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In this paper, we discuss the conditions for mapping the geometric description of the kinematics of particles that probe a given Hamiltonian in phase space to a description in terms of Finsler geometry (and vice-versa). [ABSTRACT FROM AUTHOR]

In this work, we investigate the existence of neutron stars (NS) in the framework of f (T , T) gravity, where T is the torsion tensor and T is the trace of the energy–momentum tensor. The hydrostatic equilibrium equations are obtained, however, with p and ρ quantities passed on by effective quantities p ¯ and ρ ¯ , whose mass–radius diagrams are obtained using modern equations of state (EoS) of nuclear matter derived from relativistic mean field models and compared with the ones computed by the Tolman–Oppenheimer–Volkoff (TOV) equations. Substantial changes in the mass–radius profiles of NS are obtained even for small changes in the free parameter of this modified theory. The results indicate that the use of f (T , T) gravity in the study of NS provides good results for the masses and radii of some important astrophysical objects, as, for example, the NS of low-mass X-ray binary in NGC 6397, the millisecond pulsar PSR J0740+6620 and the GW170817 event. In addition, radii results inferred from the Lead Radius Experiment (PREX-2) can also be described for certain parameter values. [ABSTRACT FROM AUTHOR]

In this paper, we reviewtwo approaches that can describe, in a geometrical way, the kinematics of particles that are affected by Planck-scale departures, named Finsler and Hamilton geometries. By relying on maps that connect the spaces of velocities and momenta, we discuss the properties of configuration and phase spaces induced by these two distinct geometries. In particular, we exemplify this approach by considering the so-called q-de Sitter-inspired modified dispersion relation as a laboratory for this study. We finalize with some points that we consider as positive and negative ones of each approach for the description of quantum configuration and phases spaces. [ABSTRACT FROM AUTHOR]

We consider the effect of a thermal bath on quantum correlations induced by the gravitational interaction in the weak field limit between two massive cat states, called gravitational cat (gravcat) states. The main goal of this paper is to provide a good understanding of the effects of temperature and several parameters in the entanglement (measured by the concurrence) and quantum coherence (measured by the l 1 -norm that is defined from the minimal distance between the quantum state and the set of incoherent states) which are derived from the thermal quantum density operator. Our results show that the thermal concurrence and l 1 -norm can be significantly optimized by increasing the masses or decreasing the distance between them. We investigate and discuss the behavior of these quantities under temperature variations in different regimes, including some that are expected to be experimentally feasible in the future. In particular, we observe that thermal fluctuations raise non-entangled quantum correlations when entanglement suddenly drops. [ABSTRACT FROM AUTHOR]

Deformed relativistic kinematics is a framework which captures effects, that are expected from particles and fields propagating on a quantum spacetime, effectively. They are formulated in terms of a modified dispersion relation and a modified momentum conservation equation. In this work we use Finsler geometry to formulate deformed relativistic kinematics in terms of particle velocities. The relation between the Finsler geometric velocity dependent formulation and the original momentum dependent formulation allows us to construct deformed Lorentz transformations between arbitrary frames. Moreover, we find the corresponding compatible momentum conservation equation to first order in the Planck scale deformation of special relativity based on the κ-Poincaré algebra in the bicrossproduct basis. We find that the deformed Lorentz transformations, as well as the deformed time dilation factor, contain terms that scale with the energy of the particle under consideration to the fourth power. We derive how the distributions of decay products are affected when the deformed relativity principle is satisfied and find, for the case of a pion decaying into a neutrino and a muon, that the ratio of expected neutrinos to muons with a certain energy is just slightly modified when compared to the predictions based on special relativity. We also discuss the phenomenological consequences of this framework for cosmic-ray showers in the atmosphere. [ABSTRACT FROM AUTHOR]

Working in the framework of generalized statistics, the problem of establishing third law of thermodynamics in the black hole physics is studied by focusing on Schwarzschild black hole which easily and clearly exposes the violation of this law in the common approach based on Bekenstein entropy. Additionally, it is addressed that some inconsistencies between the predictions of quantum field theory and thermodynamics about the black hole temperature may be reconciled by using the thermodynamics laws in order to broaden energy definition. It claims that thermodynamics should be employed as a powerful tool in looking for more comprehensive energy definitions in high-energy physics, still mysterious. [ABSTRACT FROM AUTHOR]

In this paper, we present a generalization of Rastall's gravity in which the conservation law of the energy–momentum tensor is altered, and as a result, the trace of the energy–momentum tensor is taken into account together with the Ricci scalar in the expression for the covariant derivative. Afterwards, we obtain the field equations in this theory and solve them by considering a spherically symmetric spacetime. We show that the external solution has two possible classes of solutions with spherical symmetry in the vacuum in generalized Rastall's gravity, and we analyze one of them explicitly. The generalization, in contrast to constant value k = 8 π G in general relativity, has a gravitational parameter k that depends on the Rastall constant α. As an application, we perform a careful analysis of the effects of the theory on neutron stars using realistic equations of state (EoS) as input. Our results show that important differences on the profile of neutron stars are obtained within two representatives EoS. [ABSTRACT FROM AUTHOR]

In this paper, the thermodynamics of Reissner–Nordström-anti de Sitter black hole surrounded by quintessence is studied and the impact of the Gauss–Bonnet term is measured. The modified entropy, first law of thermodynamics and corresponding Smarr relation are derived due to the combined action of the Gauss–Bonnet term and quintessence fluid. We study the so-called black hole chemistry from the analysis of the corresponding equation-of-state, conjugate potential and the critical points in the extended phase space. To study the phase transitions, we plotted P − v , T − v and G − T diagrams and analyzed the conditions for the coexistence of phases. [ABSTRACT FROM AUTHOR]

We show that the definition of proper time for Weyl-invariant space-times given by Perlick naturally extends to spaces with arbitrary non-metricity. We then discuss the relation between this generalized proper time and the Ehlers–Pirani–Schild definition of time when there is arbitrary non-metricity. Then we show how this generalized proper time suffers from a second clock effect. Assuming that muons are a device to measure this proper time, we constrain the non-metricity tensor on Earth's surface and then elaborate on the feasibility of such assumption. [ABSTRACT FROM AUTHOR]

We analyze how the hypotheses of Penrose's singularity theorem (1965) are modified by the action of disformal transformations (defined in terms of light-like vectors) upon a given space-time metric. In particular, we investigate the transformation of the null energy condition and the existence of closed trapped surfaces in such scenario, in order to derive conditions upon the background metric and the disformal vector that guarantee the validity of Penrose's theorem for disformal metrics. Then, we explain how to apply this technique for static and spherically symmetric space-times in general. [ABSTRACT FROM AUTHOR]

A promising theory in modifying general relativity (GR) by violating the ordinary energy-momentum conservation law in curved spacetime is the Rastall theory of gravity. In this theory, geometry and matter fields are coupled to each other in a nonminimal way. Here, we study thermodynamic properties of some black hole (BH) solutions in this framework, and compare our results with those of GR. We demonstrate how the presence of these matter sources amplifies the effects caused by the Rastall parameter in thermodynamic quantities. Our investigation also shows that BHs with radius smaller than a certain amount () have negative heat capacity in the Rastall framework. In fact, it is a lower bound for the possible values of horizon radius satisfied by the stable BHs. [ABSTRACT FROM AUTHOR]

We constructed thin-shell wormholes using the well-known "cut and paste" technique for static black holes sourced by an anisotropic fluid within the context of the Rastall gravity. Using the generalized Lanczos equations we explored the energy conditions at the wormhole's throat along with the traversability condition. We determined the stability regions when the wormhole configurations are surrounded by different bulk sources and obtained that the stability regions are considerably modified due to the non-trivial dependence of the Rastall parameter in the effective potential energy. [ABSTRACT FROM AUTHOR]

A Weyl structure is usually defined by an equivalence class of pairs (g , ω) related by Weyl transformations, which preserve the relation ∇ g = ω ⊗ g , where g and ω denote the metric tensor and a 1-form field. An equivalent way of defining such a structure is as an equivalence class of conformally related metrics with a unique affine connection Γ (ω) , which is invariant under Weyl transformations. In a standard Weyl structure, this unique connection is assumed to be torsion-free and have vectorial non-metricity. This second view allows us to present two different generalizations of standard Weyl structures. The first one relies on conformal symmetry while allowing for a general non-metricity tensor, and the other comes from extending the symmetry to arbitrary (disformal) transformations of the metric. [ABSTRACT FROM AUTHOR]

We study the black hole thermodynamics in the presence of a string cloud matter distribution, considering a work term due to a variable cosmological “constant” in arbitrary dimensions. Then, we explore the criticality of the system and the behavior of the black hole as a heat engine in the context of general relativity and metric f(R) gravity. [ABSTRACT FROM AUTHOR]

The spacetime solution for a black hole, surrounded by an exotic matter field, in Rastall gravity, is calculated in an arbitrary d-dimensional spacetime. After this, we calculate the scalar quasinormal modes of such solution, and study the shift on the modes caused by the modification of the theory of gravity, i.e., by the introduction of a new term due to Rastall. We conclude that the shift strongly depends on the kind of exotic field one is studying, but for a low density matter that supposedly pervades the universe, it is unlikely that Rastall gravity will cause an instability for the probe field. [ABSTRACT FROM AUTHOR]