Modified cosmology through Kaniadakis horizon entropy

We apply the gravity-thermodynamics conjecture, namely the first law of thermodynamics on the Universe horizon, but using the generalized Kaniadakis entropy instead of the standard Bekenstein–Hawking one. The former is a one-parameter generalization of the classical Boltzmann–Gibbs–Shannon entropy, arising from a coherent and self-consistent relativistic statistical theory. We obtain new modified cosmological scenarios, namely modified Friedmann equations, which contain new extra terms that constitute an effective dark energy sector depending on the single model Kaniadakis parameter K. We investigate the cosmological evolution, by extracting analytical expressions for the dark energy density and equation-of-state parameters and we show that the Universe exhibits the usual thermal history, with a transition redshift from deceleration to acceleration at around 0.6. Furthermore, depending on the value of K, the dark energy equation-of-state parameter deviates from $$\Lambda $$ Λ CDM cosmology at small redshifts, while lying always in the phantom regime, and at asymptotically large times the Universe always results in a dark-energy dominated, de Sitter phase. Finally, even in the case where we do not consider an explicit cosmological constant the resulting cosmology is very interesting and in agreement with the observed behavior.

Thermodynamics of Dyonic NUT Charged Black Holes with entropy as Noether charge

We investigate the thermodynamic behaviour of Lorentzian Dyonic Taub-NUT Black Hole spacetimes. We consider two possibilities in their description: one in which their entropy is interpreted to be one quarter of the horizon area (the horizon entropy), and another in which the Misner string also contributes to the entropy (the Noether charge entropy). We find that there can be as many as three extremal black holes (or as few as zero) depending on the choice of parameters, and that the dependence of the free energy on temperature — and the resultant phase behaviour — depends very much on which of these situations holds. Some of the phase behaviour we observe holds regardless of which interpretation of the entropy holds. However another class of phase transition structures occurs only if the Noether charge interpretation of the entropy is adopted.

The generalized second law of thermodynamics with Barrow entropy

We investigate the validity of the generalized second law of thermodynamics, applying Barrow entropy for the horizon entropy. The former arises from the fact that the black-hole surface may be deformed due to quantum-gravitational effects, quantified by a new exponent $$\Delta $$ Δ . We calculate the entropy time-variation in a universe filled with the matter and dark energy fluids, as well as the corresponding quantity for the apparent horizon. We show that although in the case $$\Delta =0$$ Δ = 0 , which corresponds to usual entropy, the sum of the entropy enclosed by the apparent horizon plus the entropy of the horizon itself is always a non-decreasing function of time and thus the generalized second law of thermodynamics is valid, in the case of Barrow entropy this is not true anymore, and the generalized second law of thermodynamics may be violated, depending on the universe evolution. Hence, in order not to have violation, the deformation from standard Bekenstein–Hawking expression should be small as expected.

Generalized Misner–Sharp energy in generalized Rastall theory

Employing the unified first law of thermodynamics and the field equations of the generalized Rastall theory, we get the generalized Misner–Sharp mass of space–times for which gtt = –grr = –f(r). The obtained result differs from those of the Einstein and Rastall theories. Moreover, using the first law of thermodynamics, the obtained generalized Misner–Sharp mass, and the field equations, the entropy of static spherically symmetric horizons are also addressed in the framework of the generalized Rastall theory. In addition, by generalizing the study to a flat Friedmann–Robertson–Walker (FRW) universe, the apparent horizon entropy is also calculated. Considering the effects of applying the Newtonian limit to the field equations on the coupling coefficients of the generalized Rastall theory, our study indicates (i) the obtained entropy–area relation is the same as that of the Rastall theory, and (ii) the Bekenstein entropy is recovered when the generalized Rastall theory reduces to the Einstein theory. The validity of the second law of thermodynamics is also investigated in the flat FRW universe.

Mechanics of isolated horizons in scalar-tensor theories

Based on the first-order action for scalar-tensor theories with the Immirzi parameter, the symplectic form for the spacetimes admitting a weakly isolated horizon as internal boundary is derived by the covariant phase space approach. The first law of thermodynamics for the weakly isolated horizons with rotational symmetry is obtained. It turns out that the Immirzi parameter appears in the expression of the angular momentum of isolated horizon, and the scalar field contributes to the horizon entropy.

Cosmological consequences and thermodynamics of modified gravity with extended nonminimal derivative couplings

We consider the newly proposed gravitational modifications that go beyond Horndeski’s theory, named as theories with extended nonminimal derivative couplings. By these modifications, the coefficient functions depend on the scalar field and its kinetic energy. These theories become ghost-free in cosmological background. We consider the flat FRW universe and explore the equation-of-state parameter, [Formula: see text]–[Formula: see text] plane and the squared speed of sound. The equation-of-state parameter exhibits phantom behavior of the universe, [Formula: see text]–[Formula: see text] plane represents the freezing region of the universe while the squared speed of sound denotes the stability of the model for the specific choice of constant parameters. Also, we investigate the validity of generalized second law of thermodynamics on the Hubble horizon taking into account the Bekenstein, power-law, Renyi and logarithmic corrections to the horizon entropy.