Narrow Results

We have analyzed the thermodynamics of slowly rotating magnetized Kerr black-hole following Newman–Janis prescription with typical spin parameter $a\le 0.1$ (nearly static) in the background of nonlinear electrodynamics. The nonlinear electrodynamics is parameterized with two parameters $\beta =1$ and $\gamma$. We consider two values of the $\gamma$, namely $\frac{1}{2}$ and $\frac{1}{3}$. In particular, we have studied the Bekenstein–Hawking entropy, Hawking temperature, angular momentum, specific heats at constant angular momentum. The specific heat profiles show that the black-hole becomes unstable for all the values of event horizon radius.

General Relativity is a hugely successful description of gravitation. However, both theory and observations suggest that General Relativity might have significant classical and quantum corrections in the Strong Gravity regime. Testing the strong field limit of gravity is one of the main objectives of the future gravitational wave detectors. One way to detect strong gravity is through the polarization of gravitational waves. For quasi-normal modes of black-holes in General Relativity, the two polarization states of gravitational waves have the same amplitude and frequency spectrum. Using the principle of energy conservation, we show that the polarizations differ for modified gravity theories. We obtain a diagnostic parameter for polarization mismatch that provides a unique way to distinguish General Relativity and modified gravity theories in gravitational wave detectors.

We point out a sufficient condition for existence of a stable attractor in the two-body restricted problem. The result is strictly dependent on making reference to relativistic equations and could not be derived from classical analysis. The radius of the stable attractor equals the well known Schwarzschild radius of General Relativity (GR). So we establish a bridge between Special Relativity (SR) and GR via Stability Theory (ST). That opens one way to an innovative study of black-holes and of the cosmological problem. A distinguishing feature is that no singularities come into evidence. The application of the Direct Method of Lyapunov (with a special Lyapunov function that represents the local energy) provides us the theoretical background.