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.

learn more… | top users | synonyms (1)

15
votes
5answers
943 views

Does GR provide a maximum electric field limit?

Does GR provide a limit to the maximum electric field? I've gotten conflicting information regarding this, and am quite confused. I will try to quote exactly when possible so as not to confuse ...
15
votes
4answers
2k views

Can spacetime be non-orientable?

This question asks what constraints there are on the global topology of spacetime from the Einstein equations. It seems to me the quotient of any global solution can in turn be a global solution. In ...
15
votes
1answer
2k views

How to prove that a spacetime is maximally symmetric?

In Carroll's book on general relativity ("Spacetime and Geometry"), I found the following remark: In two dimensions, finding that $R$ is a constant suffices to prove that the space is maximally ...
15
votes
3answers
992 views

Is simultaneity well defined in general relativity?

In special relativity for each event and reference frame we can find a plane of simultaneous events. I wonder is it possible to do the same in general case in curved space? Is simultaneity even ...
15
votes
2answers
1k views

Conformal Compactification of spacetime

I have been reading Penrose's paper titled "Relativistic Symmetry Groups" where the concept of conformal compactification of a space-time is discussed. My other references have been this and this. In ...
15
votes
2answers
627 views

Brachistochrone problem in general relativity

This question Brachistochrone Problem for Inhomogeneous Potential has the obvious extension. Namely the same question, when gravity is treated according to general relativity. To make it specific let'...
15
votes
3answers
2k views

Why can't General Relativity be written in terms of physical variables?

I am aware that the field in General Relativity (the metric, $g_{\mu\nu}$) is not completely physical, as two metrics which are related by a diffeomorphism (~ a change in coordinates) are physically ...
15
votes
1answer
971 views

If two ultra-relativistic billiard balls just miss, will they still form a black hole?

This forum seems to agree that a billiard ball accellerated to ultra-relativistic speeds does not turn into a black hole. (See recent question "If a 1kg mass was accelerated close to the speed of ...
15
votes
2answers
1k views

The Role of Active and Passive Diffeomorphism Invariance in GR

I'd like some clarification regarding the roles of active and passive diffeomorphism invariance in GR between these possibly conflicting sources. 1) Wald writes, after explaining that passive ...
15
votes
1answer
537 views

A Theorem Due to Hodge: Hawking/Ellis

This is probably quite an obscure question but hopefully somebody has a simple answer. I'm studying the proof of the topology theorem on black holes due to Hawking and Ellis (Proposition 9.3.2, p. 335 ...
15
votes
2answers
628 views

Stokes theorem in Lorentzian manifolds

I've fallen accross the following curious property (in p.10 of these lectures): in order to be able to apply Stokes theorem in Lorentzian manifolds, we must take normals to the boundary of the volume ...
15
votes
2answers
412 views

Newtonian gravity from the holographic principle?

Can one understand Newton's law of gravitation using the holographic principle (or does such reasoning just amount to dimensional analysis)? Following an argument similar to one given by Erik ...
14
votes
3answers
1k views

What is the most compelling evidence of General Relativity in the presence of matter and energy?

The most oft-cited triumphs of GR are things such as the shifting perihelion of Mercury, gravitational redshift experiments, and gravitational lensing. But, as far as I know, these are only ...
14
votes
5answers
16k views

Why can't light escape from a classical black hole?

Photons do not have (rest) mass (that's why they can move at speed of "light"). So, my question is how the gravity of classical$^1$ black hole can stop light from escaping? -- $^1$ We ignore ...
14
votes
5answers
2k views

Newton's Bucket

Newton's Bucket This thought experiment is originally due to Sir Isaac Newton. We have a sphere of water floating freely in an opaque box in intergalactic space, held together by surface tension and ...
14
votes
1answer
1k views

Why is there no dynamics in 3D general relativity?

I heard a couple of times that there is no dynamics in 3D (2+1) GR, that it's something like a topological theory. I got the argument in the 2D case (the metric is conformally flat, Einstein equations ...
14
votes
1answer
1k views

How does the Hubble parameter change with the age of the universe?

How does the Hubble parameter change with the age of the universe? This question was posted recently, and I had almost finished writing an answer when the question was deleted. Since it's a shame to ...
14
votes
6answers
1k views

Why must a singularity form inside a black hole? [duplicate]

What is the exact reason that normal matter can not exist within an event horizon? I can understand how a super-dense object like a neutron star could accrete mass until its physical radius is less ...
14
votes
1answer
694 views

Lagrangian for Euler Equations in general relativity

The stress energy tensor for relativistic dust $$ T_{\mu\nu} = \rho v_\mu v_\nu $$ follows from the action $$ S_M = -\int \rho c \sqrt{v_\mu v^\mu} \sqrt{ -g } d^4 x = -\int c \sqrt{p_\mu ...
14
votes
1answer
1k views

Why are anti-de Sitter spaces so interesting when we believe the universe is expansionary?

Perhaps this is a naive question, but in my recent (admittedly limited) readings about AdS spaces, I keep wondering why they seem to be such a hotbed for theoretical research (AdS/CFT correspondence, ...
14
votes
5answers
2k views

Does the amount of gravitational potential energy in the universe increase as it expands?

It seems to me that extra gravitational potential energy is created as the universe expands and the distance between massive objects such as galaxy clusters increases; this implies that energy is not ...
14
votes
2answers
1k views

If a Kerr-Newman black hole is like a charged, spinning, heavy magnet, what kind of magnet is it like?

I was reading up on De Sitter spaces, which states that the gravitational effects from a black hole is indistinguishable from any other spherically symmetric mass distribution. This makes a lot of ...
14
votes
3answers
730 views

Extremal black hole with no angular momentum and no electric charge

A black hole will have a temperature that is a function of the mass, the angular momentum and the electric charge. For a fixed mass, Angular momentum and electric charge are bounded by the extremality ...
14
votes
1answer
245 views

What happened to the black hole firewall theory?

What happened to the black hole firewall theory? Back in 2012, some physicists apparently came up with strong evidence that one of three things must be wrong for black holes to work the way we thought ...
14
votes
3answers
423 views

Is the flatness of space a measure of entropy?

This is a bit quirky: For a very long time I've found Stephen Hawking's evaporating small black holes a lot more reasonable and intuitive than large black holes. The main reason is that gravity is ...
14
votes
1answer
239 views

Is period of rotation relative?

My question is inspired by the following answer by voix to another problem: "There is a real object with relativistic speed of surface - millisecond pulsar. The swiftest spinning pulsar currently ...
13
votes
8answers
11k views

Is gravity just electromagnetic attraction?

Recently, I was pondering over the thought that is most of the elementary particles have intrinsic magnetism, then can gravity be just a weaker form of electromagnetic attraction? But decided the ...
13
votes
3answers
4k 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 ...
13
votes
2answers
833 views

How can we recover the Newtonian gravitational potential from the metric of general relativity?

The Newtonian description of gravity can be formulated in terms of a potential function $\phi$ whose partial derivatives give the acceleration: $$\frac{d^2\vec{x}}{dt^2}=\vec{g}=-\vec{\nabla}\phi(x)=\...
13
votes
4answers
567 views

Is the concept of tensor rank useful in physics?

The term 'tensor rank' is sporadically used in the mathematical literature to denote the minimum number of simple terms (i.e. tensor products of vectors) needed to express the tensor. This is ...
13
votes
2answers
2k views

Why is spacetime not Riemannian?

I apologize if this is a naïve question. I'm a mathematician with, essentially, no upper-level physics knowledge. From the little I've read, it seems that spacetime is Lorentzian. Unfortunately, the ...
13
votes
5answers
9k views

Is the total energy of the universe constant?

If total energy is conserved just transformed and never newly created, is there a sum of all energies that is constant? Why is it probably not that easy?
13
votes
3answers
989 views

Is “now” or “the present moment” properly defined in GR?

My question is about the extent to which "now" is defined in GR. In Minkowski spacetime, it's possible to define a "now" for an inertial observer by finding a spacelike 3-plane such that, in the ...
13
votes
5answers
672 views

What are some ways to justify the Einstein field equations?

Since they are a postulate of general relativity, it is not really possible to "derive" the Einstein field equations $$R_{ab} + \left(\Lambda - \frac{1}{2}R\right)g_{ab} = -8\pi T_{ab}$$ in any very ...
13
votes
4answers
824 views

Coulomb's Law in the presence of a strong gravitational field

I was under the impression that the $1/r^2$ falloff of various forces were because of the way the area of a expanding sphere scales. But that strict $1/r^2$ falloff would only be globally true in a ...
13
votes
3answers
3k views

Gravity as a gauge theory

Currently, (classical) gravity (General Relativity) is NOT a gauge theory (at least in the sense of a Yang-Mills theory). Why should "classical" gravity be some (non-trivial or "special" or extended)...
13
votes
7answers
881 views

Can a ultracentrifuge be used to test general relativity?

With today's ultracentrifuge technology, they can spin so fast that the sample can be subjected to accelerations of up to 2 millions Gs. That is equivalent to two solar masses. Has someone tried to ...
13
votes
2answers
859 views

Is spacetime simply connected?

As I've stated in a prior question of mine, I am a mathematician with very little knowledge of Physics, and I ask here things I'm curious about/things that will help me learn. This falls into the ...
13
votes
1answer
2k views

What is the maximum time dilation factor when orbiting a rotating black hole?

Suppose one spaceship is stably orbiting a rotating black hole and another is far away from the black hole. What is the maximum time dilation factor between the two ships? Can it be made arbitrarily ...
13
votes
5answers
2k views

The definition of an inertial reference frame in Einstein's relativity

I'm reading Sean Carroll's book on general relativity, and I have a question about the definition of an inertial reference frame. In the first chapter that's dedicated to special relativity, the ...
13
votes
2answers
340 views

Did merging Black Holes in GW150914 give up entropy and information to the gravitational waves, since they lost 3 solar masses?

Since the final Black Hole (BH) had 3 solar masses less of mass than the original binary BH, it seems the 2 BHs lost mass, and with it event surface area, entropy, and information. If that came from ...
13
votes
9answers
7k views

What is the difference between translation and rotation?

What is the difference between translation and rotation ? If this were a mathematics site, the question would be at best naive. But this is physics site, and the question must be interpreted as a ...
13
votes
1answer
620 views

What is the status of existing measurements of the speed of gravity?

In replying to a recent question I stated: Gravitational waves have not been yet experimentally observed so as to have their velocity measured. Which after the fact prompted me to try and verify ...
13
votes
2answers
852 views

Energy-Momentum Tensor in QFT vs. GR

What is the correspondence between the conserved canonical energy-momentum tensor, which is $$ T^{\mu\nu}_{can} := \sum_{i=1}^N\frac{\delta\mathcal{L}_{Matter}}{\delta(\partial_\mu f_i)}\partial^\nu ...
13
votes
1answer
577 views

What are the local covariant tensors one can form from the metric?

Normally in differential geometry, we assume that the only way to produce a tensorial quantity by differentiation is to (1) start with a tensor, and then (2) apply a covariant derivative (not a plain ...
13
votes
1answer
207 views

Highest symmetric non-maximally symmetric spacetime

What is the highest number of symmetries (Killing vectors) that a (4-dimensional) spacetime can have without being maximally symmetric? From what I can see, it seems to be 7 (which includes the ...
13
votes
1answer
740 views

Is this a quaternion representation of the equations of motion of General Relativity?

In The Quaternion Group and Modern Physics by P.R. Girard, the quaternion form of the general relativistic equation of motion is derived from $du'/ds = (d a / d s ) u {a_c}^* + a u ( d {a_c}^* / ...
13
votes
1answer
281 views

Gravitational collapse of a photon cloud

The Schwarzschild solution shows that a spherically symmetric, static fluid will undergo gravitational collapse if too much mass-energy is concentrated together (i.e. if the fluid's radius is less ...
13
votes
2answers
464 views

Definition of stress at the microscale

Take, for simplicity, a Lennard-Jones fluid below the critical temperature, which is to say that there is a phase separation into fluid and gas and thus an interface is formed. The macroscale picture ...
13
votes
1answer
463 views

General definition of an event horizon?

Horizons are in general observer-dependent. For example, in Minkowski space, an observer who experiences constant proper acceleration has a horizon. Black hole horizons are usually defined as ...