# Curved space JesseM

## Main Question or Discussion Point

JesseM wrote

Light doesn't need to have mass to be affected by a black hole, since in general relativity you can explain the motion of light in terms of the the black hole curving spacetime, and light following a geodesic path in this curved spacetime.

I replied

as matter is sucked into a black hole the matter will begin to emanate light(photons). the light emanated may go in any direction even opposite to a vector pointing to the centre of the black hole. 2 problems I see one How does the light that is in no way following a geodeisc path suddenly start follwoing such a path back towards the black hole. 2 What phenomenon turns that photon thru 180 degrees so that it heads back to the black hole if it isnt gravity what is it?

Also curved space time looks, in 2D, like a funny shaped funnel or cone. How do you consturct (pictorially or mathematically) a similar cone in all three dimensions such that light entering from any angle will travell in a geodeisic path? For this to be true the light would have to take a geodesic path regardless of the angle of attack! I find difficulty with this as if you take a single cone shape and rotate it thru all dimensions, cone 1 overlaps cones 2,3,4,5,6,7 etc etc and the cone shape, density, morphology, topology is compeletly destroyed?

Pundits of the curved space theory beleive there is no such thing as gravity, do they. They beleive the illusion of gravity is created by curved space yes ? If this is so, You say massive objects bend space but any object no matter how tiny, as long as it exerts a garvitational "force" then it has gravity. So even tiny objects ie an electron must bend space, just less, yes ?

Related Special and General Relativity News on Phys.org
JesseM
Is there any reason you started a new thread for this? It's better not to start new threads for every question you have about a previous comment...
as matter is sucked into a black hole the matter will begin to emanate light(photons). the light emanated may go in any direction even opposite to a vector pointing to the centre of the black hole. 2 problems I see one How does the light that is in no way following a geodeisc path suddenly start follwoing such a path back towards the black hole.
Once an object is inside the event horizon of the black hole, the radial axis becomes the time axis for them--the singularity at the "center" lies in the future rather than in any spatial direction, and the event horizon lies in the past, and they can no more emit light going away from the singularity than we can emit light going backwards in time. If you're familiar with the idea of light cones in spacetime diagrams, you can look at the two images at the very bottom of this page for an illustration of how light cones become "tilted" closer and closer to the horizon, so that once inside the horizon the future light cone only points inward.

If a photon is emitted outside the event horizon, than it can of course be emitted in a direction that takes it away from the BH, in which case it will escape.
rab99 said:
Also curved space time looks, in 2D, like a funny shaped funnel or cone.
Strictly speaking the "funnel" picture of a black hole illustrates only the curvature of space, not the curvature of spacetime.
rab99 said:
How do you consturct (pictorially or mathematically) a similar cone in all three dimensions such that light entering from any angle will travell in a geodeisic path?
Mathematically you can talk about the curvature of a universe of any number of dimensions using differential geometry (which is the basis for the theory of general relativity), but since we live in 3 dimensional space our perceptual systems don't allow us to imagine anything higher than a 2D surface curved in a 3D "embedding space" (just like we can't imagine colors we've never seen, or how a person blind since birth couldn't imagine images).
rab99 said:
Pundits of the curved space theory beleive there is no such thing as gravity, do they. They beleive the illusion of gravity is created by curved space yes ? If this is so, You say massive objects bend space but any object no matter how tiny, as long as it exerts a garvitational "force" then it has gravity. So even tiny objects ie an electron must bend space, just less, yes ?
Yes, in general relativity this would be true, although if you get down to the planck scale general relativity becomes incompatible with quantum physics, so physicists think we'll need a new theory of "quantum gravity" to describe what happens at very small distances and times and very high energies.

I have a question (or two) somehow related. An object falling in the direction of increasing curvature within a gravitational field of a massive object is moving from one geodecic line to another. How does it know, or feel this direction and what makes it to go from one curvature to another. Finally what makes it stop since a planetary object does not to spiral to the center and orbits in a fixed radial distance within the gravitational field.

JesseM
I have a question (or two) somehow related. An object falling in the direction of increasing curvature within a gravitational field of a massive object is moving from one geodecic line to another.
I think you're misunderstanding the term geodesic--the object's entire path through curved spacetime as it falls into the BH is a geodesic, it's following the path that maximizes the proper time (time as measured by a clock carried with the object).

tiny-tim
Homework Helper
How does the light that is in no way following a geodeisc path suddenly start follwoing such a path back towards the black hole. 2 What phenomenon turns that photon thru 180 degrees so that it heads back to the black hole if it isnt gravity what is it?
Hi rab99!

That is really a question about photons.

You're asking, since the photon had the same velocity as the matter that produced it, how does it acquire a different velocity?

The answer is that the photon never existed before … it was created with its own personal speed-of-light velocity!

(and btw, both the free-fall matter and the photon always follow a geodesic)

JesseM
You're asking, since the photon had the same velocity as the matter that produced it, how does it acquire a different velocity?
I don't think that's what he was asking--I think he was asking about a photon that was emitted by matter already inside the black hole, and what would happen to "turn it around" if it was initially emitted in a direction that takes it away from the center. As I said, this is based on the misconception that someone inside the black hole sees the singularity lying in a certain direction in space, rather than in the future direction of time.

Dale
Mentor
How does the light that is in no way following a geodeisc path suddenly start follwoing such a path back towards the black hole. ... How do you consturct (pictorially or mathematically) a similar cone in all three dimensions such that light entering from any angle will travell in a geodeisic path? For this to be true the light would have to take a geodesic path regardless of the angle of attack!
An object falling in the direction of increasing curvature within a gravitational field of a massive object is moving from one geodecic line to another. How does it know, or feel this direction and what makes it to go from one curvature to another. Finally what makes it stop since a planetary object does not to spiral to the center and orbits in a fixed radial distance within the gravitational field.
Hi rab and harry, I will try to respond to these together since they both ask about geodesics. First, you can think of a geodesic as "a straight line in a curved space". At each point along the line it is locally straight, but because the space itself is intrinsically curved it is not straight in a global sense. If you were moving about the surface of a sphere you would travel in great arcs which are locally everywhere "straight lines" but curve in a global sense.

Now, if you start at any point on the surface of a sphere you can draw an infinite number of great arcs, one for every direction that you could travel. Thus, there is a geodesic in every direction from any point. But once you start on a geodesic path, if you deviate from that path or "switch geodesics" then your overall path is no longer a geodesic. A free-falling massive object or light each follow a single geodesic path (they don't switch geodesics) that can be completely determined from a knowledge of the starting conditions and the spacetime curvature. For an orbiting body the geodesic is a helix for a circular orbit, or some distorted "almost-helix" for an elliptical orbit.

You might wonder if both light and a satellite follow geodesics then what about a beam of light that is tangent to the satellite's orbit? Isn't it on the same geodesic and therefore shouldn't it orbit as the satellite does? The answer is that in GR it is not space that is curved but spacetime. The light and the satellite are going in the same direction at different speeds in space, but they are going at the same speed in different directions in spacetime. Thus, they are each on a different geodesic through spacetime.

In general relativity, geodesics generalize the notion of "straight lines" to curved spacetime. This concept is based on the mathematical concept of a geodesic. Importantly, the world line of a particle free from all external force is a particular type of geodesic. In other words, a freely moving particle always moves along a geodesic.

In general relativity, gravity is not a force but is instead a curved spacetime geometry where the source of curvature is the stress-energy tensor (representing matter, for instance). Thus, for example, the path of a planet orbiting around a star is the projection of a geodesic of the curved 4-D spacetime geometry around the star onto 3-D space.

You are correct. However, I was refering to orinary planetary systems and not BH. I must appologize for changing the subject a little. My question relates to classical GR in which any objects follows a geodesic line, which is a 4-D straight line, wether it is its orbital path, or its free-falling path of the object. I agree with our freind DaleSpam in his comments
"Thus, there is a geodesic in every direction from any point. But once you start on a geodesic path, if you deviate from that path or "switch geodesics" then your overall path is no longer a geodesic. A free-falling massive object or light each follow a single geodesic path (they don't switch geodesics) that can be completely determined from a knowledge of the starting conditions and the spacetime curvature. For an orbiting body the geodesic is a helix for a circular orbit, or some distorted "almost-helix" for an elliptical orbit."
My question is why the planetary objects in a fixed orbit do not move like a falling object such as a stone which moves in the radial direction of the sphere on which the planets move in their orbit.

My question is why the planetary objects in a fixed orbit do not move like a falling object such as a stone which moves in the radial direction of the sphere on which the planets move in their orbit.
I might be misunderstanding you, but are you simply asking why objects in orbit around the Earth (for example) follow repeating orbits, whereas stones and other falling objects fall "downward" toward the Earth? The answer is very simple: it's a matter of their velocities. If you could throw a stone with sufficiently high velocity (and there were no atmosphere to hinder its motion), you could throw it into a trajectory that would cause it to orbit the Earth. Conversely, if you were to slow an orbiting satellite to a much lower velocity than it has in orbit, it would drop like a stone.

In my business, which has to do with orbiting satellites, we sometimes hear the statement that "an orbit is just free-fall that keeps missing the Earth." This is meant to emphasize there there is no fundamental difference between a falling rock and an orbiting satellite.

tiny-tim
Homework Helper
… jump … !

"an orbit is just free-fall that keeps missing the Earth."
Exactly!

Or, to put it the other way round:
Anything in free-fall is in orbit … but the orbit gets interrupted by the Earth!​

If a stone drops vertically over the North pole, and if there just happens to be a convenient tunnel through the Earth to the South pole, then the stone will carry on indefinitely in orbit … it'll just be an extremly flat orbit!

So if you jump in the air … right now … try it! … you'll, very briefly, be in orbit!

Based on Newton's explanation, and to some extent GR's explanation I agree with what you have said. What I am asking is how does an object know it is in a curved space and which direction is increasing or decreasing curvature, since there is no "ATTRACTION FORCE", or poential which is dependent on any property of the falling object. The gravitatioal field or the curved space-time of general relativity is essentially a function of the gravitating mass/energy. By other words how does it know where earth is and why some miss it and some dont. This might seem nonsensical but needs a mechanism not provided, as far as I know, by general relativity.

tiny-tim
Homework Helper
… it "blindly" follows a geodesic …

Hi harryjoon!

It doesn't "know where earth is" … all it "knows" is the bit of space it's in at the moment.

It obeys Newton's first law … no force is acting on it, so it "blindly" follows the geodesic it happens to already be on.

It doesn't "ask why", or need to know why!

Based on Newton's explanation, and to some extent GR's explanation I agree with what you have said. What I am asking is how does an object know it is in a curved space and which direction is increasing or decreasing curvature, since there is no "ATTRACTION FORCE", or poential which is dependent on any property of the falling object. The gravitatioal field or the curved space-time of general relativity is essentially a function of the gravitating mass/energy. By other words how does it know where earth is and why some miss it and some dont. This might seem nonsensical but needs a mechanism not provided, as far as I know, by general relativity.
I agree with tiny-tim's response, but I'll add that I believe it is a postulate that Newton's First Law should be translated from motion in a straight line to motion along a geodesic. In other words, it is not a result derived from more fundamental principles, but rather is an observation of nature.

I honestly don't recall if this is presented as a postulate of GR, however - can someone answer that for me?

Hi belliott4488
I agree in GR Newtons laws hold locally. OK I put it even more nonsensically, Why do I fall down after I jump up! Where I am standing I am happy in my geodesic. I jump, i.e. I put myself in a new geodesic which is in the direction of decreasing curvature, which I would follow eternally had there not been an earth so close by. What you are saying is that if I jump high enough so that I reach a geodecic which does not collid with the earth I would be in a permanent orbit around the earth. After I am in orbit if I were to lose my orbital velocity say by radiating a definite amount of energy the extent of which is totally at my disposal, I would reverse the above process and fall down to earth. This change of velocity over time, acceleration, would not be limited to that of gravitational accelration, this would be in contradiction to the observed fact in gravitational systems all bodies fall with the same acceleration, g, independent of their internal contitution.

JesseM
Hi belliott4488
I agree in GR Newtons laws hold locally. OK I put it even more nonsensically, Why do I fall down after I jump up! Where I am standing I am happy in my geodesic.
If you're standing, you're not on a geodesic path--only a free-falling object whose path is influenced solely by gravity follows a geodesic, on the ground you're being pushed up by the electromagnetic force between the floor and your feet, which keeps you from falling on a geodesic path to the center of the Earth (and up the other side) as you would if gravity were the only force acting on you.
harryjoon said:
I jump, i.e. I put myself in a new geodesic which is in the direction of decreasing curvature, which I would follow eternally had there not been an earth so close by.
When you jump, it's electromagnetic forces between atoms again changing your path, although once you're in the air you are following a geodesic until you hit the ground (at least if we ignore air resistance).
harryjoon said:
What you are saying is that if I jump high enough so that I reach a geodecic which does not collid with the earth I would be in a permanent orbit around the earth.
It has nothing to do with height--it would be possible to "orbit" the Earth at sea level if your initial velocity in the sideways direction were high enough and air resistance could be ignored. And even if your jumping velocity is small, if there were no forces acting on you other than gravity so that you could fall straight through the ground towards the center of the Earth, you would pass by the center at high speed and pop up to ground level on the other side, then fall down again, over and over, so this would itself be a kind of highly elliptical orbit.
harryjoon said:
After I am in orbit if I were to lose my orbital velocity say by radiating a definite amount of energy the extent of which is totally at my disposal, I would reverse the above process and fall down to earth. This change of velocity over time, acceleration, would not be limited to that of gravitational accelration, this would be in contradiction to the observed fact in gravitational systems all bodies fall with the same acceleration, g, independent of their internal contitution.
If you cause yourself to deviate from a geodesic path by "radiating energy" in some form, then you are not in freefall, and the "observed fact in gravitational systems all bodies fall with the same acceleration" only applies to objects in freefall (and at about the same position in the gravitational field, so that differences in the strength of the field don't come into play).

If you cause yourself to deviate from a geodesic path by "radiating energy" in some form, then you are not in freefall, and the "observed fact in gravitational systems all bodies fall with the same acceleration" only applies to objects in freefall (and at about the same position in the gravitational field, so that differences in the strength of the field don't come into play).
Thank you JesseM for you comments. Would you explain in what way I would be different from a falling stone, a falling satalite or airplain etc, and how is the gravitational acceleration differentin this case. Galileo found it to be the same.

If you cause yourself to deviate from a geodesic path by "radiating energy" in some form, then you are not in freefall, and the "observed fact in gravitational systems all bodies fall with the same acceleration" only applies to objects in freefall (and at about the same position in the gravitational field, so that differences in the strength of the field don't come into play).
Gas and particles falling into the accretion disc of a black hole are thought to radiate huge amounts of energy in the form of x-rays. Some sources say possible up to 100% of the mass of the particles is converted into energy by this process. The principle is that particles undergoing extreme acceleration radiate and this is observed in cyclotrons. What puzzles me is that particles falling towards a black hole are presumably in free fall and therefore should not "experience" acceleration in theor own frame. If the particles do not "feel" acceleration, how do they "know" to radiate?

P.S. It's amazing that Galileo discovered something about gravity that was considered accurate for a century, simply by rolling cylinders down a plank and timing them with a water clock.

Thank you JesseM for you comments. Would you explain in what way I would be different from a falling stone, a falling satalite or airplain etc, and how is the gravitational acceleration differentin this case. Galileo found it to be the same.
Sorry, it's belliott4488 (Bruce) this time ... The airplane is different if it is flying, because it depends on the atmosphere for lift, which pulls it off of the geodesic it would otherwise follow. If you get rid of the atmosphere, then you, the falling satellite, and the airplane all follow geodesics. You will probably follow different geodesics, though, even if you start at the same point, due to your different velocities - this is what is different from Galileo's case. If you are inside the airplane, then you will float, apparently weightless, as you and the airplane follow the same geodesic. Perhaps you've seen pictures of the 747 airliner that NASA uses for training? The plane flies in such a way that it follows the geodesic that it would follow with no atmosphere (it must use power to overcome the air resistance), and the passengers inside float weightlessly. They are all on geodesics.

tiny-tim
Homework Helper
What puzzles me is that particles falling towards a black hole are presumably in free fall and therefore should not "experience" acceleration in theor own frame. If the particles do not "feel" acceleration, how do they "know" to radiate?
Puzzles me too.

wikipedia on black holes says that xrays are radiation caused by heating caused by pressure friction etc http://en.wikipedia.org/wiki/Black_hole#Accretion_disk:
Black holes give off radiation because matter falling into them loses gravitational energy which may result in the emission of radiation before the matter falls into the event horizon
But wikipedia on x-ray astronomy says that xrays are caused by loss of gravitational energy http://en.wikipedia.org/wiki/X-ray_source#Astronomical_sources_of_X-rays:
Black holes give off radiation because matter falling into them loses gravitational energy which may result in the emission of radiation before the matter falls into the event horizon.
Which is right?

JesseM
Thank you JesseM for you comments. Would you explain in what way I would be different from a falling stone, a falling satalite or airplain etc, and how is the gravitational acceleration differentin this case. Galileo found it to be the same.
I don't understand the question. When you say "in what way I would be different", are you imagining yourself being in frefall, or yourself being on the ground? And what do you mean when you say the gravitational acceleration is different?

I don't understand the question. When you say "in what way I would be different", are you imagining yourself being in frefall, or yourself being on the ground? And what do you mean when you say the gravitational acceleration is different?
The equation of geodesic(http://en.wikipedia.org/wiki/Geodesic_equation) relates the acceleration directly to the curvature of space-time. The greater the curvature the greater the acceleration, a fact which is observed in gravitational field of earth (or any other). Not only this acceleration can not be detected locally(in the rest frame of the object) by using any local parameter, analogous to the relative velocity of an object, it increases as we approach the center of the gravitational field. The lateral acceleration of an object moving on or around earth, increases the further we go away from the center of gravitational field. The former is a property of the gravitational field only, while the latter is a property of the moving object only. Furthermore, the method of energy loss of the object ( friction etc) should not affect our definition of a free-falling object, since even in the absence of air a fallining object loses energy, of course far more slowly if it is is a stable orbit. Hence, my question remains, how is a falling man any different from a falling stone? and why do I fall back down to earth, not according to Newton, but according to GR.

Dale
Mentor
If you are a person jumping, a rock falling, or a satellite orbiting you are traveling on a geodesic in GR. If the geodesic intersects the worldline of the earth then you fall back down, if not then you orbit or escape. It is as simple as that

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There are number of points which I believe suggest that it is not that simple;
1)-Worldline of objects may or may not intersect. If it does it is given that they will meet.
2)-Worldline of an object may or may not be along the geodesic line of the curved space-time field produced by Earth's mass.
3)-A free-falling object travells along a geodesic of the curved space-time field produced by Earth's mass, which is also its worldline.
4)-The world line of the Earth is NOT along a geodesic of its curved space-time field (produced by Earth's mass).
5)- Earth must carry its curved space-time field produced by its mass, along its worldline, which means that the world line of an object orbitting say one meter above earth surface, i.e following a geodesic of the field which is a meter above the surface of the earth, will always be one meter above the Earth surface, independent of the position of earth along its worldline. A contrarry sugestion would mean objects will be left behind as Earth travells along its worldline, which is contrary to our observation.

Dale
Mentor
There are number of points which I believe suggest that it is not that simple;
You are over-doing things here. It is that simple (except for the process of actually calculating a geodesic).

1)-Worldline of objects may or may not intersect. If it does it is given that they will meet.
2)-Worldline of an object may or may not be along the geodesic line of the curved space-time field produced by Earth's mass.
3)-A free-falling object travells along a geodesic of the curved space-time field produced by Earth's mass, which is also its worldline.
4)-The world line of the Earth is NOT along a geodesic of its curved space-time field (produced by Earth's mass).
All true, but none of it contradicts what I said above.

5)- Earth must carry its curved space-time field produced by its mass, along its worldline, which means that the world line of an object orbitting say one meter above earth surface, i.e following a geodesic of the field which is a meter above the surface of the earth, will always be one meter above the Earth surface, independent of the position of earth along its worldline. A contrarry sugestion would mean objects will be left behind as Earth travells along its worldline, which is contrary to our observation.
Neglecting air resistance, and assuming a perfectly spherical earth and circular orbit, yes. It still doesn't contradict the above.

JesseM
There are number of points which I believe suggest that it is not that simple;
1)-Worldline of objects may or may not intersect. If it does it is given that they will meet.
If they interact through any non-gravitational forces, like the electromagnetic forces between atoms, then this can cause them to deviate from a geodesic when they meet. Idealized non-interacting particles will just pass by (or through) each other when they meet, traveling on different geodesics because their velocities at the point they meet are different.
harryjoon said:
2)-Worldline of an object may or may not be along the geodesic line of the curved space-time field produced by Earth's mass.
As long as the object is not being acted on by non-gravitational forces, it will always follow a geodesic (at least if its mass is small compared to the Earth--I'm not sure if two objects which are both massive enough to significantly affect each other's motion are still following geodesics, you'd have to ask someone with more expertise in GR).
harryjoon said:
3)-A free-falling object travells along a geodesic of the curved space-time field produced by Earth's mass, which is also its worldline.
4)-The world line of the Earth is NOT along a geodesic of its curved space-time field (produced by Earth's mass).
The worldline of the center of the Earth might indeed be a geodesic in the curved space-time produced both by the Earth and the Sun, though I'm not totally sure about this for the reason mentioned above.
harryjoon said:
5)- Earth must carry its curved space-time field produced by its mass, along its worldline, which means that the world line of an object orbitting say one meter above earth surface, i.e following a geodesic of the field which is a meter above the surface of the earth, will always be one meter above the Earth surface, independent of the position of earth along its worldline. A contrarry sugestion would mean objects will be left behind as Earth travells along its worldline, which is contrary to our observation.
Sure, spacetime is curved by the presence of mass and energy in GR, so it makes sense that the curvature would move along with a moving mass.