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Register a new userProperties of Discrete Black Hole Hair
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Added by
Isabel Garcia Garcia
Publication date
2018
fields
Physics
and research's language is
English
Authors
Isabel Garcia Garcia
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We revisit the physical effects of discrete $mathbb{Z}_p$ gauge charge on black hole thermodynamics, building on the seminal work of Coleman, Preskill, and Wilczek. Realising the discrete theory from the spontaneous breaking of an Abelian gauge theory, we consider the two limiting cases of interest, depending on whether the Compton wavelength of the massive vector is much smaller or much larger than the size of the black hole -- the so-called thin- and thick-string limits respectively. We find that the qualitative effect of discrete hair on the mass-temperature relationship is the same in both regimes, and similar to that of unbroken $U(1)$ charge: namely, a black hole carrying discrete gauge charge is always colder than its uncharged counterpart. In the thick-string limit, our conclusions bring into question some of the results of Coleman et al., as we discuss. Further, by considering the system to be enclosed within a finite cavity, we argue how the unbroken limit may be smoothly defined, and the unscreened electric field of the standard Reissner-Nordstrom solution recovered.
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We show that a black hole surrounded by scalar dark matter develops scalar hair. This is the generalization of a phenomenon pointed out by Jacobson, that a minimally coupled scalar with a non-trivial time dependence far away from the black hole would endow the black hole with hair. In our case, the time dependence arises from the oscillation of a scalar field with a non-zero mass. We systematically explore the scalar profile around the black hole for different scalar masses. In the small mass limit, the scalar field has a $1/r$ component at large radius $r$, consistent with Jacobsons result. In the large mass limit (with the Compton wavelength of order of the horizon or smaller), the scalar field has a $1/r^{3/4}$ profile yielding a pile-up close to the horizon, while distinctive nodes occur for intermediate masses. Thus, the dark matter profile around a black hole, while challenging to measure, contains information about the dark matter particle mass. As an application, we consider the case of the supermassive black hole at the center of M87, recently imaged by the Event Horizon Telescope. Its horizon size is roughly the Compton wavelength of a scalar particle of mass $10^{-20}$ eV. We consider the implications of the expected scalar pile-up close to the horizon, for fuzzy dark matter at a mass of $10^{-20}$ eV or below.
The specific nonlinear vector $sigma$-model coupled to Einstein gravity is investigated. The model arises in the studies of the gravitating matter in non-commutative geometry. The static spherically symmetric spacetimes are identified by direct solving of the field equations. The asymptotically flat black hole with the ``non-commutative vector hair appears for the special choice of the integration constants, giving thus another counterexample to the famous ``no-hair theorem.
We show that the nonlinear $sigma-$model in an asymptotically $AdS_3$ space-time admits a novel local symmetry. The field action is assumed to be quartic in the nonlinear $sigma-$model fields and minimally coupled to gravity. The local symmetry transformation simultaneously twists the nonlinear $sigma-$model fields and changes the space-time metric, and it can be used to map an extremal $BTZ$ black hole to infinitely many hairy black hole solutions.
We study a hairy black hole solution in the dilatonic Einstein-Gauss-Bonnet theory of gravitation, in which the Gauss-Bonnet term is non-minimally coupled to the dilaton field. Hairy black holes with spherical symmetry seem to be easily constructed with a positive Gauss-Bonnet coefficient $alpha$ within the coupling function, $f(phi) = alpha e^{gamma phi}$, in an asymptotically flat spacetime, i.e., no-hair theorem seems to be easily evaded in this theory. Therefore, it is natural to ask whether this construction can be expanded into the case with the negative coefficient $alpha$. In this paper, we present numerically the dilaton black hole solutions with a negative $alpha$ and analyze the properties of GB term through the aspects of the black hole mass. We construct the new integral constraint allowing the existence of the hairy solutions with the negative $alpha$. Through this procedure, we expand the evasion of the no-hair theorem for hairy black hole solutions.
Motivated by black hole solutions with matter fields outside their horizon, we study the effect of these matter fields in the motion of massless and massive particles. We consider as background a four-dimensional asymptotically AdS black hole with scalar hair. The geodesics are studied numerically and we discuss about the differences in the motion of particles between the four-dimensional asymptotically AdS black holes with scalar hair and their no-hair limit, that is, Schwarzschild AdS black holes. Mainly, we found that there are bounded orbits like planetary orbits in this background. However, the periods associated to circular orbits are modified by the presence of the scalar hair. Besides, we found that some classical tests such as perihelion precession, deflection of light and gravitational time delay have the standard value of general relativity plus a correction term coming from the cosmological constant and the scalar hair. Finally, we found a specific value of the parameter associated to the scalar hair, in order to explain the discrepancy between the theory and the observations, for the perihelion precession of Mercury and light deflection.
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