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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Schwarzschild Metric coordinate sign change in $0\leq r \leq 2GM$

In the event horizon of the Schwarzschild-metric not only the time coordinate but also the radial space coordinate seems to change sign: ...
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Would the inside of a black hole be like a giant mirror?

As any light reflected or emitted from objects inside a black hole (if it is possible to be there) does not leave the event horizon and comes back inside, would it be like seeing yourself? What I ...
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Newtonian Physics vs Relativity - the results [closed]

Does anyone have examples of the results calculated by using Newtonian physics vs the same ones calculated using relativity, compared with real measurements obtained in those experiments? Please ...
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293 views

Is there any relationship between gauge field and spin connection?

For a spinor on curved spacetime, $D_\mu$ is the covariant derivative for fermionic fields is $$D_\mu = \partial_\mu - \frac{i}{4} \omega_{\mu}^{ab} \sigma_{ab}$$ where $\omega_\mu^{ab}$ are the spin ...
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The border of the System

In General Relativity, if the system accelerates, the inside of the system and the outside of the system will have different speed of time. Where is the boundary of the system? If a human ...
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Why is spacetime curved by mass but not charge?

It is written everywhere that gravity is curvature of spacetime caused by the mass of the objects or something to the same effect. This raises a question with me: why isn't spacetime curved due to ...
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Global Properties of Spacetime Manifolds

When solving the Einstein field equations, $$R_{\mu\nu}-\frac{1}{2}g_{\mu\nu}R = 8\pi GT_{\mu\nu}$$ for a particular stress-energy tensor, we obtain the metric of the spacetime manifold, ...
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52 views

Isotropy of Space

Weinberg writes in his Cosmology text "Likewise,isotropy requires the mean value of any three-tensor $t_{ij}$ at $x=0$ to be proportional to $\delta_{ij}$ and hence to $g_{ij}$, which equals ...
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52 views

de Rham Cohomology of Schwarzschild Manifold

Let $C^p(M)$ denote the group of closed $p$-forms on the manifold $M$, and $Z^p(M)$ the group of all exact $p$-forms on the manifold $M$. The de Rham cohomology is given by the quotient, ...
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86 views

proper distance and proper length

I am wondering if I mix up the notion of proper distance and proper length. I have two cuves in Schwarzschild space-time describing the flight of two photons (think of it as photons guided in by ...
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115 views

Is Space-Time a special form of energy?

I know space-time can be influenced by matter and energy, so it must be somehow mingled in with the mix of it all, but does space-time have a fundamental particle? Can we make a little bit of ...
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263 views

Space-time Topologies?

When it comes to questions of existence of bounds for PDE's and such, one must often make some assumptions regarding the topology of the space-time to use well known theorems. My question is ...
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32 views

Differences between strong, weak, and micro lensing distinct or subtle?

In gravitational lensing, there are three categories of lensing: strong, weak, and micro. As I understand it, strong lensing (just as the name implies) occurs when a source and a gravitational lens ...
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Rocky Planet in the center of System [duplicate]

We all know that mostly stars are at the center of planetary systems, but is it possible that instead of star there was a rocky planet in the center with stars (and other planets and moons) orbiting ...
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111 views

Equivalency of Gauge Conditions

How is the Lorenz gauge condition $\partial_\mu \overline{h}^{\mu \nu}=0$ equivalent to the harmonic gauge condition $\Box x^\mu=0 $?
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77 views

Trajectory of a photon around a Schwarzschild black hole?

Consider a photon coming from the infinity in a unbounded orbit to a Schwarzschild black hole (Schwarzschild radius $r_{s}$) (see this for illustration). Its impact parameter is $b$ and its distance ...
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222 views

Is there a simple layman way to explain the incompatibilities between quantum mechanics and (general) relativity to high school students?

Is there a simple layman way that I can use to explain the incompatibilities between quantum mechanics and (general) relativity to high school students (people with not much knowledge of the intricate ...
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201 views

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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159 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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64 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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79 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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50 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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212 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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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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124 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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533 views

Is gravitational time dilation fundamentally different than other forms of time dilation?

Is gravitational time dilation caused by "Gravity"...or is it simply an effect of the inertial force caused by gravity? Is gravitational time dilation fundamentally different than time dilation due ...
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102 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 kinetic energy of a system while keeping the center of energy at rest, its ...
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139 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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146 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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160 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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60 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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92 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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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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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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74 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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210 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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78 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
62 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
326 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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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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65 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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79 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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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
72 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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75 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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'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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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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Energy-Momentum Tensor under Lorentz Transformation

In relativity, the symmetric energy-momentum tensor is given by $$ T^{ij}, $$ where $T^{00}$ is the energy density and $\frac{1}{c}T^{10}$ is the momentum density. Thus: $$ \left(\frac{1}{c}T^{00}dV, ...