[TOP]: Improved PAGE NAVIGATION Edit: 03-Oct-15 11:10 PM
In many discussions for science consuming audiences, the BH is described [paraphrased] "as a voracious monster consuming wayward mass never to be seen again." and "GRAVITY IS SO STRONG AT THE EVENT HORIZON NOT EVEN LIGHT CAN ESCAPE." Then uttered in the same breath: "powerful jets are seen 'spewing out' matter at nearly light speed along the spin axis; This jet phenomenon is poorly understood."
Need a break..., cannot have it both ways; nothing can escape, and the Jets spewing out!, all in the same breath. I would reply: "What happened to the voracious gravity field that nothing, not even light can escape?, How does matter leave the BH whilst creating observable jets along the spin axis and, indeed, escape from the BH?" To hear my Proposed_Theory read on . . .
The geometrically to-scale computational animation to the right BELOW is to aid visualization of the Binary BH geometry in 3-dimensions. Axes tics are increments of Schwarzschild Radius. The visible Z-axis plasma jets are caused by Hyper Energetic Particle (HEP) head-on collisions. In-fall from +Z encounters egress mass that entered from from -Z. The RED profile represents the combined EH data from the analytical chart to the left. Notice spiral in the jets which should exist due to extreme gravitational frame dragging affecting the jet plasma.
Notice that interloping material can in-fall along the Z-axis completely unperturbed by X and Y-forces. This material is subject to intense Z-acceleration (while approaching X-Y plane) and Z-deceleration (while leaving the X-Y plane). In-fall material, other than along (near) Z-axis, would follow randomly scattered trajectories into ~4PI steradians of space. Opportunity for collisions not on the Z-axis exist as well, but the probability of head-on particle alignment may be greatly reduced off axis. Go back to main GS_0.html menu to see this particular BH Binary from a side view. This side view shows the actual Event Horizon Profile most clearly.
The mutual (M0) and (M1) singularity separation distances (chart above) were set at radii of 36.4 miles from the mutual CG (Barycenter). This distance is the ~maximum singularity separation for a 10-SM binary that would have a single contiguous event horizon (EH) that extends between them. The Black Holes are located and spin in the X-Y (horizontal) plane. Each BH taken individually has a Schwarzschild event horizon radius of 18.35 miles and are shown as RED circles. The red upper and lower RED boundaries portray the combined (computed) Schwarzschild event horizon (see Schwarzschild Definition). In-falling matter can pass unobstructed along the Z-axis at relativistic speeds.
The white lines represent in-fall trajectories of (M2) objects placed initially stationary at (an engineer's) +infinity, these (M2's) are attracted by (M0 & M1) and fall in inertial space depicted by the white line trajectories from the +Z top to -Z bottom of page. The solver tracks the X-Z position and velocity of the (M2) mass as it is accelerated downward past the binary BH.
The violet lines represent in-fall trajectories of (M2) objects initially placed at ~infinity (-6000 miles) in the -Z direction. Notice that nearly adjacent trajectories are nearly parallel.
When the accumulated gravitational energy of (M2's) reach (Newtonian) velocity equal to or exceeding 'c', the trajectory is colored blue. When (M2's) pass across the X-Y plane, gravitational force begins slowing (M2's). The accumulated in-fall kinetic energy then begins conversion back to gravitational potential energy. When (M2) kinetic energy drops back to the 'Schwarzschild energy', the trajectory trace(s) revert to white (or violet) color
The pictured data is generated by an initial-valued 3-Body (M0, M1, M2) solver that iteratively applies mutual vector force(s) [F=GmM/R/R] of each of (M0 & M1) bodies upon the (M2) body. This force is allowed to act for a short period of time such as 3-12 nanoseconds per iteration. These 3 forces produce acceleration of each body which integrates to new velocity and new position for each of the 3 bodies. Relativistic effects are ignored and are not needed (as will be explained later) for purpose of arriving at a correct supposition. To decrease runtime, the solver (M2) motion is constrained to two dimensions (2D) in the X-Z plane.
The binary BH pair spin in the X-Y plane about the mutual CG (barycenter) which is located at (0,0,0) miles on the X-axis. The Z-spin rate is 204.5 revolutions per second for this model and geometry.
As the two BH's are placed closer together, the combined event horizon (outer RED lines) becomes oval in shape. The tighter the (M0 to M1) coupling, the faster they spin (see next chart). When the two BH CG's are merged, the combined event horizon becomes circular (spherical) with radius of 36.7 miles, that of a single 20 solar mass BH. BTW, What happens to spin rate for two merged BH's obeying conservation of angular momentum is virtually unimaginable which is why BH's with spin (Kerr) are described as infinitely thin washer shaped rather than point singularities. (A LARGER QUESTION is: If gravitational radiation power is a real phenomenon, why is not all orbital spin energy of a Binary BH radiated away before final merger to a 'non-Kerr BH???'.)
The chart portrays (M2) motion in the X-Z plane. Get your head into the geometry: Were the solver 3D, the binary BH masses would be spinning in the (X-Y) horizontal plane with masses (M0) and (M1) repeatedly moving in front of and behind the screen (chart). Spin centrifugal force [F=M*w*w*R] would balance the gravitational force [F=G*m0*m1/R/R]. The white (m2) trajectories would move (pseudo randomly) out of the X-Z plane into fully 3D space.
The solver algorithm works in 2D to provide the data result sought because spin of (M0) and (M1) about Z is not needed to maintain the chosen (M1) and (M0) radial positions from the binary CG. The solver force(s) (M0-on-M1) and (M1-on-M0) are program disabled so that the two BH singularities are stationary in inertial space. Only the vector forces of (M0-on-M2's) and (M1-on-M2's) are allowed to act on trajectory bodies. This creates an 'on the cheap' Black Hole Laboratory, so to speak with non-Z-spinning BH's that don't attract each other & do stay put.
At solver start t=0, (M2) bodies (one at a time) are placed radially a 'great distance' (say 6000 miles, an engineers approximate infinity) away from the binary BH and released at various angles (30 to 150 degrees and 210 to 330 degrees) from the binaries CG in the X-Z plane. For two 10 Sol binary BH masses 72.8 miles apart, a 6000 mile gravity drop distance manifests error less than 1/3% in the combined Schwarzschild EH (computed on the basis of Newtonian 'c' speed energy).
After all, keep in mind, to actually drop M2 particles from infinity would result in NO ACTION since inverse square law force on the particle at infinity would be zero. I had found the integration time from 6000 miles to be about as long as I could stand (hours per scan). I thus accepted the 1/3% error that slightly shrunk the computed EH position.
Brainstorm: At solver start t=0, (M2) bodies (one at a time) are now placed radially a 'modest distance' say 300 miles from the binary barycenter and released at various angles 5 to 175 degrees in 5 degree increments. For two 10 Sol binary BH masses, this gravity drop distance for initial Vx2 and Vy2 of zero would cause large error of about 12.2%. At 300 remaining miles the in-fall should have attained velocity 0.35c, not zero. The program now computes this velocity for any radial release position and and assigns the respective X-Y components of velocity to the M2 in-fall mass at release. This looks like a hyperbolic orbit but is not; it is a parabolic orbit. This computational goody dramatically speeds up the in-fall analysis and ELIMINATES velocity error for Schwarzschild energy determination.
So totally disregard the 'RELATIVELY Speaking' two paragraphs above. Computation is now exact.
Notice that a (M2) particle mass placed at 90 degrees (along Z-axis) will always travel in a dead straight vertical line along Z and pass mid-way between the two (M1=M0) singularities at the CG of the binary. The X-direction component(s) of the vector forces (F02) and (F12) are always equal and opposite in magnitude (cancel). Only particle masses traveling along the Z-axis will tend to stay traveling along Z-axis. The particle will enter the red Schwarzschild event horizon (trace turns blue), pass through the CG (barycenter) and emerge at the lower (RED) event horizon along the -Z axis.
POSIT: The above described event represents SUCCESSFUL ENTRY AND ESCAPE From INSIDE THE EVENT HORIZON of a Binary Black Hole. BTW, when the particle mass emerges the lower EH, it will be traveling at near light speed of ~0.786c and have a mass 1.618 times rest mass according to special relativity (see Fibonacci). This experimental description codifies the assertion; To escape from inside any event horizon is not a matter of velocity, or of having to travel faster than the speed of light! ENERGY IS (M2's) ticket back out... (light cannot but mass can escape a Binary BH). And I believe, also, that mass can escape the EH of any Black Hole as long as the in-fall trajectory is not radial (targeting the singularity).
The last sentence may be considered be crazy and refuted. But, I believe it will be difficult for those of opposing view to avoid the conclusion of 'entry and escape' from a equal mass Binary Black hole for Z-axis in-fall due to symmetry cancellation of off-axis forces (and gravitational radiation). And opposing views may be obliged to explain why and how conservation (energy and momentum) is suspended inside the EH, which view is required to make Z-axis in-fall mass make a turn toward the (a) singularity upon entering the EH of the binary.
The 'motive' that enables mass to escape from inside the event horizon is ENERGY (not velocity per se). Gravity is A CONSERVATIVE FIELD. Energy gained by (M2) falling into the gravity-well will be subsequently used by (M2) to climb back out of the (M1+M0) gravity well. Depending on how close a particle mass approaches the singularity (is the collapsed mass a point?, maybe, maybe not), the (M2) velocity could closely approach c (0.99999c, etc. see relativistic chart) and the relativistic particle mass would correspondingly grow to 100's or 1000's of times the (M2) rest mass. This accumulated in-fall gravity energy is conserved as manifest in kinetic energy. The laws of physics are not to be violated. Energy and Momentum must be [and are] conserved!, methinks. What do you think?
Consider that (M2) particle masses can also enter along the -Z binary BH spin axis. Such particles would be moving upward headlong into oncoming in-fall from the +Z axis position. Opportunity of collision of these particle masses traveling in opposing directions would, upon collision, form observable jets of plasma along the Z-spin axis (an astronomically observed phenomenon). I posit that jets observed at locations believed to be black holes may be exactly that; highly populated particle collision tracts of ionized particles along the spin axis of pairs of black holes forming a binary. When the jets are seen, closer inspection may betray a Binary BH lurking within.
In fact, the symmetry of an equal mass binary pair of BH's would create a temporal stable "trapped situation" where axial infall mass could repeatedly positionally oscillate along (very close to) the Z-axis of the binary until happenstance of collision with opposite traveling matter. This oscillation corredor along the Z-spin axis could load up with captured mass that would oscillate along +Z and -Z until collision(s) occurred, which high energy collisions would be the observed jets plasma. The closer along the Z-axis that acretion mass particles enter the fray, the more stable will be the oscillation for that particle, until opposing collision.
The region around the binary would need sufficient accretion particle mass (dirty neighborhood: dust, asteroids, etc) to feed the opposing +Z and -Z axes ingress and subsequent egress to enable collisions to cause visible jets.
As (M2) in-fall trajectories approach the BH-binary away from the Z-axis, their trajectories will have severe 3D curvature and close(r) Perimelasma. Gravity gradient greatly increases with decreasing distance to a singularity. This would 'spaghettify' and disperse materials into fractional masses, dust, atoms, etc reducing particle collision energy(per unit mass) and collision probability due to trajectory dispersion and particle size.
Note that all the (M2) particles are (stay) in the X-Z plane. These (M2) particles and (M1 & M0) all had Y=0 position and no initial Y-velocity therefore there are no Y-components of force from (M1) and (M0) acting on (M2) particles. In a full 3D analysis binary (M1 & M0) are spinning at a 18.4 mile radius about Z. In the 3D case, only (M2) particle masses with trajectories along the Z-axis (very close to Z) will remain along the Z-axis because all Fx and Fy component forces from (M1) and (M0) acting on Z-axis (M2) particles cancel. This could be the reason for the narrowly defined jets that are observed.
Convert the 2D analysis to 3D by setting (M1) and (M0) spinning about the Z-axis (see Animation above). All in-fall aligned with the Z-axis would still accelerate along the Z-axis (as with the 2D case). But (M2) in-fall entering oblique to the Z-axis would be propelled into and ejected from a solid angle of space around the Z-axis. The collision probability is greatly enhanced along the Z-axis and greatly reduced off axis by the large solid dispersion angle compared to the tiny solid angle around the Z-axis and by effects noted in heading above "Why Just ON-Axis Jets?".
The 1st chart (at the TOP of page) shows the max separation (4x Rs) to just barely merge the two Schwarzschild EH surfaces in the vicinity of the barycenter. The 3D shape of this binary BH EH looks somewhat like a dumbbell or two tear drops connected at the points in opposing directions and whirling about the Z-axis along a line perpendicular to Z passing through the barycenter.
The chart (below) shows a Binary BH with the masses placed such that the individual EH's (RED circles) are tangent. This configuration increases the spin rate to 571.3 rps. The combined event horizon thickness along the Z-axis is greater than the Rs for either BH as an individual black hole.
This chart (below) shows the results for the Event Horizons 50% overlapped. The RPM is 1616 revolutions per second (RPS)!. Notice the two (M1 & M0) masses are so close (18.34 miles) that the combined Event Horizon is approaching spherical. The classical EH transit time for Z-axis in-fall is 0.279 mSec from EH-ingress to EH-egress.
As the two 10 SM singularity CG's are merge into one BH, the combined mass produces one 20 Sun BH with a 36.7 mile Rs.
I will be enhancing the Solver program code to capture more information such as the combined EH coordinates.I can add an array that captures the (M2) xy(1:n,1:2) position and vector velocity during transit. I may add a chart in the graphics for these runs that depicts the relativistic mass increase and velocity inside the combined EH. The program presently permits from one to many (m2) masses to be dropped through the binary gravity field. In the all present cases the T_e2e transit time is posted in the 4 line of the chart table.
Further, the CG position would exhibit stable Z-position equilibrium but..., unstable position equilibrium in X and Y-axis directions. Imagine a 2.15 + 2.15 million Sun (galactic) BH Binary with Tangent EH's; To have a walkable 1-g plane surface, the beam-in position would need to be on a plane 2.73 z-miles above the barycenter which creates normal 1-gravity to provide 'shoe-traction'. The lateral force (if my numbers are correct) tugging a 200 Lb man who ventured radially 4150 ft from the barycenter would be 115.5 Lbf (.0278 Lbf/Foot radial gradient). The Binary BH spin rate would about 0.0028 Hz so the radial force would oscillate from zero to F=(0.0278 x dist) at 0.0056 Hz (~once every 3 minutes; frequency is double the spin rate). This would give the person the feeling that the floor or disk he was standing on was alternately tilting from level to 30 deg. 'down hill' toward the closer BH and back to level every 3 minutes. Somewhere near this 4150 ft displacement (@ 115.5 lateral force) he would probably be whisked off his feet to a 'singular' death at one BH or the other. Tickets, anyone?...
Before poo-pooing the theory on mass gaining kinetic energy on in-fall that will be available/converted back to gravitational potential energy when climbing back out, Remember: The only actionable force on a (M2) interloper trekking the Z-axis is Z-force; no x-axis force, no y-axis force. (M1 & M0) X & Y forces acting on (M2) are mutually cancelling entirely along the Z-axis. Where am I going wrong?
I try to stay tuned to the BH topic as much as possible (Astronomy and other pubs). From my wanderings, reading, and watching science shows, most everyone I've heard (SEE NOTE) believes that ANY (nay, ALL) mass entering the event horizon of any BH zooms right to the singularity 'fait accompli'. It will take a good argument to convince me how hitting the singularity is inevitable and why this 'happening' does not violate conservation.
The TWO Arguments: 1) TRUE: nothing can exceed the speed of light and 2) TRUE: light cannot escape the event horizon lead to a trap; an incorrect conclusion that, as articulated, nothing can escape the event horizon, how could it escape since it must travel slower than light?, The error in this fatal logic is that energy, not speed, is required to escape the event horizon. After all, if you were standing on a (somehow) fixed ladder leading through the event horizon of a large Black Hole, you could simply climb out through the event horizon one step at a time at speed far less than the speed of light. You read that here.
I ran some numbers to size the needed Black Hole to create 1.0 G's acceleration AT the Event Horizon. See chart Below... it is BIG.
The BH would would be 1.55 million million solar masses, but it would work. the Schwarzschild event horizon radius would be ~30,500 AU. I don't think a BH that big has been found, it would be ~388,000 times more massive than our Milky Way Galaxy's BH. - BUT you could climb down a massless ladder right through the event horizon and back out!
Note: The G's equation is included on the BH_0 Equations Page.
If gravity stops being a conservative field inside the event horizon (EH), I would surely like to know how and why. Non-Conservative gravity ANYWHERE messes with my head. Let the 1st scientist to violate 'conservation' cast the 1st stone.
NOTE: I Heard the science channel today 6-Feb-11 talking about entering and leaving the event horizon, finally. A next big question will be "how big is the actual singularity" inside the event horizon. Popular conception is a point which gets relativity into trouble with infinite density, force, spin-rate from angular momentum (Kerr BH with finite disc), etc. I believe the singularity will (may) eventually be found to have finite dimensions. And those dimensions will likely leave 'space' between singularities and the inside of the event horizon for interloping mass to travel on trajectories which will be able to re-emerge and escape the EH by virtue of conservation of energy. By the way, how are the searches for gravity waves (LIGO, etc) progressing?