A static axisymmetric exact solution of f (R)-gravity
AC Gutiérrez-Piñeres, CS López-Monsalvo - Physics Letters B, 2013 - Elsevier
Physics Letters B, 2013•Elsevier
We present an exact, axially symmetric, static, vacuum solution for f (R)-gravity in Weylʼs
canonical coordinates. We obtain a general explicit expression for the dependence of df
(R)/dR upon the r and z coordinates and then the corresponding explicit form of f (R), which
must be consistent with the field equations. We analyze in detail the modified Schwarzschild
solution in prolate spheroidal coordinates. Finally, we study the curvature invariants and
show that, in the case of f (R)≠ R, this solution corresponds to a naked singularity.
canonical coordinates. We obtain a general explicit expression for the dependence of df
(R)/dR upon the r and z coordinates and then the corresponding explicit form of f (R), which
must be consistent with the field equations. We analyze in detail the modified Schwarzschild
solution in prolate spheroidal coordinates. Finally, we study the curvature invariants and
show that, in the case of f (R)≠ R, this solution corresponds to a naked singularity.
We present an exact, axially symmetric, static, vacuum solution for f(R)-gravity in Weylʼs canonical coordinates. We obtain a general explicit expression for the dependence of df(R)/dR upon the r and z coordinates and then the corresponding explicit form of f(R), which must be consistent with the field equations. We analyze in detail the modified Schwarzschild solution in prolate spheroidal coordinates. Finally, we study the curvature invariants and show that, in the case of f(R)≠R, this solution corresponds to a naked singularity.
Elsevier
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