# Tagged Questions

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.

858 views

### Difference between $\partial$ and $\nabla$ in general relativity

I read a lot in Road to Reality, so I think I might use some general relativity terms where I should only special ones. In our lectures we just had $\partial_\mu$ which would have the plain partial ...
13k views

### Why does time stop in black holes?

Everyone says that time stops in the black hole. It's a "fact". However, I have never heard everyone explaining that. Of course, I know that observer in weaker gravitational field sees that something ...
706 views

### The Big Bang in an infinite universe

If the universe is spatially infinite (and assuming, if it makes a difference, that we don't have eternal inflation), what actually happened 13.7 billion years ago? Was the energy density infinite (or ...
1k views

### Are covariant vectors representable as row vectors and contravariant as column vectors

I would like to know what are the range of validity of the following statement: Covariant vectors are representable as row vectors. Contravariant vectors are representable as column vectors. ...
107 views

### What's the definition of distance in curved space-time in general relativity?

While I'm learning general relativity, the definition of the distance really confuses me. For example, we observe the distance between the Earth and the Sun (usually by a transit of Venus), what does ...
651 views

### How to show that every Killing vector field is a matter collineation?

Various texts make this claim, but no proof is given. Explicitly, let $L$ denote the Lie derivative. Suppose $L_X g_{ab} = 0$ for some vector field $X$, called a Killing vector field. Suppose that ...
588 views

### Equivalence principle and radiation from falling particle

I am currently having a hard time solving a problem of GR from Lasenby's book. I can't make it more clear than by quoting the exercise: 7.2 A charged object held stationary in a laboratory on the ...
278 views

### What is the generalization, if any, of the weak and dominant energy conditions to SUGRA?

In standard general relativity, we have the null energy condition, the weak energy condition related to stability, and the dominant energy condition related to forbidding superluminal causal ...
156 views

### Kerr solution for finite collapse time

The Kerr black hole solutions gives an analytic continuation that is asymptotically flat. Some people have argued that this is another universe, but others state that the analytic continuation ...
2k views

### Is time going backwards beyond the event horizon of a black hole?

For an outside observer the time seems to stop at the event horizon. My intuition suggests, that if it stops there, then it must go backwards inside. Is this the case? This question is a followup ...
163 views

### Do semiclassical GR and charge quantisation imply magnetic monopoles?

Assuming charge quantisation and semiclassical gravity, would the absence of magnetically charged black holes lead to a violation of locality, or some other inconsistency? If so, how? (I am not ...
162 views

### What are the current experimental restrictions of the possible speeds of gravitation? [duplicate]

Somewhere I read that the Hulse-taylor binary pulsar can not differentiate between competing theories assuming different speeds of gravity. Is it mathematically true in general, that the orbital decay ...
110 views

### Charged versus rotating black holes as different kinds of wormholes

I've heard that a maximally extended charged black hole can be a traversable wormhole to the same universe whereas a maximally extended uncharged rotating black hole can only be a wormhole to ...
654 views

### Positive Mass Theorem and Geodesic Deviation

This is a thought I had a while ago, and I was wondering if it was satisfactory as a physicist's proof of the positive mass theorem. The positive mass theorem was proven by Schoen and Yau using ...
963 views

### A Hollow Black Hole

I was just reading a question about the gravity inside a hollow neutron star. It was a trivial question, obviously there is no force felt. But then it got me thinking. Suppose you had a hollow sphere ...
332 views

### Kerr Metric in Orthogonal form

I've seen the Kerr metric usually presented in the Boyer-Lindquist coordinates where there is a cross term in the $d\phi$ and $dt$ term. I've done a good bit of searching and cannot find any ...
6k views

### Black hole - white hole (collision)

A non-spinning, equally massive black hole and white hole experience a direct collision. What shall happen? What shall be the result of such a collision?
72 views

### Radiative equilibrium in orbit of a black hole

According to Life under a black sun, Miller's planet from Interstellar, with a time dilation factor of 60,000, should be heated to around 890C by blue-shifted cosmic background radiation. How they ...
273 views

### Huygen's principle in curved spacetimes

Does Huygen's principle hold in even dimensional (2m+1,1) curved spacetimes, or are there certain necessary conditions for it to hold? In other words, if I have Cauchy data for a field satisfying the ...
361 views

### Is the equivalence principle strictly fulfilled by general relativity?

The equivalence principle states The outcome of any local experiment in a freely falling laboratory is independent of the velocity of the laboratory and its location in spacetime. Any real local ...
639 views

### Does spacetime in general relativity contain holes?

Are there physical models of spacetimes, which have bounded (four dimensional) holes in them? And do the Einstein equations give restrictions to such phenomena? Here by holes I mean constructions ...
932 views

### what is the difference between a blackhole and a point particle

Theoretically, What is the difference between a black hole and a point particle of certain nonzero mass. Of-course the former exists while its not clear whether the later exists or not, but both have ...
572 views

### 6 independent Einstein field equations?

I can't understand the comment on page 409, Gravitation, by Misner, Thorne, Wheeler It follows that the ten components $G_{\alpha\beta} =8\pi T_{\alpha\beta}$ of the field equation must not ...
542 views

### Did people realize that gravity accelerated things before Einstein's elevator thought experiment?

I'm reading about the (very near) equivalence of gravitational mass and inertial mass in my undergrad GR course, and the text (Lambourne) describes this equivalence as the inspiration for Einstein's ...
3k views

### Can anyone please explain Hawking-Penrose Singularity Theorems and geodesic incompleteness?

Can anyone please explain Hawking-Penrose Singularity Theorems and geodesic incompleteness? In easy to understand plain English please.
2k views

### What role does electrical charge play in black holes?

Not having studied General Relativity, I have sometimes been puzzled by references to the behaviour for "classic" black holes — as they are popularly portrayed — as being true for black ...
547 views

### Source term of the Einstein field equation

My copy of Feynman's "Six Not-So-Easy Pieces" has an interesting introduction by Roger Penrose. In that introduction (copyright 1997 according to the copyright page), Penrose complains that Feynman's "...
3k views

### Would a wormhole in space look like anything at all?

In movie "Interstallar", the wormhole is elaborately depicted as a sphere, complete with explanation about why it is spherical, and as it is approached, it looks like a sphere containing fabulous ...
303 views

### Is dark energy around a black hole locally curved?

The repartition of dark energy in the vacuum is homogeneous all over the universe. The diagram below represents space with a black hole in the middle. The square is divided in small unit squares. If ...
86 views

### Are orbits possible in de sitter space?

Since the de sitter space has constant positive curvature does that mean that objects can't orbit around other objects?
465 views

### What would happen if a negative mass crossed the event horizon of a black hole?

If negative mass really existed and somehow a very fast traveling negative mass object reached near the black hole's event horizon. What would happen when it crosses the event horizon? According to ...
541 views

### Can gravitational waves escape from inside of black holes? [duplicate]

I understand that light cannot escape from inside of an event horizon because the spacetime curvature is too warped for photons to escape. On the other hand, gravitational waves are ripples of ...
1k views

### Are Wormholes predicted by the theory of general relativity?

Just like it predicted gravitational time dilation, gravitational lensing. What does it mean to predict something, Does it mean that we'll find wormholes in nature one day?
355 views

### Dirac operator in curved spacetime in 2 dimensions – hermitian?

I'm currently trying to learn about the Dirac equation in curved spacetime and have come across an odd remark in Nakahara's well-known textbook "Geometry, Topology and Physics" that I would like to ...
352 views

### Boundary term in Einstein-Hilbert action

Why is the boundary term in the Einstein-Hilbert action, the Gibbons-Hawking-York term, generally "missing" in General Relativity courses, IMPORTANT from the variational viewpoint, geometrical setting ...
2k views

### Does electric charge affect space time fabric?

I am confused with this question. Does electric charge affect the space time fabric? If so, why? Also if electric charge does not affect the space time fabric, how can we interpret the origin of the ...
378 views

### Behavior of black holes in higher- and lower-dimensional space-times

The behavior of black holes in 3+1 dimensional space-time as our own is rather well known: formation, event-horizon size, mass, spin, radiation etc. However, my question is what would black holes ...
Let's have metric $$ds^2 = dt^2 - dx^2 - dy^2 - dz^2 - 2f(t - z, x, y)(dt - dz)^2.$$ I need to prove that it is an exact solution for Einstein equations in vacuum for $\partial_{x}^{2}f + \partial_{... 1answer 214 views ### How does nature prevent transient toroidal event horizons? How does nature prevent transient toroidal event horizons?.. and does it really need to? Steps to construct a (transient) toroidal event horizon in a asymptotically flat Minkowski spacetime: take a ... 1answer 185 views ### Have general relativistic effects of all of the components of the stress-energy tensor been measured? The stress-energy tensor is: Have general relativisic effects of all of the components of the stress-energy tensor been measured? I've heard that the accelerating expansion of the universe is due to ... 4answers 719 views ### White Holes and Time-Reversed Oppenheimer-Snyder collapse So, the canned explanation that I always hear about why the white hole solution of the extended Schwarzschild solution is non-physical is that "The matter distribution cuts off the white hole solution.... 3answers 461 views ### Question on inflation I have two particular questions regarding the inflationary scenario. They are: 1.) What is the physical origin of the inflaton field? 2.) Why has the potential of the inflation field its particular ... 3answers 473 views ### How to connect Einstein's Special Relativity (SR) with General Relativity (GR)? How Einstein's SR becomes GR? $$ds^2=dr^2-c^2dt^2,$$ $$ds^2=g_{\mu\nu}dx^{\mu}dx^{\nu}.$$ When the$s$is constant$ds^2=0$, isn't it true? How to connect Einstein's SR with GR? What is the GR-... 1answer 462 views ### Are some gravitational wavelengths forbidden by causality? Consider a gravitational wave in linearized gravity$d_{\mu \nu}(X_{\eta}) = D_{\mu \nu} e^{i X_{\eta} K^{\eta}}$with$K^{\eta} = (-\omega t, \textbf{k})$. Let$d=| \textbf{D}|$the scalar maximum ... 2answers 527 views ### How do you explain the observed fact that “black hole” objects move? As per Newton objects with mass attract each other, and per Einstein this is further explained by saying that mass warps space-time. So a massive object makes a "dent" into space-time, a gravity well. ... 1answer 498 views ### Is there an algorithm for N body simulations in General Relativity [duplicate] I am new to general relativity but have a background in computer science. Why is it so hard to do n-body simulations in GR? For example, there could be a program which takes the properties (mass, ... 1answer 374 views ### Massless fields in curved spacetimes I read the following statement in one of Penrose's paper zero rest-mass field equations can, with suitable interpretations, be regarded as being conformally invariant. I take this to imply that ... 1answer 644 views ### How to explain centripetal force in terms or relativity At the end of a video of dropping a ball and feathers in a vacuum, Brian Cox explains that the Ball and Feathers, as understood in terms of General Relativity, aren't falling. (apologies I can only ... 2answers 132 views ### Does the escape velocity of a black hole exceed$c\$ *before* a singularity is created?
I am having trouble understanding how the following statement (taken from some old notes) is true: For a 2 dimensional space such that $$ds^2=\frac{1}{u^2}(-du^2+dv^2)$$ the timelike geodesics ...