Fermion tunneling, Instability and First Law of Rindler Modified Schwarzschild Black Hole as a Thermodynamic system

This study investigated quantum tunneling of spin half particles through the event horizon of Rindler modified Schwarzschild black hole (RMSBH) in the presence of quintessence matter. We analyzed the thermodynamics of RMSBH in the Kiselev coordinates. Particularly, exploring RMSBH's entropy and the thermal stability of the RMSBH. We showed that RMSBH serves an unstable system causing fluctuations. The integral formulation of the first law of RMSBH in the absence of cosmological constant was also represented. By using the first law, we finally studied the Ruppeiner geometry for Rindler acceleration and pressure with fixed ensembles .

Dirac and Klein–Gordon–Fock equations in Grumiller’s spacetime

We study the Dirac and the chargeless Klein–Gordon–Fock equations in the geometry of Grumiller’s spacetime that describes a model for gravity of a central object at large distances. The Dirac equation is separated into radial and angular equations by adopting the Newman–Penrose formalism. The angular part of the both wave equations are analytically solved. For the radial equations, we managed to reduce them to one dimensional Schrödinger-type wave equations with their corresponding effective potentials. Fermions’s potentials are numerically analyzed by serving their some characteristic plots. We also compute the quasinormal frequencies of the chargeless and massive scalar waves. With the aid of those quasinormal frequencies, Bekenstein’s area conjecture is tested for the Grumiller black hole. Thus, the effects of the Rindler acceleration on the waves of fermions and scalars are thoroughly analyzed.

Mass-independent area (or entropy) and thermodynamic volume products in conformal gravity

In this work, we investigate the thermodynamic properties of conformal gravity in four dimensions. We compute the area (or entropy) functional relation for this black hole (BH). We consider both de Sitter (dS) and anti-de Sitter (AdS) cases. We derive the Cosmic-Censorship-Inequality which is an important relation in general relativity that relates the total mass of a spacetime to the area of all the BH horizons. Local thermodynamic stability is studied by computing the specific heat. The second-order phase transition occurs at a certain condition. Various types of second-order phase structure have been given for various values of a and the cosmological constant [Formula: see text] in the Appendix. When a = 0, one obtains the result of Schwarzschild–dS and Schwarzschild–AdS cases. In the limit aM [Formula: see text] 1, one obtains the result of Grumiller spacetime, where a is nontrivial Rindler parameter or Rindler acceleration and M is the mass parameter. The thermodynamic volume functional relation is derived in the extended phase space, where the cosmological constant is treated as a thermodynamic pressure and its conjugate variable as a thermodynamic volume. The mass-independent area (or entropy) functional relation and thermodynamic volume functional relation that we have derived could turn out to be a universal quantity.

RINDLER TYPE ACCELERATION IN f(R) GRAVITY

By choosing a fluid source in f(R) gravity, defined by f(R) = R-12aξ ln |R|, where a (Rindler acceleration) and ξ are both constants, the field equations correctly yield the Rindler acceleration term in the metric. We identify domains in which the weak energy conditions (WEC) and the strong energy conditions (SEC) are satisfied.

New Black Holes Solutions in a Modified Gravity

We present some basic concepts of a theory of modified gravity, inspired by the gauge theories, where the commutator algebra of covariant derivative gives us an added term with respect to the General Relativity, which represents the interaction of gravity with a substratum. New spherically symmetric solutions of this theory are obtained and can be viewed as solutions that reproduce the mass, the charge, the cosmological constant, and the Rindler acceleration, without coupling with the matter content, that is, in the vacuum.

On the Gravitational Energy of the Hawking Wormhole

The surface energy for a conformally flat space–time which represents the Hawking wormhole in spherical (static) Rindler coordinates is computed using the Hawking–Hunter formalism for nonasymptotically flat space–times. The physical gravitational Hamiltonian is proportional to the Rindler acceleration g of the hyperbolic observer and is finite on the event horizon ξ=b (b — the Planck length, ξ — the Minkowski interval). The corresponding temperature of the system of particles associated to the massless scalar field Ψ=1-b2/ξ2, coupled conformally to Einstein's equations, is given by the Davies–Unruh temperature up to a constant factor of order unity.