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The set N of all null geodesics of a globally hyperbolic (d+1)-dimensional spacetime (M,g) is naturally a smooth (2d-1)-dimensional contact manifold. The sky of an event is the subset of N defined by all null geodesics through that event,…
We argue that the relativistic Unruh temperature cannot be associated with the bits on the screen, in the form considered by Verlinde. The acceleration $a$ is a scalar quantity (the modulus of the acceleration four vecor) and not a vector.…
It is shown that the redshift between two Cauchy surfaces in a globally hyperbolic spacetime equals the ratio of the associated contact forms on the space of light rays of that spacetime.
We investigate holographically the entanglement entropy of a nonconformal medium whose dual geometry is described by an Einstein-Maxwell-dilaton theory. Due to an additional conserved charge corresponding to the number operator, its…
We consider the interacting holographic dark energy with new infrared cutoff (involving Hubble parameter and its derivative) in non-flat universe. In this context, we obtain the equation of state parameter which evolutes the universe from…
Matter fields are supertranslated upon crossing a shock wave, which leads to entanglement of the quantum vacuum between the two regions on either side of the shock wave. We probe this entanglement for a scalar field in a planar shock wave…
A class of elliptic-hyperbolic equations is placed in the context of a geometric variational theory, in which the change of type is viewed as a change in the character of an underlying metric. A fundamental example of a metric which changes…
General relativity does not allow one to specify the topology of space, leaving the possibility that space is multiply rather than simply connected. We review the main mathematical properties of multiply connected spaces, and the different…
Entanglement entropy is crucial for understanding the link between quantum mechanics and information theory. This thesis investigates how energy fluctuations and acceleration affect entanglement entropy through three key scenarios. First,…
We employ the holographic approach to study the thermalization in the quenched strongly-coupled field theories with very general anisotropic scalings including Lifshitz and hyperscaling violating fixed points. The holographic dual is a…
We study the perception of the radiation phenomena of Hawking radiation and Unruh effect by using two main tools: the Unruh-DeWitt detectors and the effective temperature function (ETF), this last tool based on Bogoliubov transformations.…
In this paper, using Barrow entropy, we propose an interacting model of Barrow holographic dark energy (BHDE). In particular, we study the evolution of a spatially flat FLRW universe composed of pressureless dark matter and BHDE that…
We revisit the Unruh effect within a general framework based on direct, probability-level calculations. We rederive the transition rate of a uniformly accelerating Unruh-DeWitt monopole detector coupled to a massive scalar field, from both…
This chapter is an up-to-date account of results on globally hyperbolic spacetimes, and serves several purposes. We begin with the exposition of results from a foundational level, where the main tools are order theory and general topology,…
We consider the time evolution of two entropy-like quantities, the holographic entanglement entropy and causal holographic information, in a model of holographic thermalization dual to the gravitational collapse of a thin planar shell.…
Deformations of spacelike hypersurfaces in space-time play an important role in discussions of general covariance and slicing independence in gravitational theories. In a canonical formulation, they provide the geometrical meaning of gauge…
The present study explores the behavior of quaternionic four-space algebra for subluminal and superluminal spaces. We formulate the generalized Lorentz transformations for quaternionic subluminal, superluminal, and their combined Minkowski…
By incorporating the holographic principle in a time-depending Lambda-term cosmology, new physical bounds on the arbitrary parameters of the model can be obtained. Considering then the dark energy as a purely geometric entity, for which no…
A deformed relativistic kinematics can be understood within a geometrical framework through a maximally symmetric momentum space. However, when considering this kind of approach, usually one works in a flat spacetime and in a curved…
The notion of "reference frame" is a central theoretical construct for interpreting the physical implications of spacetime diffeomorphism invariance in General Relativity. However, the alternative formulation of classical General Relativity…