Recent detection of gravitational wave from nine black hole merger events and one neutron star merger event by LIGO and VIRGO shed a new light in the field of astrophysics. On the other hand, in the past decade, a few super-Chandrasekhar white dwarf candidates have been inferred through the peak luminosity of the light curves of a few peculiar Type Ia supernovae, though there is no direct detection of these objects so far. Similarly, a number of neutron stars with mass $>\! 2\, \mathrm{M}_\odot$ have also been observed. Continuous gravitational wave can be one of the alternate ways to detect these compact objects directly. It was already argued that magnetic field is one of the prominent physics to form super-Chandrasekhar white dwarfs and massive neutron stars. If such compact objects are rotating with certain angular frequency, then they can efficiently emit gravitational radiation, provided their magnetic field and rotation axes are not aligned, and these gravitational waves can be detected by some of the upcoming detectors, e.g. LISA, BBO, DECIGO, Einstein Telescope, etc. This will certainly be a direct detection of rotating magnetized white dwarfs as well as massive neutron stars.

Recent observations of several peculiar over- and underluminous type Ia supernovae infer indirect evidence for the violation of the Chandrasekhar mass limit by suggesting the existence of super- and sub-Chandrasekhar limiting mass white dwarfs. In an attempt to explain these phenomena in the context of general relativistic extensions, we study these objects in Palatini $f(R)$ gravity. We obtain the super- and sub-Chandrasekhar limiting masses as well as the dynamical instability criteria for white dwarfs in the given gravitational theory. We further demonstrate that the conventional positivity condition $\partial M/\partial {\rho }_{\mathrm{c}}>0$ with $M$ being the WD’s mass with central density ${\rho }_{\mathrm{c}}$ is also a valid criterion for stability in Palatini gravity.

After the prediction of many sub- and super-Chandrasekhar (at least a dozen for the latter) limiting-mass white dwarfs (WDs), hence apparently a peculiar class of WDs, from the observations of luminosity of Type Ia supernovae, researchers have proposed various models to explain these two classes of WD separately. We earlier showed that these two peculiar classes of WD, along with the regular WD, can be explained by a single form of the f(R) gravity, whose effect is significant only in the high-density regime, and it almost vanishes in the low-density regime. However, since there is no direct detection of such a WD, it is difficult to single out one specific theory from the zoo of modified theories of gravity. We discuss the possibility of direct detection of such a WD in gravitational wave (GW) astronomy. It is well known that in f(R) gravity more than two polarization modes are present. We estimate the amplitudes of all the relevant modes for the peculiar and the regular WD. We further discuss the possibility of their detections through future-based GW detectors, such as LISA, ALIA, DECIGO, BBO, or the Einstein Telescope, and thereby put constraints on or rule out various modified theories of gravity. This exploration links the theory with possible observations through GW in f(R) gravity.

We analyze the effects of modified gravity on specific heats of electrons and ions, Debye temperature, crystallization process, and cooling mechanism in white dwarfs. We derive the Lane-Emden-Chandrasekhar equation and relate it to the cooling process equations for Palatini $f(R)$ gravity. Moreover, for the first time in the literature, we show that the gravity model plays a crucial role not only in the mass and size of the white dwarf, but also affects their internal properties. We further demonstrate that modified gravity can decrease the cooling age significantly.

A number of recent observations have suggested that the Einstein’s theory of general relativity may not be the ultimate theory of gravity. The f(R) gravity model with R being the scalar curvature turns out to be one of the best bet to surpass the general relativity which explains a number of phenomena where Einstein’s theory of gravity fails. In the f(R) gravity, behaviour of the spacetime is modified as compared to that of given by the Einstein’s theory of general relativity. This theory has already been explored for understanding various compact objects such as neutron stars, white dwarfs etc. and also describing evolution of the universe. Although researchers have already found the vacuum spacetime solutions for the f(R) gravity, yet there is a caveat that the metric does have some diverging terms and hence these solutions are not asymptotically flat. We show that it is possible to have asymptotically flat spherically symmetric vacuum solution for the f(R) gravity, which is different from the Schwarzschild solution. We use this solution for explaining various bound orbits around the black hole and eventually, as an immediate application, in the spherical accretion flow around it.