In the light of Robinson and Wilczek's new idea, and motivated by Banerjee and Kulkarni's simplified method of using only the covariant anomaly to derive Hawking radiation from a black hole, we generally extend the work to Kerr–Newman black hole in dragging coordinates frame. It is shown that the flows introduced to cancel the anomaly at the event horizon are equal to the corresponding Hawking radiation in dragging coordinates frame, which supports and extends Robinson and Wilczek's opinion.

We present a kind of exact inflationary solution in the chaotic inflation scenario to non-minimal coupled scalar field, taking the Hubble parameter directly as a function of the scalar field ϕ, H(ϕ) = αϕ n . Using the analysis of the WMAP3 data, we give the range of power index n.

This paper presents a new exact inflationary solution to the non-minimally coupled scalar field. The inflation is driven by the evolution of a scalar field with inflation potential V(φ) = (λ/4)φ4 + b1φ2 + b2 + b3φ−2 + b4φ−4. The spectral index of the scalar density fluctuations ns is consistent with the result of WMAP3 (Wilkinson Microwave Anisotropy Probe 3) for ΛCDM (Lambda–Cold Dark Matter). This model relaxes the constraint to the quartic coupling constant. And it can enter smoothly into a radiation-dominated stage when inflation ends.