Bypassing Bekenstein's no-scalar-hair theorem without violating the energy conditions

In this work we establish in a rigorous manner, and a model independent way, the conditions for bypassing Bekenstein's no-scalar-hair theorem for static, spherically symmetric, and asymptotically flat black holes, while maintaining the validity of the energy conditions. Specifically, we argue that a hidden assumption in the theorem, namely the vanishing of the quantity \mathcal{G} = \mathcal{E} + T^\theta\!_\theta, where $\mathcal{E}$ is the energy density and T^\theta\!_\theta the corresponding component of the energy-momentum tensor of the scalar field theory, can be relaxed. Indeed, if $\mathcal{G}$ is positive, as a consequence of the assumption on the validity of the energy conditions, then scalar hair is potentially allowed in the black hole's exterior, consistently with the gravitational equations and the generic properties of the (non-trivial) energy momentum tensor. As an explicit example, in which such a behaviour is realised, we discuss the well known model of a (3+1)-dimensional Schwarzschild black hole coupled to a spontaneously broken Yang-Mills $SU (2)$ gauge theory interacting with a Higgs scalar. We present a rather novel approach to obtain analytical black hole solutions for this system (in contrast to the numerical ones in the existing literature) by applying an appropriate perturbative treatment whereby the black hole configuration is derived as a result of backreaction of Higgs and gauge fields onto an initially fixed flat spacetime. The massive nature of the scalar and gauge fields in this example requires a special treatment, because of their asymptotic form, which we discuss in some detail.Comment: 16 pages, 8 figure

Search for dark matter produced in association with bottom or top quarks in √s = 13 TeV pp collisions with the ATLAS detector

A search for weakly interacting massive particle dark matter produced in association with bottom or top quarks is presented. Final states containing third-generation quarks and miss- ing transverse momentum are considered. The analysis uses 36.1 fb−1 of proton–proton collision data recorded by the ATLAS experiment at √s = 13 TeV in 2015 and 2016. No significant excess of events above the estimated backgrounds is observed. The results are in- terpreted in the framework of simplified models of spin-0 dark-matter mediators. For colour- neutral spin-0 mediators produced in association with top quarks and decaying into a pair of dark-matter particles, mediator masses below 50 GeV are excluded assuming a dark-matter candidate mass of 1 GeV and unitary couplings. For scalar and pseudoscalar mediators produced in association with bottom quarks, the search sets limits on the production cross- section of 300 times the predicted rate for mediators with masses between 10 and 50 GeV and assuming a dark-matter mass of 1 GeV and unitary coupling. Constraints on colour- charged scalar simplified models are also presented. Assuming a dark-matter particle mass of 35 GeV, mediator particles with mass below 1.1 TeV are excluded for couplings yielding a dark-matter relic density consistent with measurements