Application of the first junction condition to a highly symmetric spacetime was investigated recently in Chin. Phys. Left. B 546 189 2006, where a partial differential equation arising from the connection of the Robertson-Walker and the Schwarzschild-de Sitter metrics was presented, but no solutions of the equation were provided. Here we provide a proof to the statement that there exist solutions of the equation. In addition, an example of the solution and some analyses associated with this issue are presented. We find that in connecting the two metrics, there are three conditions which should be satisfied. Of these conditions, one condition constrains the place where the two metrics can take the same value for a local system whose mass is provided which marks the boundary of the system, and the other two constrain the transformation form. In realizing the connection of the two metrics, the latter two conditions are required to be satisfied only at the boundary defined by the former condition.
We report the result of simultaneous multi-wavelength observations of the TeV blazar Mrk 421 during February - March 2003. We observed Mrk 421 using the Pachmarhi Array of Cerenkov Telescopes （PACT） of Tata Institute of Fundamental Research at Pachmarhi, India. Other simultaneous data were taken from the literature and public data archives. We have analyzed the high quality X-ray （2-20 keV） observations from the NASA Rossi X-Ray Timing Explorer （RXTE）. We obtained a possible correlated variability between X-ray and J band （1.25 μ） near infrared （NIR） wavelength. This is the first case of X-ray and NIR correlated variability in Mrk 421 or any high energy peaked （HBL） blazar. The correlated variability reported here indicates a similar origin for the NIR and X-ray emissions. The emission is not affected much by the environment of the surrounding medium of the central engine of Mrk 421. The observations are consistent with the shock-in-jet model for the emissions.
Alok C. GuptaB. S. AcharyaDebanjan BoseVarsha R. ChitnisJun-Hui Fan
