Geometry and Thermodynamics of Black Holes in Magnetic Fields ...

More documents

Recommendations

Info

Conical Singularities and Force Balancing• To avoid conical singularity at the North (South) pole, φshould be identified with different periods at each:N pole :S pole :∆φ = 2π ∏ i∆φ = 2π ∏ i(1 + 1 2 B ip i ) ,(1 − 1 2 B ip i ) .In general, there is no single choice of period ∆φ that eliminatesboth conical singularities. This reflects the fact thatthere is a net force on the black hole, and it must thereforebe supported by a “strut,” which is described by an energymomentumtensor with a delta-function singularity on theaxis. This happens, for example, for a magnetic Reissner-Nordström black hole in an external magnetic field. (Or theS-dual, an electric black hole in an external electric field.)• With four separate gauge fields in the STU model we cantune the fields and the charges to achieve a force balance:∏(1 + 1 2 B ip i ) = ∏ (1 − 1 2 B ip i ) .iiThis provides families of non-singular magnetic black holesin external magnetic fields. These provide interesting modelsfor investigating thermodynamics of systems in externalbackgrounds.
Conclusions and Open Problems• A rotating generalisation of the asymptotically-Melvin magnetisedSchwarzschild solution does exist, but it must carry avery specific electric charge, related to its mass and angularmomentum and the external B field. Otherwise, it has anergoregion extending to infinity close to the axis.• The thermodynamics is quite subtle, owing to the unusualasymptotic behaviour of the Melvin type background. Chargeand angular momentum can be calculated from conservedcurrents, but ab initio computation of angular velocity, electricpotential and magnetic moment is more difficult. Framedraggingof the magnetic field is rather complex.• More extensive analysis of the global structure is needed.Also, a detailed investigation of “asymptotically Melvin” boundaryconditions for fields.• Melvin/CFT type dualities?• Magnetisation of black holes in supergravities opens up newpossibilities; non-singular magnetised magnetic black holes,etc.• Recent work (Cvetič, Guica, Saleem) has shown how relatedsolution-generating transformations can be used to interpolatebetween black hole backgrounds and “subtracted geometries”that can be used for studying the microscopic entropy.We are investigating these further.
Page 1 and 2: Geometry and Thermodynamics of Blac
Page 3 and 4: Exact Solution with Back Reaction?
Page 5 and 6: Rotating Generalisations?• Rotati
Page 7 and 8: Magnetisation of Kerr-Newman Black
Page 9 and 10: Magnetisation of Kerr-Newman Black
Page 11 and 12: • This is evident in the cylindri
Page 13 and 14: Asymptotically-Melvin Magnetised Ke
Page 15 and 16: ξ = ∆φ2π e−2ϕ (dφ + 2Ā) a
Page 17: Magnetised Black Holes in STU Super

Geometry and Thermodynamics of Black Holes in Magnetic Fields ...

Create successful ePaper yourself

Delete template?

Save as template?