In this article we will modify the Einstein field equations by promoting Newton's constant G to a covariant differential operator ( ) Λ G g composed of two terms which operate in different energy regimes (IR and UV). The IR term inside the covariant differential operator acts like a high-pass filter with a macroscopic distance filter scale Λ and effectively degravitates energy sources characterized by wavelengths larger than the filter scale. While this term is predominant for cosmological energy processes it is almost inessential on astrophysical scales where the UV contribution inside ( ) Λ G g leads to much stronger deviations compared to GR. In the context of this particular theory of gravity we work out the effective relaxed Einstein equations, the effective 1.5 post-Newtonian near zone mass for n-body systems as well as the IR and UV modified Schwarzschild metrics. We use these results in the context of the Double Pulsar binary system and observe that we recover, in the limit of vanishing UV-IR modification parameters, the corresponding general relativistic results.

It was argued in a number of papers that the gravitational potential calculated by using the modified QFT that follows from the Planck-length deformed uncertainty relation implies the existence of black-hole remnants of the order of the Planck-mass. Usually this sort of QFTs are endowed with two specific features, the modified dispersion relation, which is universal, and the concept of minimum length, which, however, is not universal. While the emergence of the minimum-length most readily leads to the idea of the black hole remnants, here we examine the behaviour of the potential that follows from the Planck-length deformed QFT in absence of the minimum length and show that it might also lead to the formation of the Planck mass black holes in some particular cases. The calculations are made for higher-dimensional case as well. Such black hole remnants might be considered as a possible candidates for the dark-matter.Comment: 18 pages, published versio

In this manuscript we review the theoretical foundations of gravitational waves in the framework of Albert Einstein's theory of general relativity. Following Einstein's early efforts we first derive the linearised Einstein field equations and work out the corresponding gravitational wave equation. Moreover we present the gravitational potentials in the far away wave zone field point approximation obtained from the relaxed Einstein field equations. We close this review by taking a closer look on the radiative losses of gravitating n-body systems and present some aspects of the current interferometric gravitational waves detectors. Each section posses a separate appendix-contribution where further computational details are displayed. To conclude we summarize the main results and present a brief outlook in terms of current ongoing efforts to build a spaced based gravitational wave observatory.