Objects Entering Black Holes: The "Spaghetti" Effect

[cooldude3122]

If an object is entering a black hole, it would be accelerating at a constant rate. If that object's matter was accelerating at the same rate then why do people theorize that the object would have a "speghetti" effect?

 

[marcus]

If an object is entering a black hole, it would be accelerating at a constant rate. If that object's matter was accelerating at the same rate then why do people theorize that the object would have a "speghetti" effect?

the closer to center, the stronger the force

that's true in ordinary Newtonian gravity as well
the acceleration falls off as the square of distance.
so as you get closer it increases-----if you get only half as far from center, then the acceleration is FOUR TIMES more
if you get only a third as far, the acceleration is NINE times stronger.

so at some point as you fall in, your feet will be experiencing much more acceleratation than your head

the only way for your feet to be falling faster than your head is if you are being stretched

===================
your problem is you were assuming that acceleration of gravity is constant. that is not true.
even on Earth it is different at the top of a mountain from what it is at sealevel
and it is even different at different latitudes-----they tell you in school it is 9.8 m per sec per sec
or 32 feet per sec per sec but that is just a handy approximation

 

[Chris Hillman]

If an object is entering a black hole, it would be accelerating at a constant rate.

Hang on a moment--- are you asking about our gold standard theory of gravitation, namely gtr? If not, what gravitation theory do you have in mind? If so, I think you are mixing up Newtonian and relativistic physics.

Certainly, if you are asking about an object which is falling freely into a black hole, as treated in gtr, then said object feels no force and its world line is a timelike geodesic. But by definition the acceleration (path curvature) of a geodesic vanishes (this happens in Lorentzian geometry for the same reason it happens in Riemannian geometry).

If that object's matter was accelerating at the same rate then why do people theorize that the object would have a "speghetti" effect?

Now I think you are asking about something yet again, tidal forces as treated in gtr. Indeed, an object near a compact body will feel tidal forces (in gtr, in Newtonian gravitation, in any decent gravitation theory), and these will scale rougly twice as fast radially as tangentially. In particular, an object falling into a black hole will experience radial tension and orthogonal comopression, and eventially will break and the bits will be drawn into a long thing shape as they fall. (Physics students should consult the disucssion in MTW.)

Don't confuse tidal forces on a small extended object, which are identified in gtr with (part of) the curvature tensor of spacetime itself, with acceleration of a pointlike object, which is identified in gtr with the path curvature of the world line of that object! The first kind of curvature is tensorial and has geometric units of inverse area (as does Gaussian curvature); the second kind of curvature is vectorial and has geometric units of inverse length (as does "path curvature" in the Frenet-Serret theory from the study of curves in a euclidean three-space).