# Non-Turing Computations Via Malament–Hogarth Space-Times

@article{Etesi2001NonTuringCV, title={Non-Turing Computations Via Malament–Hogarth Space-Times}, author={G{\'a}bor Etesi and Istv{\'a}n N{\'e}meti}, journal={International Journal of Theoretical Physics}, year={2001}, volume={41}, pages={341-370} }

We investigate the Church–Kalmár–Kreisel–Turing theses theoretical concerning (necessary) limitations of future computers and of deductive sciences, in view of recent results of classical general relativity theory. We argue that (i) there are several distinguished Church–Turing-type theses (not only one) and (ii) validity of some of these theses depend on the background physical theory we choose to use. In particular, if we choose classical general relativity theory as our background theory…

## 203 Citations

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## References

SHOWING 1-10 OF 32 REFERENCES

### The Geometry Of Kerr Black Holes

- Physics
- 1992

This book offers an up-to-date look at black holes from a mathematical perspective containing many results never before published. It can be read as a broadly based introduction to modern techniques…

### Inner structure of a charged black hole: An exact mass-inflation solution.

- PhysicsPhysical review letters
- 1991

An exact mass-inflation solution of the Einstein-Maxwell equations is constructed, and it is found that this singularity is weak enough that its tidal gravitational forces do not necessarily destroy physical objects which attempt to cross it.

### Radiation-reaction-induced evolution of circular orbits of particles around Kerr black holes.

- PhysicsPhysical review. D, Particles and fields
- 1996

It is demonstrated that, in the adiabatic approximation, nonequatorial circular orbits of particles in the Kerr metric remain circular under the influence of gravitational radiation reaction.

### Are physical objects necessarily burnt up by the blue sheet inside a black hole?

- PhysicsPhysical review letters
- 1995

The electromagnetic radiation that falls into a Reissner-Nordstrom black hole develops a "blue sheet" of infinite energy density at the Cauchy horizon, and the effects of these fields on infalling objects within a simplified model are investigated.

### Radiative Evolution of Orbits around a Kerr Black Hole

- Physics
- 1995

We propose a simple approach for the radiative evolution of generic orbits around a Kerr black hole. For a scalar-field, we recover the standard results for the evolution of the energy E and the…

### Forever Is a Day: Supertasks in Pitowsky and Malament-Hogarth Spacetimes

- PhysicsPhilosophy of Science
- 1993

The standard theory of computation excludes computations whose completion requires an infinite number of steps. Malament-Hogarth spacetimes admit observers whose pasts contain entire future-directed,…

### Can an Infinitude of Operations be performed in a Finite Time

- Philosophy, Mathematics
- 1969

In his book Philosophy of Mathematics and Natural Science, the renowned mathematical physicist Hermann Weyl raised the following question: Is it kinematically feasible that a machine carry out an…

### Comments on Laraudogoitia's ‘Classical Particle Dynamics, Indeterminism and a Supertask’

- PhysicsThe British Journal for the Philosophy of Science
- 1998

We discuss two supertasks invented recently by Laraudogoitia [1996, 1997]. Both involve an infinite number of particle collisions within a finite amount of time and both compromise determinism. We…