<><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>

A Simple Explanation of Black Holes

Louis N. Proyect:

I was trying to follow a one-hour lecture on Black Holes [podcast] but gave up after fifteen minutes and switched to Jay Leno’s garage to hear what he had to say about the 1955 Packard Caribbean.

Manuel García, Jr.:

Hawking’s “A Brief History of Time” is a pretty good book about it, for the general public.

Theoretically, Black Holes are a consequence of Einstein’s General Relativity (the effect of gravity on space-time): with enough concentrated mass, and insufficient thermal-nuclear energy generation (a star uses up its “fuel”) to keep that mass puffed out, its mutual gravity draws it into a spherical center, and since mass-gravity “curves” space-time (an effect that diminishes with radial distance from the center) and since space-time curvature is expressed/observed as the bending of light rays; at a particular radial distance (the Schwarzschild Radius) light rays are curved completely by 360 degrees – into circles.

Light emitted and/or passing by a Black Hole outside the SR is bent (by quite a bit but less than 360 degrees close to the SR, and less so with increasing distance from the SR). Light emitted at distances less than the SR are infinitely bent (curly cues), and never travel beyond the SR – they are trapped. Hence “Black Holes” because no light is emitted from them.

Black Holes can be detected by measuring how light rays from a known distance source are bent on passing (outside the SR) near a Black Hole. When Quantum Mechanics is added to the theoretical description of Black Holes, then more odd possibilities arise having to do with matter popping into and out of existence in the vicinity of the SR, but somehow entangled with mirror quantum interactions inside the Black Hole, and from that Hawking proposed ways for gaining information from inside a Black Hole despite the barrier to (non quantum)) information flow, by the SR.

Hawking also presented a theory that such “quantum flickering” (my term, here) could lead to Black Holes steadily ‘evaporating’ into non-existence; analogous to a soap bubble popping. Hawking’s way of describing it for the public is, naturally, very good; but the math behind it all is massively complicated and above my pay grade.

Louis N. Proyect:

I can’t wrap my head around space-time. When I go to the CVS across the street, it takes about 3 minutes. How can a Manhattan avenue and the time it takes to cross it occupy the same continuum?

Manuel García, Jr.:

Think of it this way, first in 2 space dimensions: imagine a checkerboard of grid lines for length and width, and their intersections “define” points in space, or locations. Maritime navigation uses this idea, where the 2D surface happens to be the surface of a sphere (latitude, longitude).

Now, at any single location (say, your desert island) time proceeds forward from a past to a future (you are always in a “now” that is the experienced part of this ‘perpetual’ stream). So now we imagine our checkerboard having vertical “time lines” piercing the horizontal spatial (2D) plane at each “location.”

Hence, the complete description of the 3D space-time of every location is defined by its x and y coordinates (spatial coordinates, like latitude and longitude) PLUS a time coordinate, t, noting the ‘time” point of whatever event is being denoted for location x-y (e.g., your 70th birthday on your desert island).

George Pal’s 1960 movie of H.G.Wells’ “The Time Machine” presented a beautiful description and use of this concept: the Time Machine could go into the past or the future but always fixed to one spot on Earth.

Now, given our actual (or perceived) 3D spatial world, we then exist in a 4D space-time. It is just impossible to draw a visual image of a 4D grid in the 3D space we experience, or on our 2D papers and art pads. But mathematics can describe 4D with exactitude (as multi-dimensional geometry, and with tensor mathematics).

Now for curvature. If you use a checkerboard quilt as a bedspread (to lay out an x-y grid of straight lines (called a Euclidian Space or Euclidian Geometry) and then place a bowling ball in the middle of it, the quilt will be deformed by the weight of the ball (gravity) and the grid lines near the ball will appear curved — because the originally flat surface they were defined in has been warped out of its original “2D-ness.”

That warping of the originally flat surface has a funnel shape: no warping (which is “down”) far away, and increasing warping as one gets closer to the bowling ball. If you now imagine a 2D (spatial) Black Hole, the funneling becomes increasingly vertical (“plunging”) on approach to the SR until it becomes perfectly vertical at the SR.

So, as light rays are in fact the grid lines forced to remain on the spatial surface, however it is warped, then the grid line at the infinite bottom of the funnel (which occurs at the SR) is a perfect circle, and can never “climb out.”

So now, for 3D space it is impossible to draw gravity-induced warping of space-time (which is 4D: 3 space dimensions, 1 time dimension), but the idea is exactly as described above.

To add more fun to it all, by Einstein’s General Relativity, the curving of light rays is equivalent to a slowing of them (analogous to taking your sports into a curve after racing down the Mulsanne Straight). So, with infinite curvature (the situation at the SR) time becomes infinite: or “stops.” Light rays at or below the SR are in “suspended animation” or “eternity,” they are stuck forever.

Lots of science fiction is based on the idea of the “light cones” centered on the “time axis” piercing our spatial here-and-now, coming to our specific (x,y,z,t) out of the past (“history”), narrowing down from the totality of events of the distant past to the single moment-spot of our specific here-now (x,y,z,t); and projecting into the future with an expanding range of possibilities as one projects into the more distant future.

It is easy enough to find images (sketch representations, cartoons, videos) on the internet of this light-cone limitation of the possible causes of this here-now, and its range of possible future effects.

BTW, the “grid lines” in “surfaces” (forming the coordinate system that maps them out) are called geodesics.

Have fun.

Thanks to Louis N. Proyect for asking good questions, and being patient enough to let the explanation unroll.

<><><><><><><>