Related papers: Numerical solutions to Einstein's equations in a s…
We consider a brane-world of co-dimension one without the reflection symmetry that is commonly imposed between the two sides of the brane. Using the coordinate-free formalism of the Gauss-Codacci equations, we derive the effective Einstein…
We argue that generic off-diagonal vacuum and nonvacuum solutions for Einstein manifolds mimic physical effects in modified gravity theories (MGTs) and encode certain models of the $f(R,T,...)$, Ho\v{r}ava type with dynamical Lorentz…
Some of the dark matter in the Universe is made up of massive neutrinos. Their impact on the formation of large scale structure can be used to determine their absolute mass scale from cosmology, but to this end accurate numerical…
The standard cosmological model is inherently relativistic, and yet a wide range of cosmological observations can be predicted accurately from essentially Newtonian theory. This is not the case on `ultra-large' distance scales, around the…
Multi-parameter solutions to the Einstein equations in 2+1 dimensions are presented, with stress-energy given by a rotating dust with negative cosmological constant. The matter density is uniform in the corotating frame, and the ratio of…
The Newtonian simulations describing the formation of large-scale structures do not include relativistic effects. A new approach to this problem is proposed, which consists of splitting the Hawking-Hayward quasi-local energy of a closed…
In this short paper we investigate quantum gravitational effects on Einstein's equations using effective field theory techniques. We consider the leading order quantum gravitational correction to the wave equation. Besides the usual…
A solution of linearized Einstein field equations in vacuum is given and discussed. First it is shown that, computing from our particular metric the linearized connections, the linearized Riemann tensor and the linearized Ricci tensor, the…
We study the fractional gravity for spacetimes with non-integer dimensions. Our constructions are based on a geometric formalism with the fractional Caputo derivative and integral calculus adapted to nonolonomic distributions. This allows…
Recent developments in observational cosmology have led to attempts to make modifications on both sides of the Einstein equation to explain some of the puzzling new findings. What follows is an examination of the source of gravity that we…
We introduce a new geometrically invariant prescription for comparing two different spacetimes based on geodesic deviation. We use this method to compare a family of recently introduced analytical spacetime representing inspiraling…
We construct a self-consistent relativistic Newtonian analogue corresponding to gravitational static spherical symmetric spacetime geometries, staring directly from a generalized scalar relativistic gravitational action in Newtonian…
A relativistic theory of gravity like general relativity produces phenomena differing fundamentally from Newton's theory. An example, analogous to electromagnetic induction, is gravitomagnetism, or the dragging of inertial frames by…
The structure of the full Einstein equations in a coordinate gauge based on expanding null hypersurfaces foliated by metric 2-spheres is explored. The simple form of the resulting equations has many applications -- in the present paper we…
The discovery of the accelerated expansion of the universe highlighted General Relativity's inability to naturally account for dark energy without invoking a finely tuned cosmological constant. In response, a wide range of alternative…
In recent years, the use of conformal transformation techniques has become widespread in the literature on gravitational theories alternative to general relativity, on cosmology, and on nonminimally coupled scalar fields. Typically, the…
We present a method to calculate the gravitational energy when asymptotic boundary conditions for the space-time are not given. This is the situation for most of the cosmological models. The expression for the gravitational energy is…
We present a gravitational quantum dynamics theory that combines quantum field theory for particle dynamics in space-time with classical Einstein's general relativity in a non-Riemannian Finsler space. This approach is based on the…
Special theory of relativity has been formulated in a vacuum momentum-energy representation which is equivalent to Einstein special relativity and predicts just the same results as it. Although in this sense such a formulation would be at…
We extend the conformal gluing construction of Isenberg-Mazzeo-Pollack [18] by establishing an analogous gluing result for field theories obtained by minimally coupling Einstein's gravitational theory with matter fields. We treat classical…