The rigidity of the Riemannian positive mass theorem for asymptotically hyperbolic manifolds states that the total mass of such a manifold is zero if and only if the manifold is isometric to the hyperbolic space. This leads to study the stability of this statement, that is, if the total mass of an asymptotically hyperbolic manifold is almost zero, is this manifold close to the hyperbolic space in any

We investigate complex quaternion-valued exterior differential forms over 4-dimensional Lorentzian spacetimes and explore Weyl spinor fields as minimal left ideals within the complex quaternion algebra. The variational derivation of the coupled Einstein–Weyl equations from an action is presented, and the resulting field equations for both first and second order variations are derived and simplified

We consider mimetic Horava gravity, where the scalar field of mimetic gravity was used in the construction of diffeomorphism invariant models reducing to Horava gravity in the synchronous gauge. It will be shown that the gravitational action with the addition of the Gibbons–Hawking–York term and the mimetic Horava action are equivalent for manifolds whose topology is \(R \times \Sigma \), where \(\Sigma

This work builds upon the previous article (Lima in Symmetry 15:150, 2023) and explores the solution of the charged black string introduced in Lemos (Phys Rev 54:3840-3853, 1996). The black bounce regularization method, based on the Simpson-Visser solution, is employed by transforming the radial variable using \(r\rightarrow \sqrt{r^2+a^2}\). The regular charged black string metric is defined, and

There are several well-established methods for computing thermodynamics in single-horizon spacetimes. However, understanding thermodynamics becomes particularly important when dealing with spacetimes with multiple horizons. Multiple horizons raise questions about the existence of a global temperature for such spacetimes. Recent studies highlight the significant role played by the contribution of all

In higher co-dimension, we discuss the Hamilton–Jacobi formalism for brane gravity described by the Regge–Teitelboim model, in higher co-dimension. Considering that it is originally a second-order in derivatives singular theory, we analyze its constraint structure by identifying the complete set of Hamilton–Jacobi equations, under Carathéodory’s equivalent Lagrangians method, which goes hand in hand

We consider a hybrid bimetric model where, in addition to the ordinary metric tensor that determines geometry, an informational metric is introduced to describe the reference frame of an observer. We note that the local information metric being Minkowskian explains one of the key aspects of the Einstein equivalence principle. Our approach has the potential to justify the three-dimensional nature of

We present a covariant study of static space-times, as such and as solutions of gravity theories. By expressing the relevant tensors through the velocity and the acceleration vectors that characterise static space-times, the field equations provide a natural non-redundant set of scalar equations. The same vectors suggest the form of a Faraday tensor, that is studied in itself and in (non)-linear electrodynamics

The non-trivial naked singularities that possess directional behavior in the charged and uncharged Zipoy-Voorhees (ZV) spacetimes, known as \( \gamma - metrics \) are investigated within the context of quantum mechanics. Classically singular spacetime is understood as a geodesic incompleteness with respect to a particle probe, while quantum singularity is understood as a non-unique evolution of test

We investigate the thermodynamical properties of de Sitter black holes in (2+1) dimensional Einstein gravity with torsion, induced by spinors. Using the methods of Kraus, Keski-Vakkuri, and Wilczek, we calculate the entropy, temperature, and Hawking radiation from the dS black hole with torsion that has the event and cosmological horizons due to the presence of a positive cosmological constant. We

Algebraic properties are explored for the curvature tensors of Riemannian manifolds, using the irreducible decomposition of curvature tensors. Our method provides a powerful tool to analyze the irreducible basis as well as an algorithm to determine the linear dependence of arbitrary Riemann polynomials. We completely specify 13 independent basis elements for the quartic scalars and explicitly find

Dissipative force–flux relations are established in a strict covariant fashion for a relativistic fluid in a general curved space–time within the framework of kinetic theory. The Boltzmann equation is addressed to first order in the gradients by employing the Chapman–Enskog expansion and the corresponding constitutive equations are derived by considering a relaxation approximation. It is shown that

The present study investigates the coupling of the hyperbolic potential and conformal Liouville potential to the phonon field in two-dimensional gravity. The specific values of the horizon coordinate, Hawking temperature, phonon mass, and fluid velocity were calculated, and the change in physical quantities with the field coefficient \(\delta\) and central charge c was discussed. In the hyperbolic

The elusive physical nature of Horndeski gravity is elucidated in a new approach depicting this class of theories as a dissipative effective fluid. Requiring the constitutive equations of the latter to be those of a Newtonian fluid restricts the theory to only two disconnected subclasses of “viable” Horndeski gravity. Therefore, a stress-energy tensor of the Horndeski effective fluid, linear in the

The pilot-wave theory is an alternative, but less used, interpretation of Quantum Mechanics. In that framework, elementary particles are guided by a wave and move along well defined trajectories. A fascinating idea is the possibility to describe the de Broglie wave as oscillations of the gravitational field, thereby giving geometrical meaning to the pilot-wave of a quantum corpuscle. In this work we

Quantum atmosphere effective radii for the emission of spin-0, 1/2, 1, and 2 massless fields from Schwarzschild, Tangherlini, non-commutative geometry inspired, and polymeric black holes are calculated. The power observed from the black hole at spatial infinity taking greybody factors into account is compared to an equal-power black-body radiator of the same temperature but different effective radius

The present paper is devoted to analyzing light deflection caused by the presence of a cosmological constant in a space-time described by the Szekeres–Szafron metric. We use the orbital equation for light to calculate the deflection angle in gravitational lensing in the equatorial plane of the Szekeres–Szafron metric. The present study confirms that the cosmological constant has an effect on gravitational