Related papers: Perturbative analysis of generalized Einstein's th…
It is shown that a first-order cosmological perturbation theory for the open, flat and closed Friedmann-Lema\^itre-Robertson-Walker universes admits one, and only one, gauge-invariant variable which describes the perturbation to the energy…
Some black hole mimickers, as well as black strings and other higher-dimensional spacetimes, exhibit stable light rings-regions where light or high-frequency gravitational waves can be trapped. In these regions, linear perturbations decay…
Einstein's theory of general relativity models the physical universe using spacetimes which satisfy Einstein's gravitational field equations. To date, Einstein's theory has been enormously successful in modeling observed gravitational…
A certain vector-tensor (VT) theory is revisited. It was proposed and analyzed as a theory of electromagnetism without the standard gauge invariance. Our attention is first focused on a detailed variational formulation of the theory, which…
We investigate the cosmological background evolution and perturbations in a general class of spatially covariant theories of gravity, which propagates two tensor modes and one scalar mode. We show that the structure of the theory is…
Using the cosmological perturbation theory in terms of the delta-N formalism, we find the simple formulation of the evolution of the curvature perturbation in generalized gravity theories. Compared with the standard gravity theory, a…
We study the long-term dynamics of a planetary system composed of a star and a planet. Both bodies are considered as extended, non-spherical, rotating objects. There are no assumptions made on the relative angles between the orbital angular…
We present a complete resolution of the Abraham-Minkowski controversy . This is done by considering several new aspects which invalidate previous discussions. We show that: 1)For polarized matter the center of mass theorem is no longer…
Many of the technical complications associated with the general theory of relativity ultimately stem from the nonlinearity of Einstein's equation. It is shown here that an appropriate choice of dynamical variables may be used to eliminate…
Taking a hint from Dirac's large number hypothesis, we note the existence of cosmic combined conservation laws that work to cosmologically long time. We thus modify or generalize Einstein's theory of general relativity with fixed…
A new covariant generalization of Einstein's general relativity is developed which allows the existence of a term proportional to $T_{\alpha\beta}T^{\alpha\beta}$ in the action functional of the theory ($T_{\alpha\beta}$ is the…
The various methods to derive Einstein conservation laws and the relevant definitions of energy-momentum tensor density for gravitational fields are studied in greater detail. It is shown that these methods are all equivalent. The study on…
The problem of explaining the acceleration of the expansion of the universe and the observational and theoretical difficulties associated with dark matter and dark energy are discussed. The possibility that Einstein gravity does not…
We review the underpinnings of the standard Newton-Einstein theory of gravity, and identify where it could possibly go wrong. In particular, we discuss the logical independence from each other of the general covariance principle, the…
Along the general framework of the gauge invariant perturbation theory developed in the papers [K. Nakamura, Prog. Theor. Phys. {\bf 110} (2003), 723; {\it ibid}, {\bf 113} (2005), 481.], we formulate the second order gauge invariant…
Using the basic ingredient of supersymmetry, we develop a simple alternative approach to perturbation theory in one-dimensional non-relativistic quantum mechanics. The formulae for the energy shifts and wave functions do not involve tedious…
In this study, the effects of the generalized uncertainty principle on the theory of gravity are analyzed. Inspired by Verlinde's entropic gravity approach and using the modified Unruh temperature, the generalized Einstein field equations…
Increasingly accurate observations are driving theoretical cosmology toward the use of more sophisticated descriptions of matter and the study of nonlinear perturbations of FL cosmologies, whose governing equations are notoriously…
A discrete space-time structure lying at about the Planck scale may become manifest in the form of very small violations of the conservation of the matter energy-momentum tensor. In order to include such kind of violations, forbidden within…
We address the problem of the energy conditions in modified gravity taking into account the additional degrees of freedom related to scalar fields and curvature invariants. The latter are usually interpreted as generalized {\it geometrical…