Abstract
Abstract Starting from a metric Ansatz permitting a weak version of Birkhoff’s theorem we find static black hole solutions including matter in the form of free scalar and p-form fields, with and without a cosmological constant Λ. Single p-form matter fields permit multiple possibilities, including dyonic solutions, self-dual instantons and metrics with Einstein-Kälher horizons. The inclusion of multiple p-forms on the other hand, arranged in a homogeneous fashion with respect to the horizon geometry, permits the construction of higher dimensional dyonic p-form black holes and four dimensional axionic black holes with flat horizons, when Λ < 0. It is found that axionic fields regularize black hole solutions in the sense, for example, of permitting regular — rather than singular — small mass Reissner-Nordstrom type black holes. Their cosmic string and Vaidya versions are also obtained.
Highlights
Multiple ways were found of circumventing this conjecture by evading one of the hypotheses of the black hole theorems or by including some non-trivial matter fields and couplings in between them
Starting from a metric Ansatz permitting a weak version of Birkhoff’s theorem we find static black hole solutions including matter in the form of free scalar and p-form fields, with and without a cosmological constant Λ
What is the situation concerning the dressing of D-dimensional black holes with free p-form fields beyond the case of electromagnetism? This includes the case of cosmological constant, multiple scalar fields, three-forms, spacetime filling forms and so on
Summary
∂[j Ei1...ip−2] = 0, ∂[j Bi1...ip] = 0 These harmonic forms define the polarization on H of the electric and magnetic parts of the field H and, as we shall show, they correspond to the conserved charges associated to the field H. To obtain a stress tensor of the form (1.12), the component Ttt cannot depend on the transverse coordinates yi. When the spacetime dimension is even and 2p = n + 3, the r-dependence of the electric and the magnetic parts of Tij coincide, and the isotropy constraint is weakened, 1)(p (2.15) In this case, we will see that dyonic solutions exist. Observe that one can define a new rank two anti-symmetric tensor for dyonic solutions, as the contraction of the electric and magnetic polarization forms, Aij = Bijk1...kp−2 Ek1...kp−2. We will start doing so with one single form field, and extend the construction in cases where multiple form fields H[(pi]) are available
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