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I will prove that general relativity (GR) is self-inconsistent. First some supporting info (or skip to “

From pg. 1-19 of

From the glossary of

GR predicts that an inertial frame can exist everywhere except at the center of a black hole. Here are confirmations:

A definition of

Let

Note that:

I will prove that general relativity (GR) is self-inconsistent. First some supporting info (or skip to “

**Now the proof**” near the end):From pg. 1-19 of

*Exploring Black Holes*by Taylor and Wheeler: “The spacetime arena for special relativity is the*free-float (inertial) frame*, one in which a free test particle at rest remains at rest and a free test particle in motion continues that motion unchanged. We call a region of spacetime*flat*if a free-float frame can be set up in it. ... In principle one can set up a latticework of synchronized clocks in a free-float frame. The position and time of any event is then taken to be the location of the nearest lattice clock and the time of the event recorded on that clock. The*observer*is the collection of all such recording clocks in a given reference frame.”From the glossary of

*Exploring Black Holes*:*flat spacetime*: Region of spacetime in which it is possible to set up a free-float (inertial) reference frame.

*horizon*: One-way surface surrounding a black hole, defined by the property that anything may pass inward through the horizon, but (in the non-quantum description) nothing, not even light, may pass outward.

*inertial frame (free-float frame)*: Generally, a reference frame in which a free test particle initially at rest remains at rest. More technically, a reference frame with respect to which relative (tidal) accelerations of test particles can be neglected for the purposes of a given experiment.

*tidal acceleration [(tidal force)]*: Relative acceleration of two free test particles located in different parts of a reference frame.

*Black Holes & Time Warps*by Thorne:*event*: A point in spacetime; that is, a location in space at a specific moment of time. Alternatively, something that happens at a point in spacetime, for example, the explosion of a firecracker.

*freely falling object*: An object on which no forces act except gravity.

*local inertial reference frame*: A reference frame on which no forces except gravity act, that falls freely in response to gravity’s pull, and that is small enough for tidal gravitational accelerations to be negligible inside it.

*tidal gravity [(tidal force)]*: Gravitational accelerations that squeeze objects along some directions and stretch them along others. Tidal gravity produced by the Moon and Sun is responsible for the tides on the Earth’s oceans.

- Spacetime curvature and tidal gravity [(tidal force)] are different names for the same thing. (Taylor and Wheeler concur on pg. 2-7 of
*Exploring Black Holes*.)

- The spacetime throughout an inertial frame is flat.

- The definition of an inertial frame allows them to be arbitrarily large (they need be only “small enough”).

*Black Holes & Time Warps*(the italicized statement is Einstein’s): “*In any small, freely falling reference frame anywhere in our real, gravity-endowed Universe, the laws of physics must be the same as they are in an inertial reference frame in an idealized, gravity-free universe*. Einstein called this the*principle of equivalence*, because it asserts that small, freely falling frames in the presence of gravity are equivalent to inertial frames in the absence of gravity. This assertion, Einstein realized, had an enormously important consequence: It implied that, if we merely give the name "inertial reference frame" to every small, freely falling reference frame in our real, gravity-endowed Universe (for example, to a little laboratory that you carry as you fall over a cliff), then everything that special relativity says about inertial frames in an idealized universe without gravity will automatically also be true in our real Universe. Most importantly, the*principle of relativity*must be true: All small, inertial (freely falling) reference frames in our real, gravity-endowed Universe must be "created equal"; none can be preferred over any other in the eyes of the laws of physics.”GR predicts that an inertial frame can exist everywhere except at the center of a black hole. Here are confirmations:

- From pg. 2-4 of
*Exploring Black Holes*: “Our old, comfy, free-float (inertial) frame carries us unharmed to the center of a black hole. Well, unharmed*almost*to the center! ... No one can stop us from observing a black hole from an unpowered spaceship that drifts freely toward the black hole from a great distance, then plunges more and more rapidly toward the center. Over a short time the spaceship constitutes a "capsule of flat spacetime" hurtling through curved spacetime. It is a free-float frame like any other. Special relativity makes extensive use of such frames, and special relativity continues to describe Nature correctly for an astronaut in a local free-float frame, even as she falls through curved spacetime, through the horizon, and into a black hole.” From pg. 2-6: “Confronted by tidal accelerations, how can we define a free-float frame falling into a black hole? At the center of the black hole we cannot; general relativity predicts infinite tidal accelerations there. However, short of the center, [we limit] the space and the time—the region of*spacetime*!—in which experiments are conducted.” See also the section*free-float frame*on pg. 2-31.

- From pg. 21 of
*Black Holes: A Traveler’s Guide*by Pickover: “If you were approaching a 10 solar masses black hole with a radius of 30 kilometers, you would be killed long before you reached the horizon, at an altitude of 400 kilometers. However, you could reach the horizon of a 1,000 solar masses black hole, and even be able to explore the*interior*of a 10 million solar masses black hole. The tidal forces at the horizon of this gigantic black hole would be weaker than those produced by Earth, which are already impossible for us to feel.”

- Another online reference: “In a supermassive black hole the tidal forces are weaker, and you could survive well inside the horizon of the black hole before being torn apart.”

*Black Holes FAQ*: “You can think of the horizon as the place where the escape velocity equals the velocity of light. Outside of the horizon, the escape velocity is less than the speed of light, ...”A definition of

*escape velocity*: “In physics, for a given gravitational field and a given position, the escape velocity is the minimum speed an object without propulsion needs to have to move away indefinitely from the source of the field, as opposed to falling back or staying in an orbit within a bounded distance from the source.”**Now the proof**:Let

*X*be an inertial frame falling through the horizon of a black hole. Since the spacetime throughout an inertial frame is flat, it must be possible to set up an inertial frame*Y*that extends throughout*X*and in which a free test particle, that is above the horizon and moves away from the black hole indefinitely, stays at rest. But GR predicts that nothing may pass outward through a horizon. Then*Y*cannot extend below the horizon (if only because otherwise a latticework of synchronized clocks, that stays at rest with respect to*Y*and is spread throughout*Y*, would be passing outward through the horizon), and so the spacetime cannot be flat throughout*X*. Then*X*cannot be an inertial frame. That is, an inertial frame cannot fall through the horizon of a black hole. GR required this conclusion, yet the theory predicts otherwise, contradicting itself, so it is self-inconsistent.Note that:

- The definitions of
*flat spacetime*and*inertial frame*in the supporting info account for the tidal force. The tidal force in*X*need not be nonexistent.

*X*can be arbitrarily small and its duration can be arbitrarily short. Then the tidal force in*X*can be nonexistent*in the limit*.

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