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 (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.

Weak-field limit of $f(R)$ gravity to unify peculiar white dwarfs

“…However, this is not the primary concern for this work, and hence, it is beyond the scope of this paper. In the future, detecting these peculiar WDs through gravitational waves can put better constraints on the various modified gravity theories [14].…”

“…In the weak-gravity limit, we assume g µν = η µν + h µν and R = R 0 + R 1 , such that |h µν | |η µν |, where η µν is the background Minkowski metric and R 0 is the background scalar curvature, while h µν and R 1 are their corresponding tensor and scalar perturbations. Now perturbing Equations ( 2) and (3) with these relations, the linearized field and trace equations are given by [14,51,55]…”

Stability criterion for white dwarfs in Palatini $f(R)$ gravity

“…Research along these lines is essential to understand those fascinating objects and fully exploit the upcoming observational events. Detections of various compact objects, including WDs, by the use of gravitational wave detectors, such as aLIGO, Einstein Telescope, LISA, TianQin, BBO, DE-CIGO [101,102] can put constraints on these theories of gravity, or they might shed light on features of the GR extensions [19].…”

“…A simple form of scalar-tensor theory is the f (R) gravity [12] with R being the scalar curvature, which is based on generalizing the Lagrangian of the Einstein-Hilbert action. Instead of using an action linear in R as in GR, f (R) theory considers an action in which the Lagrangian density is an arbitrary function of R. Based on the form of f (R) and the values of the model parameters, this theory has been extensively used to study various phenomena, including inflation [13][14][15], dark energy problem [16,17], gravitational waves [18,19], compact objects like neutron stars [20][21][22][23][24], and also the recently inferred super-and sub-Chandrasekhar limiting mass white dwarfs (WDs) [25][26][27][28]. The so-called metric approach to f (R) gravity, as studied in the works mentioned above, leads to the fourth-order field equations for the metric, 1 which can impose some practical difficulties to work with.…”

Asymptotically flat black hole solution in modified gravity

“…Capozziello and his collaborators used different forms of f (R) gravity to explain the massive neutron stars 2 . Similarly, Kalita & Mukhopadhyay used f (R) gravity to unify the physics of all white dwarfs, including those possessing sub-and super-Chandrasekhar limiting masses 3 , and show that they can be detected by various proposed gravitational wave detectors 4 .…”