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.

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Could an ultra-relativistic particle tunnel directly through a stellar mass black hole?

It occurred to me in passing that the Lorentz contraction of a black hole from the perspective of an ultra-relativistic (Lorentz factor larger than about 10^16) particle could reduce the thickness of ...
3
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1answer
174 views

Going through a ring of black holes

Mathematician here with a speculative physical question -- feel free to boot me if the level isn't right. Suppose one finds, or builds, a constellation of several black holes arranged in a circle. ...
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0answers
42 views

Dark energy lorentz invaraince

Dark energy (or the cosmological constant) is stated as Lorentz Invariant, form websites like: http://cerncourier.com/cws/article/cern/28917 In newtonian mechanics, this is correct. But time dilation ...
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2answers
292 views

Why does $8\pi/3$ appear in the equations describing cosmological expansion?

What is the significance of $8\pi/3$ in the first Friedmann Equation, and in the question concerning the time independence of the Hubble Constant? Is it the 'same' $8\pi/3$ that appears in the total ...
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1answer
709 views

What are the Conflicting Predictions of General Relativity & Quantum Mechanics? [duplicate]

I see a lot of questions in various sites about why the 2 theories are or aren't incompatible, I'm satisfied as to why that's the case. However it has been mentioned that both theories make ...
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2answers
535 views

Why does the event horizon of a black hole not look like a bright sphere?

All infalling matter-energy appears to an external observer as frozen in time at the event horizon. Why then is this horizon not extremely bright due to radiation that is able to escape radially? So ...
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3answers
1k views

A Cosmological horizon at the Hubble radius?

I have calculated that if one extends a rigid ruler into space by a fixed proper distance $D$ then a clock at the end of the ruler, running on proper time $\tau$, will run more slowly than time $t$ at ...
5
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1answer
135 views

Are third derivatives of metric perturbations zero?

I'm working on a problem related to fluid perturbations of stars. I'm following this paper. They start with the Einstein equation: $$G_{\alpha \beta} = 8 \pi G T_{\alpha \beta}$$ and then perturb the ...
2
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1answer
88 views

Are there bounds or measurements on the derivative of acceleration (jerk)

The title says it all. Is there a physical maximum value to the 3rd derivative of position? Common Lore says that there is not and that jerk does not play any role in physics. My guess is that there ...
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3answers
2k views

Action principle for the Electromagnetism and Gravity

Here is the formula for the stress energy tensor: $$ T_{\mu\nu} = - {2\over\sqrt{ |\det g| }}{\delta S_{EM}\over \delta g^{\mu\nu}} $$ (This follows from varying the total action $S ...
6
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2answers
517 views

The General Relativity from String Theory Point of View [duplicate]

I have a hard time understand the statement that When you only look at the classical limit or classical physics, string theory exactly agrees with general relativity Because from what I know, ...
1
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1answer
467 views

Schwarzschild solution

I am calculating for many hours and I am really confused with this exercise. Consider a comoving observer sitting at constant spatial coordinates$(r∗,θ∗,φ*)$, around a Schwarzschild black hole of ...
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2answers
407 views

Derivation of freely falling frame in Schwarzschild spacetime

Thinking about the equivalence principle, is there a nice, simple way to show that a local, freely falling frame in Schwarzschild spacetime is described by the Minkowski metric ...
0
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1answer
174 views

Can inertial mass affect gravity of the object? [duplicate]

Every time I watch this TV program that discusses about all the facts about the universe , and it came to a point where they said that as an object approaches the speed of light the mass of the object ...
1
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1answer
293 views

What happens when I increase the density of a stellar object so that its mass surpasses the Schwarzschild limit?

We know that every object that has mass, also has a Schwarzschild radius $r_s$: $$r_s = \frac{2Gm}{c^2}$$ With $G$ being Newton's gravitational constant, $m$ the mass of the object and $c$ the speed ...
4
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3answers
262 views

Basic Question About General Relativity?

I'm a layman that loves Physics. I'm also horrible at math. Having said that I have many, many questions in regards to physics and General Relativity in-particular. I will try to keep my question(s) ...
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7answers
2k views

What determines which frames are inertial frames?

I understand that you can (in principle) measure whether "free particles" (no forces) experience accelerations in order to tell whether a frame is inertial. But fundamentally, what determines which ...
2
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1answer
134 views

Membrane-reversed black holes and their relationship to white-holes

We usually think of white holes as 'thermodynamically reversed black-holes', and this kind of membranes have not been observed in our universe. However, there is some other kind of 'topologically ...
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0answers
84 views

Preservation of a scalar along geodesic trajectory

Let $u^\mu$ be the velocity of a particle , and $\xi^\mu$ be a killing vector. would taking a contravariant derivative of to scalar product $\xi_\mu u^\mu$ , and showing that it equals to 0 shows that ...
6
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2answers
230 views

AdS/CFT and boundary translational invariance

I work in quantum information theory/condensed matter and have some very basic questions about AdS/CFT correspondence. For simplicity, I would like to restrict to 1+1 CFT <-> 2+1 AdS. I apologize ...
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6answers
2k views

Why do we still need to think of gravity as a force?

Firstly I think shades of this question have appeared elsewhere (like here, or here). Hopefully mine is a slightly different take on it. If I'm just being thick please correct me. We always hear ...
2
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1answer
154 views

Does the positive mass conjecture indicate a necessity of interactions in our universe?

The positive mass conjecture was proved by Schoen and Yau and later reproved by Witten. Total mass in a gravitating system must be positive except in the case of flat Minkowski space, where energy is ...
2
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2answers
426 views

What is an analog to QM's Hilbert space in GR?

I've read that QM operates in a Hilbert space (where the state functions live). I don't know if its meaningful to ask such a question, what are the answers to an analogous questions on GR and ...
7
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0answers
167 views

What really are exotic supersymmetric black holes?

I have just read (in the black holes chapter 14 on p244 of this book Ref.1) that in string theory, when one adds an (electric?) charge $Q$ to a static black hole, one can arrive at an exotic ...
5
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2answers
329 views

Does general relativity fail in conditions with very large gravitational forces?

It is said in this wikipedia article (in the 7th paragraph) that where there exists huge masses and very large gravitational forces (like around binary pulsars), general relativistic effects can be ...
5
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1answer
235 views

Question about Komar integral derivation in Wald

I have a question about derivation 11.2.10 in Wald (page 289). Here is a screenshot of the relevant passage: I don't get the step $$-\frac{1}{4\pi}\int _{\Sigma}R^{d}{}{}_{f}\xi^{f}\epsilon_{deab} ...
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3answers
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5
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1answer
652 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 ...
5
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2answers
636 views

Does gravitational redshift imply gravitation time dilation?

The EEP is used to justify that if an observer on the ground shoots a beam of light towards a tower, then when the light reaches the tower, it will be red shifted. This is because of what happens in ...
3
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1answer
116 views

Killing vector field in terms of the tetrad basis

I have come across the following equations in Wald. For a static spherically symmetry metric $$ds^2 = -f(r)dt^2 + h(r)dr^2 + r^2 ( d{\theta^2} \sin^2{\theta}d{\phi^2})$$. If $(e_{\mu})_a$ are the ...
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1answer
381 views

Static Spherical symmetric solution of Einstein's equations with a perfect fluid

I am reading Wald for the interior solutions of a static spherical metric. Assume it to be of the form $$ds^2 = -f(r)dt^2 + h(r)dr^2 + r^2 ( d{\theta^2} \sin^2{\theta}d{\phi^2})$$ Wald states: For a ...
0
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1answer
485 views

Does the Big Bang need a cause? [duplicate]

Possible Duplicate: on causality and The Big Bang Theory Asking here in layman's terms.. When theoretical physicsists discuss the origin of our Universe, the wider consensus appears to be ...
4
votes
1answer
228 views

The metric Tensor inside a massive shell [duplicate]

Given a fixed shell with the mass of $M$ and a radius $R$ , what would be the metric tensor for $r<R$? I do know that using Birkhoff Theorem the metric for $r>R$ should be schwarzschild. I'm ...
0
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1answer
68 views

Why is it suffice to show Tensorial identity on a tensor composed of two vectors?

I've encounter many proves of Tensorail identity that begin with assuming our tensor can be written in form of: $T^{\alpha\beta}=u^{\alpha}v^{\beta}$ . As helpful is it might be, I'm not sure if its ...
4
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1answer
185 views

Is a singularity a real thing?

I've heard the work a few times now, the most recent in the star trek film. Is a singularity a real thing? If so what is it?
5
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1answer
298 views

What is a black hole?

Is there a definition of a black hole in a generic spacetime? In some books, for example Wald's, black holes are defined for asymptotically flat spacetime with strong asymptotic predictability, ...
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0answers
89 views

Would a closed field of gravity neccesarily lead to paradoxes?

I've asked wether artificial gravity, as seen in some SF-Movies, would violate known laws of physics. To recap, my idea of an Artificial Gravity (AG) system was like this: A Device that creates an ...
6
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1answer
222 views

Einstein action as a functional of the tetrad (first order formulation of gravity)

Let the Einstein-Hilbert action be rewritten as a functional of the tetrad $e$ (units shall be set to $1$) such that $S_{EH}(e)=\int \frac{1}{2}\epsilon_{IJKL}~e^I\wedge e^J\wedge F^{KL}(\omega(e))$, ...
10
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3answers
655 views

Equation of motion of a photon in a given metric

I have this metric: $$ds^2=-dt^2+e^tdx^2$$ and I want to find the equation of motion (of x). for that i thought I have two options: using E.L. with the Lagrangian: $L=-\dot t ^2+e^t\dot x ^2 $. ...
0
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1answer
85 views

What physical sense has following transformation?

Let's have an interval expression for Friedmann Universe with 3-metric of a sphere, $$ ds^{2} = c^{2}dt^{2} - c^{2}\frac{ch^{2}(Ht)}{H^{2}}\left( d\rho^{2} + sin^{2}(\rho )(d\theta^{2} + ...
1
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1answer
125 views

A physical sense of an Inertial frame

Definition clarification needed, please: I am hoping to get physical sense of an "inertial frame". Do inertial reference frames all have zero curvature for their spacetime? So is an inertial frame ...
0
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0answers
96 views

Counterpart of the Klein Gordon Equation on the “Coordinate Shell”

The relation $$\psi=Ce^{i/\hbar(Et-\mathbf{p}\cdot\mathbf{x})}\tag{1}$$ satisfies the Klein Gordon equation on the mass shell, i.e. for $E^2=p^2+m^2$. Now let's think in the reverse direction. ...
1
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1answer
467 views

Gravitational field strength and Horizon in Rindler coordinates

I came across the following statements in 't Hooft's black holes notes, but not being able to justify them. The metric in the Rindler coordinates $x=\tilde{x}, y=\tilde{y}, z= \rho \cosh{\tau}, t= ...
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5answers
471 views

Is special relativity an exact description of reality?

In discussing relativity with a (somewhat mathematical) friend the other day, I ran into a problem showing why special and/or general relativity could be considered as exact descriptions of reality ...
3
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1answer
241 views

Sign crazyness on the stress energy tensor?

I would like to know on what depends the sign of the stress energy tensor in the following formula : $T_{\mu\nu}=\pm(\rho c^2+P)u_{\mu}u_{\nu} \pm P g_{\mu\nu}$ In my case the metric is equal to ...
2
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1answer
248 views

Do physicists believe the singularity theorems to be accurate?

This question is largely based on the last post by reddit user RobotRollCall who gave some fantastic explanations of phenomena in relativity on a layman's level. About a year ago, she said: The ...
3
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2answers
815 views

Black Hole Singularity and String Theory

This question arises in a somewhat naive form because I am largely unfamiliar with String Theory. I do know that it incorporates higher space dimensions where I shall take the overall dimensionality ...
0
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1answer
156 views

the higher you go the slower is ageing [duplicate]

as per to einstein as we go far from the earth the TIME tends to slow down , so it means when I am one metre above the earth's surface , the time has slow down for me as per ...
4
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3answers
3k views

Gravitational time dilation at the earth's center

I would like to know what happens with time dilation (relative to surface) at earth's center . There is a way to calculate it? Is time going faster at center of earth? I've made other questions ...
7
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2answers
750 views

Lorentz invariance of the 3 + 1 decomposition of spacetime

Why is allowed decompose the spacetime metric into a spatial part + temporal part like this for example $$ds^2 ~=~ (-N^2 + N_aN^a)dt^2 + 2N_adtdx^a + q_{ab}dx^adx^b$$ ($N$ is called lapse, $N_a$ is ...