Mass formulae and staticity condition for dark matter charged black holes
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Regular Article - Theoretical Physics
Mass formulae and staticity condition for dark matter charged black holes Marek Rogatkoa Institute of Physics, Maria Curie-Sklodowska University, pl. Marii Curie-Sklodowskiej 1, 20-031 Lublin, Poland
Received: 30 July 2020 / Accepted: 2 September 2020 © The Author(s) 2020
Abstract The Arnowitt–Deser–Misner formalism is used to derive variations of mass, angular momentum and canonical energy for Einstein–Maxwell dark matter gravity in which the auxiliary gauge field coupled via kinetic mixing term to the ordinary Maxwell one, which mimics properties of hidden sector. Inspection of the initial data for the manifold with an interior boundary, having topology of S 2 , enables us to find the generalised first law of black hole thermodynamics in the aforementioned theory. It has been revealed that the stationary black hole solution being subject to the condition of encompassing a bifurcate Killing horizon with a bifurcation sphere, which is non-rotating, must be static and has vanishing magnetic Maxwell and dark matter sector fields, on static slices of the spacetime under consideration.
1 Introduction One of the long-standing puzzle of the contemporary physics and astronomy is the dark matter problem, ingredient which constitutes over 23% of the observable Universe, being an important factor for the construction of cosmic web on which the ordinary matter accumulate [1,2]. Nowadays dark matter sector interaction with the Standard model particles [3,4] is widely elaborated. Several new types of fundamental particles were claimed to be the candidates for the hidden sector. They are expected to interact with nuclei in detecting materials on Earth [5–7]. On the other hand, there is a resurgence of implementing physics beyond the Standard Model to explain dark matter interaction in non-gravitational sector [8–10]. The studies of gamma rays emission in dwarf galaxies, oscillation of the fine structure constant, exploration of the possible low-energy mass dark sector [11–13], studies of dark photon production in the former observations of supera e-mails: [email protected]; lublin.pl (corresponding author)
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nova 1987A event [14], Gaia-like astrometry observations [15], as well as, studies of dynamics of galaxy clusters collisions [16], are expected to deliver new way of elaborating the old problem. Recently SENSEI device [17] is dedicated for the direct-detection of dark matter in eV to GeV energy range. It is expected that it provides constraints on dark matter electron scattering and on dark photon absorption of electrons. However, the absence of evidences of the most popular particle candidates for the dark matter sector is affirmed, in some sense, as a dilemma in the hidden sector researches. It has been proposed [18] that one should carefully analyse upcoming astrophysical phenomena, such like black hole and neutron star properties, gravitational wave signals to convey complimentary information connected with the dark matter
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