Does String Theory disagree with General Relativity?

I would like to expand on what I mean by the title of this question to focus the answers.Normally whenever a theory (e.g. General Relativity) replaces another (e.g. Newtonian Gravity) there is a correspondence requirement in some limit. However there is also normally some experimental area where the new larger theory makes predictions which are different from the older theory which made predictions of the same phenomena. This is ultimately because the newer theory has a deeper view of physics with its own structures which come into play in cert...Read more

General Relativity, Curvature, and extra dimensions

Setup of ideaI had somewhat of a thought question regarding general relativity. Consider a simple situation of a sphere and arrow. You hold the arrow and walk from the equator to the north pole. Turn right but hold the stick the same direction and walk back to the equator. Now turn right and return to your starting spot. The arrow now points in the direction of the equation, showing the sphere had curvature.Modification of this experimentNow consider your "surface" is not the surface of a sphere, but the whole of R3. Now instead of holding a 1 ...Read more

general relativity - Visualization of $ dtdx$ and $dxdy$ term in metric tensor

For the sake of simplicity, lets take a 2+1 dimensional spacetime.Lets take the metric $$ds^2 = g_{tt}dt^2 + g_{xx}dx^2 + g_{yy}dy^2 + g_{tx}dtdx + g_{xy}dxdy$$ What is the visualization or physical interpretation of the $g_{tx}$ and $g_{xy}$ terms of the metric? Does $g_{tx}$ mean motion of space i.e. on object in this spacetime point will be moving w.r.t an observer at infinity? What would $g_{xy}$ mean?...Read more

general relativity - Does mass compress space-time?

My understanding of relativity explains that the presence of mass warps space-time so that light travelling through the warp follows at straight line but the warp itself is curved and therefore the light seems to an outside observer (non-local reference frame) to be travelling in an arc.If the mass is sufficiently large, such as a planet-sized body, the curvature will be centred around the centre of mass (the core) and radiate out in all directions. Like a pinch at the centre of a soft foam block.Relativity points out that at different heights ...Read more

general relativity - How do we age if we tunneled to Earth's core?

ScenarioSuppose there exists an advanced technology that can hypothetically transport living humans to study the center of the Earth, as they goes deeper underground most of the Earth's mass would be above them and thus the gravity will seems lighter.QuestionQ1. I do not know if Newton's laws of gravity can be applied when a small mass is inside a big mass, any solution?Q2. According to general relativity the effect of time dilation is more prominence as gravity increases, in this scenario how will the adventurer age?...Read more

Kinetic, potential and total orbital energy in General Relativity

In Schwarzschild geodesics the total orbital energy $E$ is$$E = \dot{t} \left( 1 - \frac{r_{\rm s}}{r} \right) m \, c^2$$with the time dilation factor $\dot{t}$ in dependence of the local velcity $v$$$\dot{t} = \frac{1}{\sqrt{ \left( 1-\frac{r_{\rm s}}{r} \right) \left( 1-\frac{v^2}{c^2} \right)}}$$so plugged into the equation for $E$ we get$$E = \frac{m \ c^2 \ (r-r_{\rm s})}{\sqrt{r \ (r_{\rm s}-r)(v^2/c^2-1)}}$$which seems to be$$E = m \ c^2 + E_{\rm \ kin} + E_{\rm \ pot}$$But how would one factor out the kinetic and the potential component...Read more

black holes - General relativity potential

In general relativity it is defined the potential$$V(r)=-\frac{GM}{r}+\frac{l^{2}}{2r^{2}}-\frac{GMl^{2}}{r^{3}}$$for massive particles with angular momenta $l$ in a gravitational field created by a mass $M$.I want to understand why the value of $l^{2}=GM\frac{r^{2}}{r-3GM}$, as well as the value of the energy $e$, go to infinity when the massive particle is in a circular geodesic of radius $r=3GM$ (so there is no possibility of circular geodesic there).I can't understand this because $V(r)$ has a maximum or a minimum, provided $l>\sqrt{12}G...Read more

general relativity - Finding the frame of reference in which Newton's law of gravitation applies

I've always wondered, in which frame of reference does Newton's law$$ \boldsymbol{g} = -\frac{GM}{r^2} \widehat{\boldsymbol{r}}$$actually apply? In general it can't be the one in which the the mass $M$ is not rotating, since otherwise geostationary satellites would fall to earth. So, how is the intended frame of reference rotating with respect to the mass $M$? I'm looking for an answer that could be used tomake predictions, so simply working backwards from a measured orbital period and Newton's law won't do.I'm sure that the Einstein Field E...Read more

general relativity - Accelerating Frame and Gravity

I have recently learned briefly that an accelerating frame is equivalent to a gravitational field in the equivalence principle. I'm sitting on a chair and I am experiencing the force of gravity and its gravitational field. I am in an accelerating frame right?However, the net force on me is zero because the force of the ground and the force of gravity cancel each other out, thus I am not accelerating. However, there still is gravity constantly acting and the gravitational field is all around me. Shouldn't I still be accelerating? And if so, what...Read more

general relativity - 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 the approach to use modified gravity to explain the problem of dark energy been abandoned?Needed to write a review about the challenges facing modified gravity, Any insight would be great. Cheers...Read more

Relation of General Relativity to Dark Matter and Dark Energy

I was reading an elementary book on dark matter (in fact, a historical perspective) and there were mentioned how the scientific community react to the idea of dark matter proposed as a solution to observed discrepancy between the actual mass of astronomical systems and the predicted mass from Newton's theory. I was wondering where Einstein theory stands in relation to dark matter, did it somehow predict it, or does dark matter prove the incompleteness of Einstein's theory? And what about dark energy?...Read more

general relativity - Could dark energy and gravity be explained as same phenomenon?

I have watched VSouce video on gravity. The idea is that gravity pulling it is just lots of mass bending space-time, and natural direction of movement becomes moving towards the mass, and since we have earth already there we get to sit on top.This got me thinking what about lack of matter to bend space-time, could it be that space-time bends in the 'opposite' 'direction' like create a slope where everything's natural movement direction is away. Could this be used to explain dark energy's anti-gravity properties? EDIT: Duplicate is about dark ma...Read more

general relativity - Is there a peak gravitational force between bodies?

Suppose Object A is exerting gravitational force on Object B. Object A increases in mass, and so increases in volume, increasing the gravitational force on Object B. But, since mass occupies space the objects will need to be moved apart in order to keep them from joining. But as Object B is moved away from Object A.Eventually Object A turns into a black hole, which further complicates the issue. Due to the event horizon, so it's radius is a definite minimum distance between the objects.Is there some sweet spot of maximum gravity?...Read more