7
Small Magnetic Black Hole
Abstract
A magnetic black hole in Einstein–Maxwell theory is described by the potential
1-form of a magnetic pole and a line element which coincides with the Reissner–
Nordström line element dependent upon two parameters representing the mass
of the magnetic pole and the magnetic monopole moment. When such an object
interacts with external fields it behaves differently to an electric black hole. This
can be exhibited most easily if one assumes that the magnetic black hole has
small mass and small magnetic monopole moment (and is therefore a small
magnetic black hole). In this case the equations of motion can be derived
approximately with sufficient accuracy to include electromagnetic radiation
reaction, external 4-force and tail terms.
7.1
Magnetic Poles
Notwithstanding the absence so far of an observation in nature of a magnetic
monopole, there exist stimulating theoretical studies associated with such objects
beginning with the seminal work of Dirac [1] and followed, most notably, by
the Wu–Yang monopole [2] and the ’t Hooft–Polyakov monopole [3, 4]. Magnetic monopole-like phenomena also occur in condensed matter physics (see, for
example, [5], ch.17). The technique for studying the motion of a small magnetic
black hole involves using the vacuum Einstein–Maxwell field equations together
with the assumptions that the small magnetic black hole is isolated and the wave
fronts produced by the motion of the black hole are smoothly deformed 2-spheres
in the vicinity of the black hole. This technique, and its historical background,
are described in detail in [6] (see also [7] and references therein). The application
described below can be found in [8].
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
P. A. Hogan, D. Puetzfeld, Frontiers in General Relativity, Lecture Notes
in Physics 984, https://doi.org/10.1007/978-3-030-69370-1_7
153
Small Magnetic Black Hole
Abstract
A magnetic black hole in Einstein–Maxwell theory is described by the potential
1-form of a magnetic pole and a line element which coincides with the Reissner–
Nordström line element dependent upon two parameters representing the mass
of the magnetic pole and the magnetic monopole moment. When such an object
interacts with external fields it behaves differently to an electric black hole. This
can be exhibited most easily if one assumes that the magnetic black hole has
small mass and small magnetic monopole moment (and is therefore a small
magnetic black hole). In this case the equations of motion can be derived
approximately with sufficient accuracy to include electromagnetic radiation
reaction, external 4-force and tail terms.
7.1
Magnetic Poles
Notwithstanding the absence so far of an observation in nature of a magnetic
monopole, there exist stimulating theoretical studies associated with such objects
beginning with the seminal work of Dirac [1] and followed, most notably, by
the Wu–Yang monopole [2] and the ’t Hooft–Polyakov monopole [3, 4]. Magnetic monopole-like phenomena also occur in condensed matter physics (see, for
example, [5], ch.17). The technique for studying the motion of a small magnetic
black hole involves using the vacuum Einstein–Maxwell field equations together
with the assumptions that the small magnetic black hole is isolated and the wave
fronts produced by the motion of the black hole are smoothly deformed 2-spheres
in the vicinity of the black hole. This technique, and its historical background,
are described in detail in [6] (see also [7] and references therein). The application
described below can be found in [8].
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
P. A. Hogan, D. Puetzfeld, Frontiers in General Relativity, Lecture Notes
in Physics 984, https://doi.org/10.1007/978-3-030-69370-1_7
153