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We construct for every fixed n ≥ 2 the metric gs = h1(r)dt − h2(r)dr − k1(ω)dω1 − ··· − kn−1(ω)dωn−1, where h1(r), h2(r), ki(ω), 1 ≤ i ≤ n− 1, are continuous functions, r = |x|, for which we consider the Cauchy problem (utt −Δu)gs = f (u) + g(|x|), where x ∈ Rn, n≥ 2; u(1,x)= u◦(x)∈ L2(Rn), ut(1,x)= u1(x)∈ Ḣ−1(Rn), where f ∈ 1(R1), f (0) = 0, a|u| ≤ f (u) ≤ b|u|, g ∈ (R+), g(r) ≥ 0, r = |x|, a and b are positive constants. When g(r)≡ 0, we prove that the above Cauchy problem has a nontrivial solution u(t,r) in the form u(t,r) = v(t)ω(r) for which lim t→0‖u‖L2([0,∞)) = ∞. When g(r) = 0, we prove that the above Cauchy problem has a nontrivial solution u(t,r) in the form u(t,r)= v(t)ω(r) for which lim t→0‖u‖L2([0,∞)) =∞.

Blow up of the solutions of nonlinear wave equation in Reissner-Nordström Metric