Abstract:We consider it worthy if we could construct a realistic model universe that would enable us to identify a clue about the source of dark energy. So, we develop a Scale Covariant Theory model universe considering a 5D spherically symmetric space-time. It is predicted that the constructed model itself behaves as a phantom energy model/source that tends to a de Sitter phase avoiding the finite-time future singularity (big rip). The model universe is isotropic and is free from an initial singularity. The gravitatio… Show more
“…Vegh introduced the dRGT-like massive theories of the different classes by modification in the reference metric. Considering this theory of massive gravity different classes of the BH solutions have been studied in [49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66].…”
In this paper, we find the new exact $AdS$ black hole (BH) solution in the presence of massive gravity and nonlinear electrodynamics (NED). The obtained black hole solution (known as $AdS$ Heyward massive BH ) interpolates with the $AdS$ Heyward BH in the absence of graviton mass ($m$) and massive BH when the magnetic charge is switched off. We calculate the exact expression of thermodynamics quantities including local (heat capacity), global (free energy), and dynamical stability (quasinormal modes) of the obtained BH solution. The heat capacity of the BH diverges where the temperature is maximum and free energy is minimum. We also study the extended thermodynamics of the BH when the cosmological constant ($\Lambda$) is treated as the thermodynamics pressure ($P=-\Lambda/8\pi$). We analyze the first and second-order phase transition by studying the behavior of Gibbs free energy and these phase transitions are similar to the van der Walls phase transition. The effect of magnetic charge and graviton mass are opposite to each other on critical values.
“…Vegh introduced the dRGT-like massive theories of the different classes by modification in the reference metric. Considering this theory of massive gravity different classes of the BH solutions have been studied in [49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66].…”
In this paper, we find the new exact $AdS$ black hole (BH) solution in the presence of massive gravity and nonlinear electrodynamics (NED). The obtained black hole solution (known as $AdS$ Heyward massive BH ) interpolates with the $AdS$ Heyward BH in the absence of graviton mass ($m$) and massive BH when the magnetic charge is switched off. We calculate the exact expression of thermodynamics quantities including local (heat capacity), global (free energy), and dynamical stability (quasinormal modes) of the obtained BH solution. The heat capacity of the BH diverges where the temperature is maximum and free energy is minimum. We also study the extended thermodynamics of the BH when the cosmological constant ($\Lambda$) is treated as the thermodynamics pressure ($P=-\Lambda/8\pi$). We analyze the first and second-order phase transition by studying the behavior of Gibbs free energy and these phase transitions are similar to the van der Walls phase transition. The effect of magnetic charge and graviton mass are opposite to each other on critical values.
“…[40,[43][44][45][46][47][48][49][50][51][52][53] One intriguing aspect of Gaussian states is that the action on the covariance matrix can characterize the transition from one Gaussian state to another. [43,[54][55][56][57] For Bosonic Gaussian states, the non-trivial components of this matrix are symmetric, while they are antisymmetric for Fermionic states. However, we found that the covariance matrix alone is insufficient for calculating Krylov complexity, as it lacks information on the relative phase.…”
The concept of complexity has become pivotal in multiple disciplines, including quantum information, where it serves as an alternative metric for gauging the chaotic evolution of a quantum state. This paper focuses on Krylov complexity, a specialized form of quantum complexity that offers an unambiguous and intrinsically meaningful assessment of the spread of a quantum state over all possible orthogonal bases. This study is situated in the context of Gaussian quantum states, which are fundamental to both Bosonic and Fermionic systems and can be fully described by a covariance matrix. While the covariance matrix is essential, it is insufficient alone for calculating Krylov complexity due to its lack of relative phase information is shown. The relative covariance matrix can provide an upper bound for Krylov complexity for Gaussian quantum states is suggested. The implications of Krylov complexity for theories proposing complexity as a candidate for holographic duality by computing Krylov complexity for the thermofield double States (TFD) and Dirac field are also explored.
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