Area products for stationary black hole horizons

Understand

Area products for multi-horizon stationary black holes often have intriguing properties, and are often (though not always) independent of the mass of the black hole itself (depending only on various charges, angular momenta, and moduli).

• Such products are often formulated in terms of the areas of inner (Cauchy) horizons and outer (event) horizons, and sometimes include the effects of unphysical "virtual" horizons.
• But the conjectured mass-independence sometimes fails.
• Specifically, for the Schwarzschild-de Sitter [Kottler] black hole in (3+1) dimensions it is shown by explicit exact calculation that the product of event horizon area and cosmological horizon area is not mass independent.