Gravitational wave in f(R) gravity: possible signature of sub- and super-Chandrasekhar limiting mass white dwarfs

Abstract

After the prediction of many sub-and super-Chandrasekhar (at least a dozen for the latter) limiting mass white dwarfs, hence apparently peculiar class of white dwarfs, from the observations of luminosity of type Ia supernovae, researchers have proposed various models to explain these two classes of white dwarfs separately. We earlier showed that these two peculiar classes of white dwarfs, along with the regular white dwarfs, 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 white dwarfs, 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 white dwarfs in gravitational wave 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 as well as the regular white dwarfs. We further discuss the possibility of their detections through future-based gravitational wave detectors, such as LISA, ALIA, DECIGO, BBO, or Einstein Telescope, and thereby put constraints or rule out various modified theories of gravity. This exploration links the theory with possible observations through gravitational wave in f (R) gravity.

Fermi gas and modified gravity

“…Let us now discuss forms of the local variables describing the statistical equilibrium. Using the results derived in the previous subsection and applying them into the distribution function (41) and equations ( 28)- (30) we have…”

“…So far, a few such tests have been proposed with the use of stellar and substellar objects [25][26][27] (for review, see [28]). The most common are altered limited masses, for example, the Chandrasekhar mass of white dwarfs [29][30][31][32][33][34][35][36], the minimum Main Sequence mass [37][38][39][40][41], Jeans [42] and opacity mass [43], or minimum mass for deuterium burning [44]. Modified gravity can also alter the light elements' abundances in stellar atmospheres [45].…”