Dilaton gravity, (quasi-) black holes, and scalar charge. (English) Zbl 1308.83128
Summary: Electrically charged dust is considered in the framework of Einstein-Maxwell-dilaton gravity with a Lagrangian containing the interaction term \(P(\chi)F_{\mu\nu}F^{\mu\nu}\), where \(P(\chi)\) is an arbitrary function of the dilaton scalar field \(\chi \), which can be normal or phantom. Without assumption of spatial symmetry, we show that static configurations exist for arbitrary functions \(g_{00}=\exp(2\gamma (x^i))\) \((i=1,2,3)\) and \(\chi=\chi(\gamma)\). If \(\chi=\mathrm{const}\), the classical Majumdar-Papapetrou (MP) system is restored. We discuss solutions that represent black holes (BHs) and quasi-black holes (QBHs), deduce some general results and confirm them by examples. In particular, we analyze configurations with spherical and cylindrical symmetries. It turns out that cylindrical BHs and QBHs cannot exist without negative energy density somewhere in space. However, in general, BHs and QBHs can be phantom-free, that is, can exist with everywhere nonnegative energy densities of matter, scalar and electromagnetic fields.
MSC:
| 83D05 | Relativistic gravitational theories other than Einstein’s, including asymmetric field theories |
| 83C57 | Black holes |
| 83C15 | Exact solutions to problems in general relativity and gravitational theory |
| 78A25 | Electromagnetic theory (general) |
| 83C22 | Einstein-Maxwell equations |
Keywords:
Majumdar-Papapetrou systems; dilaton; black holes; quasiblack holes; dilaton gravity; black holes; scalar chargeReferences:
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