The 'inner-horizon thermodynamics' of Kerr black holes

Astronomy and Astrophysics – Astronomy

Scientific paper

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Angular Momentum, Black Holes (Astronomy), Quadratic Equations, Thermodynamics, Kerr Effects, Schwarzschild Metric, Surface Temperature

Scientific paper

The thermodynamics of the event horizons and of the inner horizons are described in a unified manner by using a dimensionless parameter H. It is defined by h = a/rH = h+ on the event horizons, and varies in the range of 0 to 1, while it is also given by h = rH/a = a/r = h- on the inner horizons in the range of 1 to infinity, where a = J/Mc is the angular momentum radius and rH = r+, r- are the radii of the outer and inner horizons respectively. Every thermodynamic variable, other than the mass M and the angular momentum J, is also defined on both the outer and inner horizons, and its values form a pair of the roots of a quadratic equation with M and J contained in the coefficients, similar to the horizon radii r+/- and H+/-. It is also shown that this pair of each variable constitutes mirror images of each other with respect to the extreme Kerr state.

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