General static black holes in matter

Abstract

For arbitrary static space-times, it is shown that an equilibrium between a Killing horizon and matter is only possible for some discrete values of the parameter $w=p_1/\rho$, where $\rho$ is the density and $p_1$ is pressure in the direction normal to the horizon. In the generic situation of a simple (non-extremal) horizon and the slowest possible density decrease near the horizon, this corresponds to $w=-1/3$, the value known for a gas of disordered cosmic strings. An admixture of "vacuum matter", characterized by $w=-1$ and nonzero density at the horizon, is also admitted. This extends the results obtained previously for static, spherically symmetric space-times. A new feature as compared to spherical symmetry is that higher-order horizons can exist in the absence of vacuum matter if the horizon is a surface of zero curvature, which can occur, e.g., in cylindrically symmetric space-times.

6 pages latex

References in corpus (3)

• Horizons vs. singularities in spherically symmetric space-times
• Black holes can have curly hair
• Truly naked spherically-symmetric and distorted black holes

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