Two black holes separated by more than one Schwarzschild radii

In summary: In the same spirit, here is a generalization of the potential function for the Weyl vacuums of gtr, showing the same thing: F(x,y,z) = k_0 + k_1(x^2+y^2+z^2) + k_2(x^2+y^2+z^2)^2 + k_3(x^2+y^2+z^2)^3 + k_4(x^2+y^2+z^2)^4. http://www.geocities.com/kmar86/gravitationalfield.xlsIn summary, the potential between two black holes separated by more than one Schwarzschild radii can be less than the potential of isolated objects, due to the
  • #1
kmarinas86
979
1
If you have two black holes separated by more than one Schwarzschild radii, given a location at:
  1. The event horizon of one of the black holes.
  2. A location between both black holes
  3. A location on the axis that passes the centers of both black holes.

Wouldn't the potential there actually be less than it would be if the objects were isolated?

First, note the black holes are pulling in opposite directions, so this isn't simply the sum of the gravitational potentials (is it?), but rather a sum of their vectors! If two black holes were about to collide, couldn't the matter that is between them race out between black holes A and B? Surely the velocity the particle will encounter will only increase. With respect to our frame of reference (and time perspective), is it possible that the matter (which appears to be forever collapsing to the Schwarzschild radius) appear to us as being sucked out as the black holes approach each other?

Could the jet coming out of a black "hole" actually be the stream of particles exiting the region near the axis of rotation of two black holes? Remember that from our time perspective (our time coordinate), the matter falling in never seems to cross the Schwarzschild radius, so in a finite amount of time, the matter may be expected to be jutted out in jets (because the black holes would be orbiting each other and the vectors between them cancel). If the masses were unequal, would this stream (between the unequal masses) actually be jutted outside the axis of rotation, causing the jet to be a helix in shape? If the particles were charged a certain way, then helix could expand and become very wide. Because of their relativistic velocity, the expansion would be mostly horizontal rather than vertical.

Perhaps I am wrong when I say the vectors cancel each other. If they don't cancel, then what do they do?
 
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  • #2
Seperated by < one swarzchild radii ? Are they identical ?
i really culdn't understand that question statement only...
 
  • #3
http://www.geocities.com/kmar86/gravitationalfield.xls

I made an Excel file that I think represents what I'm talking about. Here is the math behind it:

[itex]F_x^2+F_y^2=F_r^2[/itex]

[itex]\left(F_r cos\left(\theta\right)\right)^2+\left(F_r*sin\left(\theta\right)\right)^2=F_r^2[/itex]

[itex]F_r\propto\frac{1}{r^2}=\frac{1}{x^2+y^2}[/itex]

[itex]cos\left(\theta\right)=\frac{x}{r}=\frac{x}{\sqrt{x^2+y^2}}[/itex]

[itex]sin\left(\theta\right)=\frac{y}{r}=\frac{y}{\sqrt{x^2+y^2}}[/itex]

[itex]F_x\propto}\frac{x}{\left(x^2+y^2\right)^{\frac{3}{2}}}[/itex]

[itex]F_y\propto}\frac{y}{\left(x^2+y^2\right)^{\frac{3}{2}}}[/itex]

[itex]F_x\propto\frac{1}{1-\frac{r_s}{r}}[/itex]

[itex]F_y\propto\frac{1}{1-\frac{r_s}{r}}[/itex]
 
  • #4
Are you sure you mean "potential" here?

Hi, kmarinas86,

kmarinas86 said:
If you have two black holes separated by more than one Schwarzschild radii, given a location at:
  1. The event horizon of one of the black holes.
  2. A location between both black holes
  3. A location on the axis that passes the centers of both black holes.

Wouldn't the potential there actually be less than it would be if the objects were isolated?

You'd have to explain what you mean by "potential" in the context of gtr, but in Newtonian gravitation, if you have an isolated system composed of two roughly spherical objects, then indeed, if you plot the equipotential surfaces in "space" in a comoving coordinate system, these look like nested Casini ovals, i.e. in cross section, a sepatrix shaped like a figure eight separates two separate sets of nested equipotentials shrinking onto the two objects, from exterior equipotentials which rapidly become spherelike as you move away from our isolated system.

See also http://www.math.ucr.edu/home/baez/RelWWW/weylvac.html [Broken] for a discussion of a kind of potential which can be defined (with suitable caveats) for static axisymmetric vacuum solutions in gtr (the Weyl vacuums). As it happens, in a Newtonian context, the picture of "the Potential for Two Positive Mass Monopoles on a Massless Spring" happens to shows the above mentioned exterior equipotentials becoming approximately spherical as you move away from the isolated system.
 
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What is a Schwarzschild radius?

A Schwarzschild radius is a characteristic radius associated with a black hole, which represents the distance from the center of the black hole at which the escape velocity equals the speed of light. It is calculated using the mass of the black hole and the gravitational constant.

What happens when two black holes are separated by more than one Schwarzschild radius?

When two black holes are separated by more than one Schwarzschild radius, they are considered to be in each other's event horizon. This means that they are so close together that they cannot escape each other's gravitational pull, and will eventually merge to form a larger black hole.

How does the distance between two black holes affect their gravitational pull?

The distance between two black holes directly affects their gravitational pull on each other. As the distance decreases, the gravitational pull increases, making it more difficult for the black holes to escape each other's gravitational field.

Can two black holes ever merge if they are separated by more than one Schwarzschild radius?

Yes, two black holes can still merge even if they are separated by more than one Schwarzschild radius. This process is known as a binary black hole merger, and it occurs when the black holes are close enough to each other to form a single, larger black hole.

What is the significance of two black holes being separated by more than one Schwarzschild radius?

Two black holes being separated by more than one Schwarzschild radius is significant because it marks the point at which the black holes are considered to be in each other's event horizon. This means that they are close enough to merge and form a larger black hole, which can have significant implications for the surrounding space and matter.

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