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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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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74 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
83 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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95 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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913 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
196 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
113 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
88 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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25 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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73 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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264 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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113 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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74 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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49 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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1answer
97 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
32 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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45 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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3answers
158 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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46 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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64 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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61 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
192 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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80 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
36 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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101 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
148 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
153 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 ...
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188 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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40 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
87 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 ...
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2answers
91 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 ...
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73 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
98 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 ...
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2answers
94 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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403 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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66 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 ...
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80 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
121 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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98 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
42 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
103 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 ...
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48 views

Do wormholes have a side to their path through space?

In theory do wormholes have a side to their path through space? What is there at a point in line with the entry and exit, would anything look different at that point in space? Could a space ant get ...
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56 views

How to move from Special to General Relativity

I have understood special relativity nicely, and right now I am trying to learn general relativity from D'Inverno's book. I an finding it rather difficult to understand the pre-requisite math (i.e. ...
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4answers
114 views

What is difference between Inertial mass and gravitational mass [duplicate]

I recently read that the mass we deal with in Equation $F=Ma$ is called inertial mass and the mass we deal with in $F=Mg$ is gravitational mass. Suppose I am taking a same ball in a free fall and in ...
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1answer
91 views

Why does the Alcubierre drive require negative energy?

The Alcubierre drive is an idea for a faster-than-light spaceship. It works by contracting space-time in front of the ship, and expanding it behind the ship. Physicists say that this requires the use ...
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2answers
203 views

What is the entropy of the universe today?

What's the entropy of the universe today? How does one go about calculating this? I've heard the statement that black holes account for the bulk of the entropy in the universe today, but don't know ...
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6answers
252 views

Curvature of Spacetime

I have been exploring for some time both the Special and General Relativity, hoping to glean at least a conceptual grasp of their basic tenets. In reading the book "Gravitation" by Misner, Thorne and ...
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If distant observers never see a black hole form in finite time how can the information paradox be a problem?

So, at least as reported in the media, the physics community is still struggling with the problem of resolving the impossibility of retrieving information from beyond the event horizon of a black hole ...
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In there such a thing as the Black Hole Information Paradox?

When I first heard about the black hole information paradox, I thought it had no content. At the time, papers about it had been written for numerous years and they keep on coming. Now that the press ...
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141 views

What is the meaning of the “expansion of space”?

When we say that "the space between galaxies is expanding," what do we really mean? For instance, if I think of space as being a Cartesian grid, then when space expands should I think of it as adding ...