In this paper, <math><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>,</mo><mi>T</mi><mo>)</mo></math> gravity is considered. It is a generalization of the theories <math><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo>)</mo></math> and <math><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>)</mo></math>. This modified theory of gravity exhibits strong geometry-matter coupling. The problem of causality and its violation is verified in this model. Such analysis is carried out using Gödel-type solutions considering different types of matter. It is shown that this model allows both causal and non-causal solutions. These solutions depend directly on the content of matter present in the universe. For the non-causal solution, a critical radius is calculated, beyond which causality is violated. Taking different matter contents, an infinite critical radius emerges that leads to a causal solution. To obtain a causal solution, a natural relationship arises between the parameters of the theory.

Brazil

J.S. Gonçalves

A.F. Santos

On causality and its violation in ( , , ) Gravity

In this manuscript, we investigate solutions that allow closed time-like curves (<math><mi>CTC</mi></math>s) in general relativity (<math><mi>GR</mi></math>) within the framework of a modified gravity theory. We consider here an alternative theory recently proposed in gravity theories known as <math><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi>A</mi><mo>)</mo><mo>=</mo><mo>(</mo><mi>R</mi><mo>+</mo><mi>α</mi><mspace width="0.2em"></mspace><mi>A</mi><mo>)</mo></math> gravity or Ricci-inverse (<math><mi>RI</mi></math>) gravity, α is the coupling constant. This theory incorporates modifications into the Einstein-Hilbert action through a coupling with an anti-curvature scalar derived from the anti-curvature tensor. We investigate a family of Petrov type-N solutions that are non-vacuum solutions of the field equations, characterized by a negative cosmological constant. The matter-energy content is Vaidya radiation, and its energy density may either remain constant or vary with axial distance. One distinctive feature of the considered solutions is the formation of <math><mi>CTC</mi></math>s, which violate the causality condition. Another observation is that the determinant of the Ricci tensor, <math><msup><mrow><mi>R</mi></mrow><mrow><mi>μ</mi><mi>ν</mi></mrow></msup></math>, differs from zero, confirming the existence of an anti-curvature tensor, <math><msup><mrow><mi>A</mi></mrow><mrow><mi>μ</mi><mi>ν</mi></mrow></msup></math>, the inverse of the Ricci tensor, defined as <math><msup><mrow><mi>A</mi></mrow><mrow><mi>μ</mi><mi>ν</mi></mrow></msup><mo>=</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mi>μ</mi><mi>ν</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msubsup></math>, and hence, the anti-curvature scalar <math><mi>A</mi><mo>=</mo><msub><mrow><mi>g</mi></mrow><mrow><mi>μ</mi><mi>ν</mi></mrow></msub><mspace width="0.2em"></mspace><msup><mrow><mi>A</mi></mrow><mrow><mi>μ</mi><mi>ν</mi></mrow></msup></math>. We demonstrate that the family of cosmological models serves as valid solutions within the framework of Ricci-inverse gravity model, with Vaidya radiation as the matter-energy content whose energy density is modified by the coupling parameter. Thus, our results affirm that the Ricci-inverse gravity theory allows for the existence of <math><mi>CTC</mi></math>s, similar to the case in general relativity.

India

F. Ahmed

J.C.R. de Souza

Closed time-like curves in Modified Gravity Theory

In this work, a way to consider together two originally different corrections to the Friedmann equations is presented. The first is the Barrow entropy, which imposes a fractal structure on the black hole horizon area. While the second is the well-known <math><mi>f</mi><mo>(</mo><mi>R</mi><mo>)</mo></math> gravity, which comes from a generalization of the Einstein-Hilbert action. Using the ideas of gravity-thermodynamics conjecture, these two models are combined. Then the modified Friedmann equation is obtained. Choosing a particular <math><mi>f</mi><mo>(</mo><mi>R</mi><mo>)</mo></math> model, an application is investigated. The state parameter and the density parameters for matter and dark energy are calculated. With these results, the dynamic evolution of the universe is discussed.

P.S. Ens

An attempt to add Barrow entropy in ( ) Gravity

In this paper, a massless scalar field coupled to gravity is considered. Then the Casimir effect at finite temperature is calculated. Such development is carried out in the Thermo Field Dynamics formalism. This approach presents a topological structure that allows for investigating the effects of temperature and the size effect in a similar way. These effects are calculated considering Gödel-type solutions as a gravitational background. The Stefan-Boltzmann law and its consistency are analyzed for both causal and non-causal Gödel-type regions. In this space-time and for any region, the Casimir effect at zero temperature is always attractive. However, at finite temperature, a repulsive Casimir effect can emerge from a critical temperature.

Canada

Faqir C. Khanna

Thermal Casimir effect in Gödel-type universes

The Yang-Mills-aether theory is considered. Implications of the non-Abelian aether-like term, which introduces violation of the Lorentz symmetry, are investigated in a thermal quantum field theory. The thermofield dynamics formalism is used to introduce the temperature effects and spatial compactification. As a consequence, corrections due to the non-Abelian aether term are calculated for the non-Abelian Stefan-Boltzmann law and for the non-Abelian Casimir energy and pressure at zero and finite temperature.

Non-Abelian Aether-Like Term and Applications at Finite Temperature

In this paper we examine the thermal effects of the vacuum Cherenkov radiation in a Lorentz- and CPT-violating electrodynamics. We compute the thermal contribution to the Cherenkov radiation rate within the Thermofield Dynamics approach. Since the model under consideration possesses a consistent canonical quantization and also fulfills the physical constraints in order to this vacuum process to happen, it is a perfect candidate to implement the study at finite temperature. We evaluate in details the instantaneous rate of energy loss for a charge, and show that the radiation rate is significantly modified at very high temperatures. Intriguingly, we further observe that when the temperature goes to infinity the radiation rate goes to zero even if the process is kinematically allowed.

R. Bufalo

Vacuum Cherenkov radiation at finite temperature

The Thermofield Dynamics (TFD) formalism is considered. In this context, a Lorentz-breaking scalar field theory is introduced. In contrast to the Matsubara formalism, the best-known approach to introducing the temperature effect, TFD is a real-time formalism and is a topological field theory. While in Matsubara the temperature effects are introduced as a consequence of a compactification of the field in a finite interval on the time axis, in the TFD this effect emerges through a condensed state related to the Bogoliubov transformation. An advantage of the TFD formalism is that different topologies, which lead to different effects, can be chosen. Here, three different topologies are considered. Then the Stefan-Boltzmann law and Casimir effect at zero and non-zero temperature are calculated. This is a unique feature of TFD, which allows us to treat different phenomena in the same way.

L.H.A.R. Ferreira

TFD formalism: Applications to the scalar field in a Lorentz-violating theory

The Dirac field, spin 1/2 particles, is investigated in phase space. The Dirac propagator is defined. The Thermo Field Dynamics (TFD) formalism is used to introduce finite temperature. The energy-momentum tensor is calculated at finite temperature. The Stefan-Boltzmann law is established, and the Casimir effect is calculated for the Dirac field in phase space at zero and finite temperature. A comparative analysis with these results in standard quantum mechanics space is realized.

S.C. Ulhoa

R.G.G. Amorim

J.S. da Cruz Filho

F.C. Khanna

Spin-1/2 Particles in Phase Space: Casimir Effect and Stefan-Boltzmann Law at Finite Temperature

The Thermo Field Dynamics (TFD) formalism is used to investigate the regular black holes at finite temperature. Using the Teleparalelism Equivalent to General Relativity (TEGR), the gravitational Stefan-Boltzmann law and the gravitational Casimir effect at zero and finite temperature are calculated. In addition, the first law of thermodynamics is considered. Then, the gravitational entropy and the temperature of the event horizon of a class of regular black holes are determined.

E.P. Spaniol

R. Gomes

A.E. Santana

On Regular Black Holes at Finite Temperature

Studies about a formal analogy between the gravitational and the electromagnetic fields lead to the notion of Gravitoelectromagnetism (GEM) to describe gravitation. In fact, the GEM equations correspond to the weak-field approximation of the gravitation field. Here, a non-abelian extension of the GEM theory is considered. Using the Thermo Field Dynamics (TFD) formalism to introduce temperature effects, some interesting physical phenomena are investigated. The non-abelian GEM Stefan-Boltzmann law and the Casimir effect at zero and finite temperatures for this non-abelian field are calculated.