Gordon equation in terms of Killing fields. Suppose we have a static spacetime with timelike Killingfield $\xi^{\mu}$ (e.g. Schwarzschild). Then ...
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1answer
91 views

What's wrong with Schwarzschild equations?

I don't know much about black holes physics and so I find the Schwarzschild equations with a few contradictions. In particular I am trying to understand this little puzzle. The Schwarzschild ...
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120 views

What do we learn from gravity in three spacetime dimensions?

The last decades there has been a lot of research going on in the the area of three dimensional gravity. The motivation, I understand, is threefold: Whereas gravity is not perturbatively ...
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993 views

Does space curvature automatically imply extra dimensions?

Total newbie with basically no physics knowledge here :) I would welcome any correction to the steps of my reasoning that lead to my question, which could easily turn out to be invalid :) My current ...
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2answers
262 views

Do photons and cosmic rays radiate energy through gravitational waves? If not, why not?

Due to the mass-energy equivalence, both matter and EM radiation bend spacetime, and both are capable of forming singularities (black hole, white hole/kugelblitz). In light of this, why do photons ...
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1answer
141 views

Would a collapsing Universe have the density of water?

I understand that the typical density of the super massive black hole is close that of the water. It is also my understanding that this density is not true matter density because the volume used to ...
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1answer
99 views

Normal to the Hypersurfaces

I am trying to understand the derivation of the Hilbert-Einstein action. However it requires a knowledge about hyper-surfaces for the boundaries of the integrals and also about the normal to the ...
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30 views

Do early-time black-hole infallers ruin effective field theory at the horizon for late-time observers?

I have an elementary confusion about black hole physics. The standard consensus is that if I fall into a black hole, at the horizon I don't see any violations of effective field theory for a large ...
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0answers
88 views

Wald General Relativity, Chap 7.1

On page 166 of Wald's General Relativity book, he claims that the equation (7.1.20), $$ 0 = R^t{}_t + R^\phi{}_\phi = (\nabla_a t) R^a{}_b \xi^b + (\nabla_a \phi) R^a{}_b \psi^b, $$ yields (7.1.21), ...
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328 views

The problem of self-force on point charges

Allow me to preface this by stating that I am a high school student interested in physics and self-studying using a variety of resources, both on- and off-line, primarily GSU's HyperPhysics website, ...
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2answers
128 views

What is the meaning of “background” in General Relativity?

I was reading a book on Topological defects of the very early universe as an example of the fundamental groups, and they say that "in an expanding homogeneous and isotropic universe, the background ...
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0answers
134 views

Has the Reissner-Nordstrom metric ever been experimentally verified?

In contrast to the solution of the conventional Reissner-Nordstrom problem, where the Schwarzschild metric takes on an additional $1/r^2$ term due to the added electric charge, P. Mannheim has in ...
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0answers
74 views

Moment of Inertia in SR/GR & Calculating it in General

In classical mechanics you want to calculate the moment of inertia for hollow & solid: lines, triangles, squares/rectangles, polygons, planes, pyramids, cubes/parallelepiped's, circles, ellipses, ...
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2answers
109 views

The speed of light as it approaches a massive body

No matter how fast you go, you will aways perceive the speed of light as constant. Taking that as a fact, the special relativity theory was formulated. Now, for what I understand about general ...
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1answer
114 views

Definition of vacuum in field theory; Connection between the classical definition and the connection to QFT

I am a bit confused by what is defined to be a vacuum in field theory. Classically a vaccum state is defined to be the state where the field sits at some minima of the potential $\frac{\partial ...
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1answer
40 views

Twin paradox on a cosmic scale

I am referring to yet another version as the classical twin paradox. In my version the moving apart of the twins is entirely induced by space expansion between them and they move apart each other at ...
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73 views

Timelike Shell Collapsing into a Black Hole

Does anyone know where I can find the solution for a spherically symmetric thin shell of timelike matter falling into a Schwarzschild black hole? The matter should be pressureless, so that each ...
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5answers
351 views

What is the relation between General Relativity and Newtonian Mechanics?

What is the relationship of General Relativity and Newtonian Mechanics? Namely, which laws does GR replace of Newtonian Mechanics, and which laws of Newtonian Mechanics are incorporated into it. Or is ...
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47 views

Does a black hole singularity last essentially no intrinsic time? [duplicate]

Reading an interesting article on a recent ArXiv paper by Carlo Rovelli and Francesca Vidotto on so-called Planck stars, at https://medium.com/the-physics-arxiv-blog/6cf7ec0ed28b I was struck by the ...
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82 views

Modelling a matter dominated universe collapsing into a black hole

With the FLRW equations we can get solutions for a matter dominated closed universe in which the finale is an ultimate collapse, but this is only in terms of $a$ (the scale factor) and $t$ (time) and ...
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1answer
75 views

What is actually universe? only matter or both matter and space? [duplicate]

I have googled for the "meaning of universe" where I found the following: "all existing matter and space considered as a whole; the cosmos. The universe is believed to be at least 10 billion light ...
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4answers
257 views

Is it possible to escape from within event horizon?

I always think that it is not possible to escape from within event horizon. However, some one recently told me with deep conviction that it is possible with sustained energy output. I countered with ...
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0answers
94 views

Curvature based derivation of Schwarzchild Metric

I'm a third year maths undergrad and I'm trying to find (and follow) a curvature based derivation of the Schwarzchild metric, if there exists such a proof?
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1answer
48 views

Ensuring globally hyperbolic geodesically-complete spacetimes

Let's say we have an incomplete spacetime A that is globally hyperbolic, does there necessary exist a globally hyperbolic completion? My guess is no, in which case what further restrictions can be ...
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122 views

Does gravity cause spacetime to bend? [closed]

Does gravity cause spacetime to bend even though space has no mass?
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1answer
241 views

Riemannian manifold: Integration by parts of Lie derivative

How can we apply integration by parts to the Lie derivative? Background: In the Hamiltonian formulation of general relativity, we have the momentum constraint (using abstract index notation, $D_a$ is ...
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3answers
180 views

Another question about wormhole traversability in General Relativity

It is well known that stable, traversable wormholes require exotic matter that violate the dominant energy conditions. For the purpose of the question, let's assume enough exotic matter can be ...
6
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2answers
267 views

Must every isometry have an associated Killing vector?

I understand that the flows of Killing vector fields are isometries, and that one-parameter groups of isometries have an associated Killing vector which generates them, but are your Killing vectors ...
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0answers
57 views

Warped AdS${}_3$ and symmetry breaking

In this article it is explained how on can (in suitable coordinate basis) get a so called warped AdS${}_3$ black hole, by introducing a warping factor. The original metric in 'Euler coordinates' for ...
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2answers
110 views

Hawking evaporation is due to NEGATIVE mass?

So I have seen an animation about Stephen Hawking (after his recent study state universes claim) that Hawking evaporation is due to negative mass; But how is this possible? I mean, there is no such ...
4
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2answers
113 views

Twin paradox with two intertial frames in general relativity

I assume the twin paradox from special relativity is well known. I wish to focus on the apparent symmetry of the problem: both observer seems to move away from each other, and then come back. Yet, the ...
3
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0answers
75 views

Why is general relativity considered to be a gauge theory? [duplicate]

I have studied the first five chapters of Carroll's book (up to the Schwarzschild solution). I see similarities to the Yang-Mill theories such as the covariant derivative to account for curvature in ...
2
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2answers
171 views

Changing vector basis in AdS$_3$

I have AdS${}_3$ given as a surface embedded in a 4 dimensional pseudo-Riemannian space $$x^2+y^2-u^2-y^2=-l^2$$ With metric: $$ds^2=dx^2+dy^2-du^2-dv^2$$ I have Killing vectors of that space ...
3
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2answers
114 views

Temperature as frequency spectrum of stress-energy tensor?

I am currently learning general relativity, and in the textbooks that I am reading, temperature seems to be treated as a scalar field, extraneous to the geometry of spacetime. This is puzzling me, ...
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2answers
577 views

Why does dark energy produce positive space-time curvature?

My understanding is that dark energy, or equivalently a positive cosmological constant, is accelerating the expansion of the universe and I have read that this gives empty space-time positive ...
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0answers
101 views

Is the new Hawking black hole all about photon launch angles?

The new Jan 2014 Hawking paper (arXiv:1401.5761v1) asserts on page 3: The absence of event horizons means that there are no black holes - in the sense of regimes from which light can't escape to ...
4
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0answers
131 views

No hair theorem and black hole entropy

The no hair theorem says that black holes rapidly converge to a state that is completely described just by their mass, spin and charge. Black hole thermodynamics says that the black hole entropy is ...
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2answers
242 views

Time Dilation in Orbits in the Schwarzschild Metric

I am wondering if there exist closed form-expressions for the time dilation experienced by an observer in different orbits around a Schwarzschild black hole, outside the event horizon, relative to ...
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0answers
200 views

Further explanation of the Penrose Conjecture

I'm currently a third year maths undergrad, writing a dissertation on the application of minimal surfaces in space. I have recently come across the Penrose Conjecture that the mass of a spacetime is: ...
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1answer
52 views

Schiff Equation in a polar orbit

I am aware that the formula for Schiff Equation in used to determine frame-dragging is: $$\boldsymbol{\Omega} = \frac{GI}{c^2r^3}\left( \frac{3(\boldsymbol{\omega}\cdot ...
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2answers
115 views

Inner products in relativity

In physics, the definition of a dot (inner) product is often between a vector (“contravariant vector”) and a covector (“covariant vector”). However, in mathematics, a dot product is always defined ...