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PROBABILITY FOR PRIMORDIAL BLACK HOLES PAIR IN 1/R GRAVITY
arXiv:gr-qc/0508075v1 18 Aug 2005
Dilip Paul∗and Bikash Chandra Paul† Department of Physics, North Bengal University, Siliguri, Dist. Darjeeling, Pin : 734 013, India
Abstract The probability for quantum creation of an inflationary universe with a pair of black holes in 1/R - gravitational theory has been studied. Considering a gravitational action which includes a cosmological constant (Λ) in addition to δ R−1 term, the probability has been evaluated in a semiclassical approximation with Hartle-Hawking boundary condition. We obtain instanton solutions determined by the parameters δ and Λ satisfying the constraint δ ≤
4Λ2 3 .
However, we note that two different classes of instanton
solutions exists in the region 0 < δ 0 . For a∂M > H −1 , the wave function oscillates and predicts a classical space-time. We note the following cases : • δ = 0, the action reduces to that obtained by BH. •0
