View Full Version : Negative Mass and the Schwarzschild radius

tommac

2010-Mar-23, 02:39 PM

OK all. The basis of my questions will certainly roam into ATM ... however the questions that I am going to pose should have a mainstream answer and I will be careful not to bring in ATM ideas into the questions that I am posing.

Lets assume mass can have negative values for the EFE.

then instead of there being a Schwarzschild radius as in a black hole, there would be a radius that would react similarly but at a distant right?

Would that be similar to deSitter space?

Supposed that we had a universe with say -20 solar masses of mass. Would a distant Schwarzschild-like radius exist?

The idea is that with a repulsive force and infinite space a repelled mass would continue to accelerate forever ( even though the accelerating force would become minimal after a while )

And here is my math question:

How could we calculate the radius?

Is there a critical amount of negative mass that we would need to have a negative mass Schwarzschild-like radius? or would any amount of negative mass, in an otherwise empty and infinite universe be enough for a horizon to form?

korjik

2010-Mar-23, 04:35 PM

Why dont you actually look at the equations and look at what happens if you add a minus sign?

Chances are you would end up with a negative radius.

tommac

2010-Mar-23, 06:03 PM

Why dont you actually look at the equations and look at what happens if you add a minus sign?

Chances are you would end up with a negative radius.

Yes but you cant look at it like that as it is not the same equation. It will have a negative radius for the SR because negative mass will not have a SR because it is repulsive not attractive. The result will be something different but SR-like.

The two first questions that need to be answered:

1) In an infinite and isolated universe would a mass accelerate forever away from negative mass? If so will it approach the speed of light?

2) Is there a minimum requirement for the amount of mass that would need to be present for #1 to happen.

Rs = M * 2G / c^2

when M is negative R is negative ... fine ...

I am looking for how you would calculate an outward radius of something that is pushing ... rather than in inside radius of something that is pulling.

stutefish

2010-Mar-23, 10:03 PM

I am looking for how you would calculate an outward radius of something that is pushing ... rather than in inside radius of something that is pulling.

Well, for one thing it's the same radius. One side is the outside, the other side is the inside.

For another thing, it's still gravity (or "negative gravity", or whatever you want to call it). So the pushing effect will fall off with distance from the source, just like the pulling effect of positive gravity: The further away, the weaker the effect.

Approaching the same question from a different angle: If the event horizon of a positive-gravity black hole is the boundary beyond which light cannot pass on its way away from the singularity, then the event horizon of a negative-gravity black hole would be the boundary beyond which light cannot pass on its way towards the singularity.

Not sure how the event horizon relates to the negative Schwarzchild radius, though.

WayneFrancis

2010-Mar-24, 03:55 AM

some thing with negative rest mass to our universe should not be visible. It would be causally disconnected from us because it experiences imaginary proper time. Problem solved can't be observed.

tommac

2010-Mar-24, 12:13 PM

some thing with negative rest mass to our universe should not be visible. It would be causally disconnected from us because it experiences imaginary proper time. Problem solved can't be observed.

Can you explain the imaginary proper time comment ... also we are looking for the effects on the calculation of the radius using the amount of negative mass, not sure how this fits in.

Kwalish Kid

2010-Mar-24, 12:18 PM

Can you explain the imaginary proper time comment ... also we are looking for the effects on the calculation of the radius using the amount of negative mass, not sure how this fits in.

Do the calculation yourself and you will see where the imaginary numbers come in.

tommac

2010-Mar-24, 12:19 PM

Do the calculation yourself and you will see where the imaginary numbers come in.

Formula?

gzhpcu

2010-Mar-24, 12:22 PM

Forgetting for a moment that there is no such thing as negative mass (except in math equations), if there we such an animal, how could it ever accumulate together to form a (negative) black hole in the first place, since the gravitational force it generates is repulsive?

tommac

2010-Mar-24, 07:25 PM

Forgetting for a moment that there is no such thing as negative mass (except in math equations), if there we such an animal, how could it ever accumulate together to form a (negative) black hole in the first place, since the gravitational force it generates is repulsive?

We are assuming for this mathmatical question that there are possible values for mass. Who is saying anything about it accumulating together or anything about a black hole. I am just saying that if we had any of it in an otherwise empty universe would an event horizon form ( at the edges of our universe ) given enough time ... and if it could ... would there be a requirement that a certain amount would be needed for the EH to form.

gzhpcu

2010-Mar-24, 07:34 PM

We are assuming for this mathmatical question that there are possible values for mass. Who is saying anything about it accumulating together or anything about a black hole. I am just saying that if we had any of it in an otherwise empty universe would an event horizon form ( at the edges of our universe ) given enough time ... and if it could ... would there be a requirement that a certain amount would be needed for the EH to form.

Event horizons are usually associated with black holes. Please explain how you propose to reach a critical density with negative mass.:confused:

tommac

2010-Mar-24, 08:14 PM

Event horizons are usually associated with black holes. Please explain how you propose to reach a critical density with negative mass.:confused:

Isnt the hubble radius an event horizon?

grant hutchison

2010-Mar-24, 08:25 PM

Isnt the hubble radius an event horizon?It isn't.

Take a look at Davis and Lineweaver (http://arxiv.org/abs/astro-ph/0310808) to find out why not.

Grant Hutchison

tommac

2010-Mar-24, 08:52 PM

It isn't.

Take a look at Davis and Lineweaver (http://arxiv.org/abs/astro-ph/0310808) to find out why not.

Grant Hutchison

I realized that after I posted. Thanks ... that is a great article.

tommac

2010-Mar-24, 08:56 PM

It isn't.

Take a look at Davis and Lineweaver (http://arxiv.org/abs/astro-ph/0310808) to find out why not.

Grant Hutchison

I mean the particle horizon or the acoustic horizon.

gzhpcu

2010-Mar-24, 09:14 PM

Isnt the hubble radius an event horizon?

The hubble radius is the distance at which the expansion of the universe adds up to the speed of light. (=13.6 billion light years)

The boundary past which events can't ever be observed is an event horizon, and it represents the maximum extent of the particle horizon.

it is not always the case that the particle horizon coincides with the location where the recession speed is the same as that of light. For instance, in our universe, objects beyond about a redshift of 1.4 recede faster than light.

01101001

2010-Mar-24, 10:01 PM

Isnt the hubble radius an event horizon?

No. No. No.

And no.

tommac

2010-Mar-24, 11:19 PM

No. No. No.

And no.

I meant the particle horizon or the acoustic horizon.

WayneFrancis

2010-Mar-25, 12:33 AM

I meant the particle horizon or the acoustic horizon.

The hubble volume is a particle horizon but not an event horizon. Stuff beyond the particle horizon can eventually get to us while something beyond an event horizon can not. Now that said the EH of the universe is not physically the same thing as the EH of a BH. They are similar in that the EH of both is the biggest comoving distance in which light emitted right now can ever reach us.

tommac

2010-Mar-25, 12:41 AM

while something beyond an event horizon can not. .

Huh? How about hawking radiation?

WayneFrancis

2010-Mar-25, 12:56 AM

Well, and some one pipe up if I'm wrong here, that is where the current thought is that stuff inside of the EH of a BH isn't completely causally isolated from the rest of the universe. Actually don't think it ever was. Attributes of the BH are still measurable beyond the EH, ie spin, mass, charge.

My point is the EH of a BH and the EH of our part of the universe share the same name but they are not the same dog.

That said light that is emitted from inside the EH of a black hole will never get to us and unless you consider HR as light emitted from within the EH then it still holds true.

tommac

2010-Mar-25, 01:17 AM

W

My point is the EH of a BH and the EH of our part of the universe share the same name but they are not the same dog.

Who is claiming that they are the same dog. Please read the original question.

gzhpcu

2010-Mar-25, 07:40 AM

I meant the particle horizon or the acoustic horizon.

Acoustic horizon? This has nothing to do with cosmology. This is a term in fluid dynamics.

gzhpcu

2010-Mar-25, 07:46 AM

And in respect to the Event Horizon of the universe, we do not even know if it exists:

The criterion for determining whether an event horizon for the universe exists is as follows. Define a comoving distance dE by

http://upload.wikimedia.org/math/8/5/4/8546bfc665b1de29139455d6dfd8432a.png In this equation, a is the scale factor, c is thespeed of light, and t0 is the age of the universe. If http://upload.wikimedia.org/math/9/9/b/99b079dcdb950fe92419672c436587ec.png, (i.e. points arbitrarily as far away as can be observed), then no event horizon exists. If http://upload.wikimedia.org/math/f/2/b/f2b827a526d779c6a14355a9432b99d5.png, a horizon is present.

source: http://en.wikipedia.org/wiki/Event_horizon

tommac

2010-Mar-25, 02:36 PM

Acoustic horizon? This has nothing to do with cosmology. This is a term in fluid dynamics.

well I think it is used when making the analogy for dumb holes.

tommac

2010-Mar-25, 02:37 PM

And in respect to the Event Horizon of the universe, we do not even know if it exists:

source: http://en.wikipedia.org/wiki/Event_horizon

I agree it is under debate and that is why I am asking this question.

gzhpcu

2010-Mar-25, 04:32 PM

well I think it is used when making the analogy for dumb holes.

What are "dumb holes"? :confused:

grant hutchison

2010-Mar-25, 05:04 PM

What are "dumb holes"? :confused:It's a phrase coined by Unruh, to designate the acoustic equivalent of a black hole: a region of moving fluid bounded by an acoustic horizon.

Tommac, dragging in acoustic analogies will only cause confusion, unless you've got a really good reason to do so, which you'd like to state now.

Grant Hutchison

tommac

2010-Mar-25, 05:32 PM

It's a phrase coined by Unruh, to designate the acoustic equivalent of a black hole: a region of moving fluid bounded by an acoustic horizon.

Tommac, dragging in acoustic analogies will only cause confusion, unless you've got a really good reason to do so, which you'd like to state now.

Grant Hutchison

Well from what I have been reading, some of the evidence about radiation coming from the particle horizon comes from analysis and analogies driven from dumb holes. I think the term accoustic horizon is being coined even in this context. Although maybe I am totally wrong.

grant hutchison

2010-Mar-25, 06:39 PM

I think the term accoustic horizon is being coined even in this context.Acoustic means "related to hearing", though it's often used as if it were a synonym for sonic, "related to sound". Acoustic (or sonic) horizons therefore relate only to the propagation of sound waves.

Grant Hutchison

tommac

2010-Mar-25, 07:01 PM

Acoustic means "related to hearing", though it's often used as if it were a synonym for sonic, "related to sound". Acoustic (or sonic) horizons therefore relate only to the propagation of sound waves.

Grant Hutchison

I was reading stuff like:

http://iopscience.iop.org/0264-9381/17/15/305?ejredirect=migration

and:

http://arxiv.org/abs/0908.3898

We consider an alternative to inflation for the generation of superhorizon perturbations in the universe in which the speed of sound is faster than the speed of light. We label such cosmologies, first proposed by Armendariz-Picon, {\it tachyacoustic}, and explicitly construct examples of non-canonical Lagrangians which have superluminal sound speed, but which are causally self-consistent. Such models possess two horizons, a Hubble horizon and an acoustic horizon, which have independent dynamics. Even in a decelerating (non-inflationary) background, a nearly scale-invariant spectrum of perturbations can be generated by quantum perturbations redshifted outside of a shrinking acoustic horizon. The acoustic horizon can be large or even infinite at early times, solving the cosmological horizon problem without inflation. These models do not, however, dynamically solve the cosmological flatness problem, which must be imposed as a boundary condition. Gravitational wave modes, which are produced by quantum fluctuations exiting the Hubble horizon, are not produced.

grant hutchison

2010-Mar-25, 07:25 PM

As I said. Sound waves.

Grant Hutchison

tommac

2010-Mar-25, 07:28 PM

As I said. Sound waves.

Grant Hutchison

So the speed of sound can get greater than the speed of light? Wow ... trippy.

gzhpcu

2010-Mar-25, 07:53 PM

So the speed of sound can get greater than the speed of light? Wow ... trippy.

Not sound itself, but group velocity...

The speed of light waves in vacuum, 300,000 kilometers per second (186,000 miles per second), and denoted as c, remains the absolute speed limit for transferring matter, energy, and usable signals (information). However, a wave property known as group velocity can surpass c while still complying fully with the theory of special relativity, since it is not involved in transferring information, matter, or energy.

At last week's meeting of the Acoustical Society of America in Minneapolis, Joel Mobley of the University of Mississippi (jmobley@olemiss.edu) argued that even the sound waves, which normally travel about one mile per second in water, could take on superluminal properties. Ultrasound's group velocity, he said, could jump by five orders of magnitude over its ordinary values and exceed c, when pulses of high-frequency sound strike a mixture of water and tiny (approximately 0.1-mm diameter) plastic spheres.

http://www.aip.org/pnu/2005/split/751-1.html

tommac

2010-Mar-25, 10:10 PM

Not sound itself, but group velocity...

http://www.aip.org/pnu/2005/split/751-1.html

My head is spinning with this stuff.

Can someone explain this a little?

captain swoop

2010-Mar-25, 11:12 PM

My head is spinning with this stuff.

Can someone explain this a little?

Speed of sound in air is 343 metres per second but the individual molecules of air don't travel 343 metres.

tommac

2010-Mar-26, 01:17 AM

Speed of sound in air is 343 metres per second but the individual molecules of air don't travel 343 metres.

Yes just the wave. Similar to electron drift in a wire.

But what does all of this have to do with the edge of our universe and superluminal speed of sound?

Is the group velocity the wave?

01101001

2010-Mar-26, 02:09 AM

Is the group velocity the wave?

Think about what you're asking: is some velocity a wave? Huh?

Wikipedia: Group velocity (http://en.wikipedia.org/wiki/Group_velocity)

The group velocity of a wave is the velocity with which the overall shape of the wave's amplitudes — known as the modulation or envelope of the wave — propagates through space.

tommac

2010-Mar-26, 03:16 AM

Thanks ... that cleared it up.

Think about what you're asking: is some velocity a wave? Huh?

Wikipedia: Group velocity (http://en.wikipedia.org/wiki/Group_velocity)

mmaayeh

2010-Mar-26, 08:26 PM

Not to belabor this point. However, I was looking through wiki that discusses the concepts of negative mass (http://en.wikipedia.org/wiki/Exotic_matter) perhaps this can add some context to this discussion. Of course the concepts are for hypothetical particles such as Tachyons and have never been detected or I would imagine will never be detected. However, the two physicists, Hermann Bondi and Robert L. Forward , have come up with the concepts. I thought this link may help to answer some issues in this discussion, if possible.

mugaliens

2010-Mar-29, 08:33 AM

Another negative mass thread, tommac? Negative/positive - the direction of gravitational attraction is the same! I think this has been mentioned half a dozen times.

tommac

2010-Mar-29, 03:46 PM

Another negative mass thread, tommac? Negative/positive - the direction of gravitational attraction is the same! I think this has been mentioned half a dozen times.

No ... it is not ... Negative mass repels ... positive mass attracts ...

Which ever one is greater will win the local battle. Negative mass has negative space-time curvature resulting in repulsion ... positive mass has a positive curvature and attracts.

negative mass will fall with gravity assuming that it is not pushing away the positive mass quicker than it is being attracted.

tommac

2010-Mar-29, 03:47 PM

Another negative mass thread, tommac? Negative/positive - the direction of gravitational attraction is the same! I think this has been mentioned half a dozen times.

http://en.wikipedia.org/wiki/Anti-gravity#Negative_mass

Both general relativity and Newtonian gravity appear to predict that negative mass would produce a repulsive gravitational field.

mmaayeh

2010-Mar-29, 05:40 PM

No ... it is not ... Negative mass repels ... positive mass attracts ...

Which ever one is greater will win the local battle. Negative mass has negative space-time curvature resulting in repulsion ... positive mass has a positive curvature and attracts.

negative mass will fall with gravity assuming that it is not pushing away the positive mass quicker than it is being attracted.

May I ask, what does negative or positive curvature mean? Is this a difference in shape between a spheroid vs. Saddle?

tommac

2010-Mar-29, 06:25 PM

May I ask, what does negative or positive curvature mean? Is this a difference in shape between a spheroid vs. Saddle?

Yes:

http://www.astro.rug.nl/~hidding/ao/curvature.png ( top one )

Hyperbolic curvature.

tommac

2010-Mar-29, 07:03 PM

No ... it is not ... Negative mass repels ... positive mass attracts ...

Which ever one is greater will win the local battle. Negative mass has negative space-time curvature resulting in repulsion ... positive mass has a positive curvature and attracts.

negative mass will fall with gravity assuming that it is not pushing away the positive mass quicker than it is being attracted.

I believe you need to take all of this into account in the stress energy tensor and that determines the curvature in the ricci tensor. Please correct me if I am wrong with this last statement.

mugaliens

2010-Mar-30, 04:43 AM

negative mass will fall with gravity assuming that it is not pushing away the positive mass quicker than it is being attracted.

You should read your own links:

Bondi pointed out that a negative mass will fall toward (and not away from) "normal" matter, since although the gravitational force is repulsive, the negative mass (according to Newton's law, F=ma) responds by accelerating in the opposite of the direction of the force. Normal mass, on the other hand, will fall away from the negative matter. He noted that two identical masses, one positive and one negative, placed near each other will therefore self-accelerate in the direction of the line between them, with the negative mass chasing after the positive mass.

And:

The Standard Model of particle physics, which describes all presently known forms of matter, does not include negative mass. Although cosmological dark matter may consist of particles outside the Standard Model whose nature is unknown, their mass is ostensibly known - since they were postulated from their gravitational effects on surrounding objects, which implies their mass is positive.

So, in light of the above, where are you going with this? Certainly not a space drive, for:

Notice that because the negative mass acquires negative kinetic energy, the total energy of the accelerating masses remains at zero.

Since there's no change in energy, there can be no work that's been done. No work, means no acceleration of, say, a spacecraft trying to utilize this as a means of propulsion.

WayneFrancis

2010-Mar-31, 01:55 AM

You should read your own links:

...

He probably reads them but if these threads are any example then he'll only absorb what may support his preconceptions.

tommac

2010-Mar-31, 03:46 PM

Mugs,

Negative mass, repels but falls in a gravitational field.

Positive mass attracts but is repelled in a negative gravitational field.

If positive mass is greater than the negative mass the negative mass will fall.

If negative mass is greater than positive then the postive mass will repel.

You should read your own links:

And:

So, in light of the above, where are you going with this? Certainly not a space drive, for:

Since there's no change in energy, there can be no work that's been done. No work, means no acceleration of, say, a spacecraft trying to utilize this as a means of propulsion.

gzhpcu

2010-Mar-31, 04:39 PM

Tommac,

I found this article which might interest you entitled "Black Holes of Negative Mass".

http://arxiv.org/PS_cache/gr-qc/pdf/9705/9705007v1.pdf

tommac

2010-Mar-31, 04:48 PM

Personally I wouldnt think that negative mass could form a black hole ( a future singularity ) because it doesnt clump. However it could form a past singularity. Again this is currently where my head is at and not based in anything mainstream. This all being said I will read the article when I get a chance.

Tommac,

I found this article which might interest you entitled "Black Holes of Negative Mass".

http://arxiv.org/PS_cache/gr-qc/pdf/9705/9705007v1.pdf

tommac

2010-Apr-01, 09:03 PM

A follow up to my question:

Would SR allow negative mass to accelerate a mass to speeds of greater than c?

Lets say that I had a very massive neutron str ... and then a real lot of negative mass then a star, planet, moon, particle or whatever.

If arranged properly ... could negative mass accelerate the start,planet,moon or particle to speeds greater than c away from the neutron star. Assume almost infinite supply of negative mass and an ability to inject more negative mass into the area between the neutron star and the star,planet,moon particle.

something like this

NS............planet

NS.....................planet

NS................................planet

etc. where each "." is say -1/10 the negative mass of the neutron star.

In other words does SR allow negative curvature (negative ricci tensor ) to accelerate mass to speeds greater than c?

tommac

2010-Apr-04, 08:12 PM

The answer to this is that mass or negative mass can accelerate stuff to faster than c, like in the case of a black hole. Anything that falls into the black hole, is no longer limited to SR restraints because it is beyond any distant observers detection. Please correct me if I am wrong.

A follow up to my question:

Would SR allow negative mass to accelerate a mass to speeds of greater than c?

Lets say that I had a very massive neutron str ... and then a real lot of negative mass then a star, planet, moon, particle or whatever.

If arranged properly ... could negative mass accelerate the start,planet,moon or particle to speeds greater than c away from the neutron star. Assume almost infinite supply of negative mass and an ability to inject more negative mass into the area between the neutron star and the star,planet,moon particle.

something like this

NS............planet

NS.....................planet

NS................................planet

etc. where each "." is say -1/10 the negative mass of the neutron star.

In other words does SR allow negative curvature (negative ricci tensor ) to accelerate mass to speeds greater than c?

tommac

2010-Apr-04, 08:24 PM

The answer to my original question that i got from a post on a different topic is that the SR-sh thing that I am looking for .... really is the particle horizon of a predefined universe with a high scale factor ( similar to big rip ). Again I am not saying that the particle horizon of a big rip scenerio has anything to do with negative mass or a black hole, but you could model a universal event horizon using big rip.

At this point you can close this thread or alternatively move it to ATM.

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