Detection of Gravitational Waves from Gravitationally Lensed Systems

It is accepted that quasars are powered by supermassive black holes (SMBH) with masses in the range 10 − 10M in their cores. Occasionally, compact stars can plunge into SMBH. In addition, there may be a number of such compact objects circling the central SMBH in any given quasar. Both of these processes are known to emit gravitational waves. LISA has the right sensitivity to detect these waves. We show that gravitational lenses amplify the amplitudes of these gravitational waves just as they amplify the observed light of quasars. Given the geometry of the lensing configuration, this amplification can be as large as a factor of 2 to 10, allowing the waves to be above the detection threshold of LISA. We also show that waves from lensed quasars arrive with time delays which are much larger than the coherence time of the gravitational waves, making interference effects negligible. Thus, a simple geometrical optics application leads to the lensing theory of gravitational waves. In this context, we an alyze and show in this preliminary analysis that there is an enhancement of the amplitudes of gravitational radiation coming from observed lensed quasars. It is now well accepted that the energy source of a quasar is a supermassive black hole (SMBH) [1]. The mass of the SMBH is of the order of 106−109M [2]. In this mechanism of power generation, a compact star circling the SMBH plunges into it. Both these processes, encircling and plunging, are known to emit copious amounts of gravitational radiation [3,4]. These waves can in principle undergo gravitational lensing just as electromagnetic radiation does. We shall analyze the lensing of such waves. A compact star plunging into the SMBH at the core of a quasar produces a burst of gravitational radiation which can be approximated as having gravitational strain h and frequency f . These two quantities are given by [5,6]: h ' 10−21 ( 10Mpc R )( m 1M )