Cold scalar-tensor black holes coupled to a massless scalar field

New four-dimensional black hole solutions of Brans-Dicke equations with a negative constant ω, coupled to a massless scalar field, are presented. The temperature of these black holes is zero and the horizon area is infinite. An astrophysical application is also discussed. Scalar-tensor theories of gravity are considered as the most natural generalizations of general relativity. From theoretical point of view one should mention that specific scalar-tensor theories arise naturally as a low energy limit of string theory. One of the most interesting aspects of scalar-tensor theories is the possible existence of black holes different form those in general relativity. Campanelli and Lousto [1] pointed out that, in Brans-Dicke theory with a negative coupling constant ω, there exist solutions possessing all black holes properties but with horizons of infinite area (type B black holes). Let us note that that Brans-Dicke theory with ω < 0 is also worth to study for more than its intrinsic theoretical interest. For sufficiently negative ω, the theory passes all the experimental constrains as does for possitive ω [2]. Later on the work of Campanelli and Lousto was generalized in [3] where it was shown, in the framework of a general class of scalar-tensor theories, that nontrivial black hole solutions can exist for the coupling function 2ω(Φ) + 3 < 0. These black holes solutions are divided into two classes: class B1, where horizons are attained by infalling particles in a finite proper time, and class B2, for which this proper time is infinite. The structure and stability of the scalar-tensor black holes were investigated in [4]. Charged scalar-tensor black holes were studied in [5] where it was shown that they exist for anomalous versions of the scalar-tensor theories with a negative kinetic term in the lagrangian. The temperature of these black holes is zero and the horizon area is (in most cases) infinite. Thermodynamics of the black holes with infinite horizon area was considered in [6]. Stationary, axisymmetric black holes in Bans-Dicke theory with −5/4 ≤ ω < −3/2 were discussed in [7]. These black holes are characterize with zero Hawking temperature and finite horizon area. ∗E-mail: [email protected]