Related papers: Gravitational Dimensionality Reduction Using Newto…
The historical and conceptual foundations of General Relativity are revisited, putting the main focus on the physical meaning of the invariant ds, the Equivalence Principle, and the precise interpretation of spacetime geometry. It is argued…
Conformal geometry is considered within a general relativistic framework. An invariant distant for proper time is defined and a parallel displacement is applied in the distorted space-time, modifying Einstein's equation appropriately. A…
With the theory of general relativity, Einstein abolished the interpretation of gravitation as a force and associated it to the curvature of spacetime. Tensorial calculus and differential geometry are the mathematical resources necessary to…
We use a particular machine learning approach, called the genetic algorithms (GA), in order to place constraints on deviations from general relativity (GR) via a possible evolution of Newton's constant $\mu\equiv…
Dimensionality reduction (DR) of data is a crucial issue for many machine learning tasks, such as pattern recognition and data classification. In this paper, we present a quantum algorithm and a quantum circuit to efficiently perform linear…
The construction of the cosmic distance-duality relation (CDDR) has been widely studied. However, its consistency with various new observables remains a topic of interest. We present a new way to constrain the CDDR $\eta(z)$ using different…
The principal subject of this thesis is the gravitational two-body problem in the extreme-mass-ratio regime---that is, where one mass is significantly smaller than the other---in the full context of our contemporary theory of gravity,…
The existence of gravitational radiation is a natural prediction of any relativistic description of the gravitational interaction. In this chapter, we focus on gravitational waves, as predicted by Einstein's general theory of relativity.…
Machine learning (ML) and artificial intelligence (AI) algorithms are now being used to automate the discovery of physics principles and governing equations from measurement data alone. However, positing a universal physical law from data…
A generalization of the matrix model idea to quantum gravity in three and higher dimensions is known as group field theory (GFT). In this paper we study generalized GFT models that can be used to describe 3D quantum gravity coupled to point…
A second gradient generalization of Newtonian gravity is presented within the framework of gradient field theory. Weak nonlocality is introduced via first and second gradients of the gravitational field strength in the Lagrangian density.…
Using the differential calculus on discrete group, we study the general relativity in the space-time which is the product of a four dimensional manifold by a two-point space. We generalize the usual concept of frame and connection in our…
Utilizing various gauges of the radial coordinate we give a description of static spherically symmetric space-times with point singularity at the center and vacuum outside the singularity. We show that in general relativity (GR) there exist…
Based on the Generalized Principle of Inertia, which states that: \emph{An inanimate object moves freely, that is, with zero acceleration, in its own spacetime, whose geometry is determined by all of the forces affecting it,} we geometrize…
We present a convolutional neural network to classify distinct cosmological scenarios based on the statistically similar weak-lensing maps they generate. Modified gravity (MG) models that include massive neutrinos can mimic the standard…
Three important properties of a classification machinery are: (i) the system preserves the core information of the input data; (ii) the training examples convey information about unseen data; and (iii) the system is able to treat…
Extended Theories of Gravity can be considered a new paradigm to cure shortcomings of General Relativity at infrared and ultraviolet scales. They are an approach that, by preserving the undoubtedly positive results of Einstein's Theory, is…
On the long-established classification problems in general relativity we take a novel perspective by adopting fruitful techniques from machine learning and modern data-science. In particular, we model Petrov's classification of spacetimes,…
Einstein's General Relativity (GR) is possibly one of the greatest intellectual achievements ever conceived by the human mind. In fact, over the last century, GR has proven to be an extremely successful theory, with a well established…
Dimensionality reduction is a topic of recent interest. In this paper, we present the classification constrained dimensionality reduction (CCDR) algorithm to account for label information. The algorithm can account for multiple classes as…