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Register a new userNear-horizon description of extremal magnetised stationary black holes and Meissner effect
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After a brief summary of the basic properties of stationary spacetimes representing rotating, charged black holes in strong axisymmetric magnetic fields, we concentrate on extremal cases, for which the horizon surface gravity vanishes. We investigate their properties by constructing simpler spacetimes that exhibit their geometries near degenerate horizons. Starting from the symmetry arguments we find that the near-horizon geometries of extremal magnetised Kerr-Newman black holes can be characterised by just one dimensionless parameter: effective Kerr-Newman mixing angle. Employing the near-horizon geometries we demonstrate the Meissner effect of magnetic field expulsion from extremal black holes.
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For extremal black holes, one can construct simpler, limiting spacetimes that describe the geometry near degenerate horizons. Since these spacetimes are known to have enhanced symmetry, the limiting objects coincide for different solutions. We show that this occurs for strongly magnetised Kerr-Newman solution, and how this is related to physical Meissner effect of expulsion of magnetic fields from extremal black holes.
We develop a new perturbation method to study the dynamics of massive tensor fields on extremal and near-extremal static black hole spacetimes in arbitrary dimensions. On such backgrounds, one can classify the components of massive tensor fields into the tensor, vector, and scalar-type components. For the tensor-type components, which arise only in higher dimensions, the massive tensor field equation reduces to a single master equation, whereas the vector and scalar-type components remain coupled. We consider the near-horizon expansion of both the geometry and the field variables with respect to the near-horizon scaling parameter. By doing so, we reduce, at each order of the expansion, the equations of motion for the vector and scalar-type components to a set of five mutually decoupled wave equations with source terms consisting only of the lower-order variables. Thus, together with the tensor-type master equation, we obtain the set of mutually decoupled equations at each order of the expansion that govern all dynamical degrees of freedom of the massive tensor field on the extremal and near-extremal static black hole background.
We discuss a new perturbation method to study the dynamics of massive vector fields on (near-)extremal static black hole spacetimes. We start with, as our background, a rather generic class of warped product metrics, and classify the field variables into the vector(axial)- and scalar(polar)-type components. On this generic background, we show that for the vector-type components, the Proca equation reduces to a single master equation, whereas the scalar-type components remain to be coupled. Then, focusing on the case of (near-)extremal static black holes in four-dimensions, we consider the near-horizon expansion of both the background geometry and massive vector field by a scaling parameter $lambda$ with the leading-order geometry being the so called near-horizon geometry. We show that on the near-horizon geometry, thanks to its enhanced symmetry, the Proca equation for the scalar-type components also reduces to a set of two mutually decoupled homogeneous wave equations for two variables, plus a coupled equation through which the remaining variable is determined. Therefore, together with the vector-type master equation, we obtain the set of three decoupled master wave equations, which govern the three independent dynamical degrees of freedom of the massive vector field in four-dimensions. We further expand the geometry and massive vector field with respect to $lambda$ and show that at each order, the Proca equation for the scalar-type components can reduce to a set of decoupled inhomogeneous wave equations whose source terms consist only of the lower-order variables, plus one coupled equation that determins the remaining variable. Therefore, if one solves the master equations on the leading-order near-horizon geometry, then in principle one can successively solve the Proca equation at any order.
We consider a gravitating system consisting of a scalar field minimally coupled to gravity with a self-interacting potential and an U(1) electromagnetic field. Solving the coupled Einstein-Maxwell-scalar system we find exact hairy charged black hole solutions with the scalar field regular everywhere. We go to the zero temperature limit and we study the effect of the scalar field on the near horizon geometry of an extremal black hole. We find that except a critical value of the charge of the black hole there is also a critical value of the charge of the scalar field beyond of which the extremal black hole is destabilized. We study the thermodynamics of these solutions and we find that if the space is flat then at low temperature the Reissner-Nordstrom black hole is thermodynamically preferred, while if the space is AdS the hairy charged black hole is thermodynamically preferred at low temperature.
We investigate the spherical photon orbits in near-extremal Kerr spacetimes. We show that the spherical photon orbits with impact parameters in a finite range converge on the event horizon. Furthermore, we demonstrate that the Weyl curvature near the horizon does not generate the shear of a congruence of such light rays. Because of this property, a series of images produced by the light orbiting around a near-extremal Kerr black hole several times can be observable.
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