Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1997-02-05
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
plain TeX 14 pages. Uses harvmac b and epsf. 14 figures
Scientific paper
We present analytical perturbative, and numerical solutions of the Einstein equation which describe a black hole with a nontrivial dilaton field and a purely topological gauge potential. The gauge potential has zero field strength and hence no stress-energy, but it does couple to virtual string worldsheets which wrap around the Euclidean horizon two-sphere, and generate an effective interaction in the spacetime lagrangian. We use the lagrangian with a nonstandard potential for a scalar field that reproduces the effect of the worldsheet instantons. As has been previously pointed out the topological charge Q of the gauge field can be detected by an Anharonov-Bohm type experiment using quantum strings; the classical scalar hair of the solutions here is a classical detection of Q. ADM mass, dilaton charge and Hawking temperature are calculated and compared with the known cases when appropriate. We discuss why these solutions do not violate the no-hair theorems and show that, for sufficiently small interaction coupling, the solutions are stable under linear time dependent perturbations.
Traschen Jennie
Win Kyaw Zin
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