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Black holes in loop quantum gravity: the complete space-time.

Rodolfo Gambini¹, Jorge Pullin

¹Instituto de Física, Facultad de Ciencias, Iguá 4225, esq. Mataojo, Montevideo, Uruguay.

Physical Review Letters

|November 13, 2008

Summary

Loop quantum gravity resolves the singularity in the Schwarzschild spacetime, creating a horizon. This quantum gravity approach suggests a singularity-free structure similar to Reissner-Nordström spacetime.

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Area of Science:

Quantum gravity
General relativity
Cosmology

Background:

The Schwarzschild spacetime describes a non-rotating, uncharged black hole.
Classical general relativity predicts a singularity at the center of black holes.
Loop quantum gravity offers a potential resolution to singularities in general relativity.

Purpose of the Study:

To quantize the complete extension of the Schwarzschild spacetime using loop quantum gravity.
To investigate the resulting spacetime structure and identify any singularity resolution.
To compare the quantum-corrected spacetime with classical solutions.

Main Methods:

Application of spherically symmetric loop quantum gravity.
Derivation of an exact semiclassical solution.
Numerical analysis of the spacetime properties.

Main Results:

The singularity of the Schwarzschild spacetime is eliminated through quantization.
The resulting spacetime retains a horizon.
A global structure resembling a singularity-free Reissner-Nordström spacetime with a Cauchy horizon is suggested.

Conclusions:

Loop quantum gravity successfully removes the singularity in the Schwarzschild spacetime.
The quantum-corrected spacetime exhibits features analogous to a regular black hole solution.
Further analysis is needed for a complete global characterization.