New exact spherically symmetric solutions in f (R, φ, X) gravity by Noether's symmetry approach

被引:37
作者
Bahamonde, Sebastian [1 ,2 ,3 ,4 ]
Bamba, Kazuharu [5 ]
Camci, Ugur [6 ]
机构
[1] Univ Tartu, Lab Theoret Phys, Inst Phys, W Ostwaldi 1, EE-50411 Tartu, Estonia
[2] UCL, Dept Math, Gower St, London WC1E 6BT, England
[3] Univ Lincoln, Sch Math & Phys, Lincoln LN6 7TS, England
[4] Univ Cambridge, Cavendish Lab, JJ Thomson Ave, Cambridge CB3 0HE, England
[5] Fukushima Univ, Div Human Support Syst, Fac Symbiot Syst Sci, Fukushima 9601296, Japan
[6] Siteler Mahallesi,1307 Sokak, TR-07070 Antalya, Turkey
关键词
modified gravity; GR black holes; gravity; GRAVITATIONAL-WAVES; INFLATIONARY UNIVERSE; F(R) GRAVITY; COSMOLOGY; FLATNESS; HORIZON;
D O I
10.1088/1475-7516/2019/02/016
中图分类号
P1 [天文学];
学科分类号
0704 ;
摘要
The exact solutions of spherically symmetric space-times are explored by using Noether symmetries in f(R, phi, X) gravity with R the scalar curvature, phi a scalar field and X the kinetic term of phi. Some of these solutions can represent new black holes solutions in this extended theory of gravity. The classical Noether approach is particularly applied to acquire the Noether symmetry in f(R, phi, X) gravity. Under the classical Noether theorem, it is shown that the Noether symmetry in f(R, phi, X) gravity yields the solvable first integral of motion. With the conservation relation obtained from the Noether symmetry, the exact solutions for the field equations can be found. The most important result in this paper is that, without assuming R = constant, we have found new spherically symmetric solutions in different theories such as: power-law f(R) = f(0)R(n) gravity, non-minimally coupling models between the scalar field and the Ricci scalar f(R, phi, X) = f(0)R(n)phi(m) + f(1)X(q) - V(phi), non-minimally couplings between the scalar field and a kinetic term f(R, phi, X) = f(0)R(n) + f(1)phi X-m(q), and also in extended Brans-Dicke gravity f(R, phi, X) = U(phi, X) R. It is also demonstrated that the approach with Noether symmetries can be regarded as a selection rule to determine the potential V (phi) for phi, included in some class of the theories of f(R, phi, X) gravity.
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页数:30
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