The apparent shapes of various Kerr-Newman spacetimes are plotted. For this purpose the geometry of closed photon orbits is studied, forming a subset of the bifurcation set A 4 , well known in elementary catastrophe theory. One additional result is that the cosmic censorship hypothesis guarantees that the spacetime casts a shadow, whereas naked ring singularities enable the visibility of the `anti-world' of negative radii r through its interior. Moreover, the optical restrictions to the observability of the shadow of an astronomical black hole are inferred.

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Abstrae. The covariant Weyl (spin s = 1/2) and Maxwell (s = 1) equations in certain local charts (U, 9 ) of a space-time ( M , g ) are considered. It is shown that the condition goo(z) > 0 for all z E U is necessary and sufficient to rewrite them in a unified manner as evolution equations at4 = L(,)4. Here L ( 8 ) is a linear first order differential operator on the pre-Hilbert space ( C r ( U t , C "+'), (. , . )) , where Ut C R3 is the image of the coordinate map of the spacelike hypersurface t = const, and (4,$~) = 4*Q@ d(3)2 with a suitable Hermitian n x n-matrix Q = & ( t , z ) . The total energy of the spinor field 4 with respect to Ut is then simply given by E = (+,4). In this way inequalities for the energy change rate with respect to time, &11+112 = 2 Re (4, L ( 8 , 4 ) , are obtained. As an application, the Kerr -Newman black hole is studied, yielding quantitative estimates for the energy change rate. These estimates especially confirm the energy conservation of the Weyl field and the well -known superradiance of electromagnetic waves. uiLorentz group under changes of reference frames in Minkowski space-time.Here we generalize this concept. We suppose a space-time ( M , g ) with a foliation {Ct,=r}, I c R, where each leaf Ct is a spacelike hypersurface. Just as in special relativity, we regard the integral E = JLtTijNiNjd(3)z as the total energy with respect to Ct at the time t E I , where Tij is the energy-momentum tensor of the considered matter and N j the unit normal to Ct.For quantitative calculations it is necessary to use coordinates. Thus we restrict ourselves to a suitable open subset U c M with coordinates (E', ..., z3) : U + U c R4, zo = c t , c the speed of light, where the hypersurfaces { t = const} are Ct n U. One im-1991 Mathematics Subject Classification.

The potentials of spin-weighted wave equations in various Kerr-Newman black holes are analyzed. They all form singular potential barriers at the event horizon. Applying the WKB approximation it is shown that no particle can tunnel out of the interior of a static black hole. However, photons inside a non-extremely rotating Kerr black hole may tunnel out into the outer space, whereas neutrinos, electrons, and gravitons may not. If the rotation is extremal, any particle may tunnel out, under restrictive conditions. It is unknown whether photons and gravitons may tunnel out if the black hole is charged and rotating.

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