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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Why is $S^1\times\mathbb{R}^{n-1}$ the topology of $AdS_n$?

Anti-de Sitter $AdS_n$ may be defined by the quadric $$-(x^0)^2-(x^1)^2+\vec{x}^2=-\alpha^2\tag{1}$$ embedded in ${\mathbb{R}^{2,n-1}}$, where I write ${\vec{x}^2}$ as the squared norm ${|\vec{x}|^2}$ ...
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165 views

Violating Cosmic Censorship

Let's say we try to remove the event horizon of a Kerr black hole by throwing in matter with some large angular momentum. If it starts with GM > a, could we increase a at all? Would such a particle be ...
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1answer
71 views

Friedmann Equations with varying G?

If Newton's constant $G$ actually varies with cosmological time $t$ would a suitably modified form of the Einstein field equations: $$G_{\mu \nu} + \Lambda g_{\mu \nu} = \frac{8 \pi G(t)}{c^4} T_{\mu ...
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170 views

Relation between impact parameter and distance of closest approach of a light ray in Schwarzschild Geodesics

The following wikipedia articles are incompatible : Two body problem / bending of light by gravity Schwarzschild geodesics / bending of light by gravity According to both articles, the equation ...
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66 views

Show that two families of curves are orthogonal (without using orthogonal trajectories)

I'm reading through Hartle's General Relativity and came across this question: Consider the following coordinate transformation from rectangular coordinates $(x,y)$, labeling points in the plane ...
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302 views

Suggested reading for quantum field theory in curved spacetime

I want to learn some QFT in curved spacetime. What papers/books/reviews can you suggest to learn this area? Are there any good books or other reference material which can help in learning about QFT ...
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3answers
131 views

About the speed of light and gravity

I read (I think ) that part of relativity theory is that a strong gravitational field distorts the uniform passage of time. If this is true and a lightwave 'travelling' to Earth passes a star near ...
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1answer
151 views

Is the cosmological redshift caused by the Planck mass increasing?

The standard explanation for the cosmological redshift is that photons emitted from far away galaxies have their wavelengths lengthened as they travel through the expanding Universe. But perhaps the ...
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945 views

Is gravitational time dilation different from other forms of time dilation?

Is gravitational time dilation caused by gravity, or is it an effect of the inertial force caused by gravity? Is gravitational time dilation fundamentally different from time dilation due to ...
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5answers
151 views

Can the equivalence principle be shown to follow from special relativity?

Einstein showed in various papers that the energy content of a body was a measure of its inertial mass. If you increase the internal energy of a system while keeping the center of energy at rest, its ...
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1answer
161 views

$L^{1}$ energy-momentum tensors in general relativity; semi-classical gravity

I was unsure whether to pose this question in a physics or mathematics forum, but it is an interesting idea I have been thinking about for some time. In any (semi-)classical field theory it is often ...
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1answer
187 views

What happens when an electron jumps through the event horizon of a black hole?

If quantum teleportation is performed into a black hole (by an electron for example), what happens to that electron? Let's say a hydrogen atom is very close to a black hole and the electron jumps ...
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1answer
187 views

What are the anomalies with General Relativity?

If general relativity is the newest model of Gravity which is so far been proven. Does it still have any anomalies such as the problem of Mercury's orbit during Newtonian gravity period? If so are ...
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72 views

$M^{+}_4$ Randall-Sundrum Brane Calculation

The basic Randall-Sundrum model is given by the metric, $$\mathrm{d}s^2 = e^{-2|\sigma|}\left[ \mathrm{d}t^2 -\mathrm{d}x^2-\mathrm{d}y^2 - \mathrm{d}z^2 \right]-\mathrm{d}\sigma^2$$ where $\sigma$ ...
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1answer
103 views

Do Gravitational Waves Actually Repel Spacetime?

I read something explaining that g-waves actually repel space-time. It described the following. Mass bends space-time creating gravity. An object like the sun, if it suddenly disappeared the ...
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202 views

Differential geometry of Lie groups

In Weinberg's Classical Solutions of Quantum Field Theory, he states whilst introducing homotopy that groups, such as $SU(2)$, may be endowed with the structure of a smooth manifold after which they ...
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192 views

Evaluating the Einstein-Hilbert action

The Einstein-Hilbert action is given by, $$I = \frac{1}{16\pi G} \int_{M} \mathrm{d}^d x \, \sqrt{-g} \, R \, \, + \, \, \frac{1}{8\pi G}\int_{\partial M} \mathrm{d}^{d-1}x \, \sqrt{-h} \, K$$ ...
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111 views

Are covariant derivatives of Killing vector fields symmetric?

I'm reading the Lecture Notes on General Relativity by Matthias Blau, and in section 9.1 (point 1) he writes: Let $K^\mu$ be a Killing vector field, and ${x^\mu(\tau)}$ be a geodesic. Then the ...
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293 views

Does a black hole have enough time to actually form a singularity?

I am trying to wrap my head around black holes, singularties and hawking radiation. Physics.se contains many intresting questions and answers, but from none I could so far read about the interaction ...
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1answer
85 views

Acceleration in stationary spacetime

How would I show the acceleration vector $ a^\mu = u^\nu \bigtriangledown_\nu u^\mu = \bigtriangledown^\mu lnV $ for an observer instantaneously 'at rest,' where $u^\mu = dx^\mu/d\tau$ and $V^2 = ...
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1answer
69 views

Modified gravity and dark energy

Is there a model of modified gravity that either was close to or have succeeded in modelling the problem of dark energy, and suffers from no instabilities and explains the observational data. Also has ...
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3answers
352 views

Why Hausdorff and Paracompact manifold in GR?

What can we say about the transition map if the manifold is a Hausdorff space? Why do we need the manifolds to be Hausdorff and paracompact in General Relativity?
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How to measure the curvature of the space-time?

I know G.R. change our vision of space and time as a unique surface than can bend. We can associate the curvature of the space-time as the gravity created by the mass of planets, stars... But how can ...
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382 views

Building a wormhole

We regularly get questions about wormholes on this site. See for example Negative Energy and Wormholes and How would you connect a destination to a wormhole from your starting point to travel through ...
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88 views

Why does gravitational lensing bend light rather than absorbing it?

I've read that gravitational lensing bends the light; I am a little confused about black holes and why lensing produces different results. Black holes absorb light whereas lensing should have also ...
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85 views

Photons emitted at the event horizon?

While looking through the questions, a came across a section about black holes. I immediately though; what would happen if an atom is orbiting a black hole and emitted a photon perpendicular to the ...
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173 views

Is energy conserved in general relativity? Does $\nabla_aT^{ab}=0$ represent the conservation of energy and momentum?

For example, the radiation dominated cosmology, the energy density of radiation is propotional to $a^{-4}$ and the volume is propotional to $a^3$, where $a$ is the scale factor. So the total energy ...
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28 views

2 Event Horizons come into contact [duplicate]

Just a question out of curiosity, what would happen if the event horizons of 2 black holes of the same mass were to come into contact? Would both gravitational accelerations be canceled where the ...
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2answers
77 views

Mass of a black hole

I know that if a star collapses into a volume with radius less or equal to the Schwarzschild radius $r_s=\frac{2GM}{c^2}$ then a black hole is created and it has the same mass of the star that gave it ...
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1answer
83 views

What is the energy of a black hole?

This might be a stupid question but given Einstein's general theory of relativity $E = m c^{2} $ what is the energy of a black hole? Isn't the mass of a black hole infinite? Wouldn't that be infinity ...
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0answers
87 views

'hypersurface orthogonal' component of covariant derivative of normal vector

I believe that answer to my question is rather trivial but I can't seem to get my head around it. In context of ADM formulation of gravity (or any other differential geometry context, I guess) the ...
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1answer
74 views

How to find solutions to the gravitational potential metric h

I'm working on a problem in which a star of mass M1, radius R1 is surrounded by a thin shell of mass M2, , radius R2. I want to find the solutions to the gravitational potential h in the region in ...
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139 views

How come that an Infinite universe will collapse under gravity?

In this PSE post the issue is about the stability of an infinite universe under Newtonian gravity. Here I'will drop the Newtonian constraint because we know of the finite speed of interactions and I ...
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2answers
205 views

What is the meaning of space-time curvature?

What is the difference between the Space-time curvature and Space curvature?
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315 views

Does GR really allow superluminal movement?

In this video, Michio Kaku says "...general theory of relativity, where it is possible, we think, that you might be able to go faster than the speed of light..." Does GR really allow ...
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1answer
96 views

Ricci tensor of direct product of manifolds

Imagine I have a (Lorentzian) manifold with a metric $\left[ {\begin{array}{cc} g_{\mu\nu} &0\\ 0&g_{mn}\\ \end{array} } \right]$ Will the Ricci tensor be also block diagonal ...
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2answers
183 views

Cosmological constant doubts

I have read about cosmological constant given by einstein in universe in nutshell as well as in general and special relativity. But still I am not able to understand the aim to use it or to introduce ...
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1answer
70 views

Can weakness of gravity explore new dimensions

Since gravitational force is weakest force out of the four fundamental fources at the microscopic level. Is it possible that gravitational force is strong in a particular direction at a new ...
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0answers
95 views

QFT in curved space [closed]

Can someone exactly tell me what one gains from doing QFT in curved space, and how reliable these new results are. I want to know if it is worth while putting some man hours towards this. Please ...
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112 views

Why is the Ricci tensor diagonal for isotropic spacetime?

I'm reading Zee's Einstein Gravity in a Nutshell and while calculating the Ricci tensor for FRW spacetime he claims that because the spacelike slices of constant $t$ are rotationally invariant, the ...
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3answers
89 views

Would an Object Near a Pre-Blackhole Star Experience the Same Gravity as Post-Blackhole?

My question was inspired by this question, which got me thinking. According to Newton's Law of Gravitation, $$F = G\frac{m_1m_2}{r^2},$$ the gravity of an object is inversely proportional to the ...
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1answer
73 views

How to derive the schwarzchild metric?

I'm having trouble differentiating the following when making a change of co-ordinates to determine the Schwarzchild metric. $$r'^{2}=r^{2}C(r)$$ Then taking the total derivative of both sides, the ...
3
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1answer
281 views

The Spin Connection

Why do we need to introduce the spin connection coefficients $\omega_{\mu \space \space b}^{\space \space a} $ in General Relativity? To me, they just look (mathematically) like the Christoffel ...
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50 views

Rigid rectangle in Schwarzschild

Say I build a perfect rectangle. Side lengths $l_1$ and $l_2$ and perfect right angles. I am on earth and the metric is given by the Schwarzschild metric. Setting $dt=0$ leads to the spatial ...
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1answer
98 views

Metric for infinite straight cosmic string

A string theory question on my general relativity problem set: Metric is given as $$\mathrm{d}s^2 = -A(r)\mathrm{d}t^2 + B(r)\mathrm{d}r^2 + r^2 \mathrm{d}\theta^2.$$ a) Solve the vacuum equations ...
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2answers
122 views

What is the notion of a spatial angle in general relativity?

Is there a notion of spatial angles in general relativity? Example: The world line of a photon is given by $x^{\mu}(\lambda)$. Suppose it flies into my lab where I have a mirror. I align the mirror ...
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309 views

The difference between The Dilaton and The Radion?

I have read this question on the Dilaton, but I am a little confused with the distinction between the Dilaton and the Radion. I definitely have the feeling that these two scalar fields are different ...
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Wouldn't angular momentum of a binary star system decrease?

Consider a binary star system, as these stars go around one another they would emit gravitational waves. Since, the graviton is a spin 2 particle. Wouldn't the angular momentum of the stars decrease? ...
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Why gravity is a spin-2 field? How can I read the spin from Einstein-Hilbert action?

I have often heard that the gravitational field has spin $2$. How can I read the spin of the field from the Einstein-Hilbert action $$S=\int \! \mathrm{d}^4x \,\sqrt{|g|} \, \mathcal{R} \, \, \, ?$$
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Instabilities in the CDMT

Could anyone explain or refer to references on why the CDMT f(R) gravity model suffers from Instabilities any why the sign of ${\mu}^{4}$ matters.