We introduce the notion of a local shadow for a black hole and determine its shape for the particular case of a distorted Schwarzschild black hole. Considering the lowest-order even and odd multiple moments, we compute the relation between the deformations of the shadow of a Schwarzschild black hole and the distortion multiple moments. For the range of values of multiple moments that we consider, the horizon is deformed much less than its corresponding shadow, suggesting the horizon is more 'rigid'. Quite unexpectedly we find that a prolate distortion of the horizon gives rise to an oblate distortion of the shadow, and vice-versa.

We present an approximate time-dependent metric in ingoing Eddington-Finkelstein coordinates for an evaporating nonrotating black hole as a first-order perturbation of the Schwarzschild metric, using the linearized back reaction from a realistic approximation to the stress-energy tensor for the Hawking radiation in the Unruh quantum state. I. INTRODUCTIONThe physics of black holes is an abundant field in which the convergence of gravitation, quantum theory, and thermodynamics takes place. The original derivation of Hawking radiation [1] from black holes is based on semiclassical effective field theory. Normally, quantum fields are considered test fields in the curved spacetime of a classical background geometry. A quantum field theory constructed on a curved background spacetime experiences gravitationally induced vacuum polarization and/or particle creation. These effects induce a nonzero expectation value for the stress-energy tensor. The renormalized expectation value of the complete quantum stress-energy tensor outside the classical event horizon has been calculated by various authors [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21], usually using a framework established by Christensen and Fulling [3]. In this framework, the assumptions are that the stress-energy tensor is time independent, satisfies local stress-energy conservation, and has a trace determined solely by the conformal anomaly, both for the fields that are classically conformally invariant (such as a massless scalar field and the electromagnetic field) and for the gravitational field. The quantum state considered is usually either the Hartle-Hawking state [22] or the Unruh state [23,24]. (For discussion of the various black hole vacuum states, see [25]). In the Hartle-Hawking state, one has thermal equilibrium, and zero net energy flux, with the outgoing Hawking radiation balanced by incoming radiation from an external heat bath at the Hawking temperature. In [4] a fairly good closed-form approximation for the energy density and stresses of a conformal scalar field in the Hartle-Hawking state everywhere outside a static black hole can be found.In the Unruh state, there is the absence of incoming radiation at both past null infinity and the past horizon, plus regularity of the stress-energy tensor on the future event horizon in the frame of a freely falling observer, representing a black hole formed from gravitational collapse, with nothing falling into the black hole thereafter. There have been many calculations of the quantum stress-energy tensor in the Unruh state in the Schwarzschild spacetime, both for a massless scalar field and for the electromagnetic field [5-7, 9-13, 15-17]. A method for computing the stress-energy tensor for the quantized massless spin-1/2 field in a general static spherically symmetric spacetime was presented in [18][19][20]. The canonical quantization of the electromagnetic field has also been investigated in the Kerr metric [21].One of the important questions that one wants to answer concerns...

We investigate the properties of the ergoregion and the location of the curvature singularities for the Kerr black hole distorted by the gravitational field of external sources. The particular cases of quadrupole and octupole distortion are studied in detail. We also investigate the scalar curvature invariants of the horizon and compare their behaviour with the case of the isolated Kerr black hole. In a certain region of the parameter space the ergoregion consists of a compact region encompassing the horizon and a disconnected part extending to infinity. The curvature singularities in the domain of outer communication, when they exist, are always located on the boundary of the ergoregion. We present arguments that they do not lie on the compact ergosurface. For quadrupole distortion the compact ergoregion size is negatively correlated with the horizon angular momentum when the external sources are varied. For octupole distortion infinitely many ergoregion configurations can exist for a certain horizon angular momentum. For some special cases we can have J 2 /M 4 > 1 and yet avoid the naked singularity. * Alberta-Thy-14-15 † Internet address: abdolrah@ualberta.ca ‡ Internet address: jutta.kunz@uni-oldenburg.de § Internet address: pnedkova@phys.uni-sofia.bg ¶ Internet address: tzounis@ualberta.ca 1 arXiv:1509.01665v2 [gr-qc]