The group of rigid motions is considered to guide the search for a natural system of space-time coordinates in General Relativity. This search leads us to a natural extension of the space-times that support Painlevé–Gullstrand synchronization. As an interesting example, here we describe a system of rigid coordinates for the cross mode of gravitational linear plane waves.
We add a prescription to the Newman–Janis algorithm in order to use it as a means of finding new extended rotating black hole spacetimes from static spherically symmetric ones. Then, we apply the procedure to a quantum improved black hole spacetime coming from Quantum Einstein Gravity in order to get the maximally extended spacetime corresponding to a non-singular rotating black hole. We rigourously check for the existence of scalar curvature singularities in the quantum improved rotating spacetime and we show that it is devoid of them. We also analyze the horizons and causal structure of the rotating black hole and provide Penrose diagrams for the maximally extended spacetime.
The final publication is available at Springer via 10.1007/s10714-017-2236-5
Different proposals for regular rotating black hole spacetimes have appeared recently in the literature. However, a rigorous analysis and proof of the regularity of this kind of spacetimes is still lacking. In this note we analyze rotating Kerr-like black hole spacetimes and find the necessary and sufficient conditions for the regularity of all their second order scalar invariants polynomial in the Riemann tensor. We also show that the regularity is linked to a violation of the weak energy conditions around the core of the rotating black hole.
The final publication is available at Springer via 10.1007/s10714-016-2166-7
Assuming that primordial density fluctuations are nearly Gaussian, from a frequentist viewpoint, the two-dimensional marginalized joint coincidence contour in the plane (ns,r) (being ns the spectral index and r the ratio of tensor to scalar perturbations), without the presence of running is often used to test the viability of the inflationary models. The models that provide, between 50 and 60 e-folds, a curve in that plane lying outside the 95.5% C.L are ruled out. I will basically argue that, in quintessential inflation, this low number of e-folds is unjustified, and that models leading to a theoretical value of the running different from zero must be checked with observational data allowing the running. When both prescriptions are taken into account, dealing in the context of quintessential inflation, i.e. when the potential is a combination of an inflationary with a quintessential one that leads to a kination (also called deflation) regime, inflationary models such as the quartic or the Higgs potential are allowed.
A model of a universe without big bang singularity is presented, which displays an early inflationary period ending just before a phase transition to a kination epoch. The model produces enough heavy particles so as to reheat the universe at temperatures in the MeV regime. After the reheating, it smoothly matches the standard Lambda CDM scenario.
Following on from two recent papers, here we examine the relationship between Newtonian gravitation and general relativity in more depth. This allows us to define a scalar potential which is just the proper time of the vector potential when the latter is interpreted as the geodesic velocity field. The results are closely related to
spacetimes that admit Painlevé–Gullstrand synchronization.
As an alternative to the paradigm of slow roll inflation, we propose an extended scenario of the matter bounce cosmology in which the Universe has experienced a quasi-matter contracting phase with a variable background equation of state parameter. This extended matter bounce scenario can be realized by considering a single scalar field evolving along an approximately exponential potential. Our result reveals that the rolling of the scalar field in general leads to a running behavior on the spectral index of primordial cosmological perturbations and a negative running can be realized in this model. We constrain the corresponding parameter space by using the newly released Planck data. To apply this scenario, we revisit bouncing cosmologies within the context of modified gravity theories, in particular, the holonomy corrected loop quantum cosmology and teleparallel F(T) gravity. A gravitational process of reheating is presented in such a matter bounce scenario to demonstrate the condition of satisfying current observations. We also comment on several unresolved issues that often appear in matter bounce models.
We construct a homothetic covariant Newtonian gravitation theory which unifies inertial homothetic forces and gravitational fields. This is achieved through an equivalence principle based on a local homothetic frame of motion. As a consequence, we can obtain a coherent Newtonian cosmology which admits a cosmological principle and leads to the Friedman equations for a dust universe. Finally we prove that this gravity theory can be obtained as the non-relativistic limit of a class of metrics in General Relativity. The Friedmann–Lemaître–Robertson–Walker metric and its limit are also studied.
In an effort to contribute to a better understanding of General Relativity, here we lay the foundations of generalized Newtonian gravity, which unifies inertial forces and gravitational fields. We also formulate a kind of equivalence principle for this generalized Newtonian theory. Finally, we prove that the theory we propose here can be obtained as the non-relativistic limit of General Relativity.
In an effort to contribute to a better understanding of General Relativity,
here we lay the foundations of generalized Newtonian gravity, which unifies inertial
forces and gravitational fields. We also formulate a kind of equivalence principle for
this generalized Newtonian theory. Finally, we prove that the theory we propose here
can be obtained as the non-relativistic limit of General Relativity.